I think beyond the specific elements of any domain AI eclipses humans in, overall, the notion of the thing that grants you status, prestige, and a living wage being commodified would spark in anyone a profound sense of dread.
Beyond just making you redundant in your job, the whole architecture of your existence, the thousands of hours of struggle, the sacrifice of putting off social games or personal enjoyment are now rendered moot in hindsight. You are made one step closer to complete worthlessness, which will surely continue as AI becomes a more satisfying personal companion, a more worthwhile friend, lover, etc.
How is one to feel safe in the progress of the future when the only hints of the wonderful post-scarcity utopia we can quantify so far is the removal of all human leverage via their labor? All it tells us is we will be bargaining with superintelligence with nothing to stand on, only a trust that the 5000 lab executives and researchers solved the most important research problem of all time on the first try.
> You are made one step closer to complete worthlessness, which will surely continue as AI becomes a more satisfying personal companion, a more worthwhile friend, lover, etc.
I recently thought about this and fear that AI may further drive us humans apart.
Instead of working with humans, I increasingly work with a fleet of agents.
I would recommend the work of Sherry Turkle, specifically her new book "Artifical Intimacy" - she is quite opinionated on this, in the sense that the role that AI play as a conversation partner is so frictionless, so controlled, that we get none of the rough edges of human interaction that form us into a functional social being. No real quick solution outside of deep, fearful caution when using these things - and we're not going to see that from John Q Public
It's more or less reverse to the mean. The period in which a people had both access to education and leverage through their labor and intellect is super short. For most of recorded history, the bulk of humanity lived as peasants, serfs, or slaves. They were mostly illiterate, bound to the land or to a master, and had little power to bargain over the terms of their (or their children) lives.
I'm too young to be financially secure given my impoverished background, not having parents in my life, being homeless as a teenager, etc. But too old and physically disabled to change course from tech. Nothing to do but keep walking through this tunnel and see where it ends up. It's scary!
> How is one to feel safe in the progress of the future when the only hints of the wonderful post-scarcity utopia we can quantify so far is the removal of all human leverage via their labor?
I'm sure the Telegraph operators, human calculators, mine workers and all sorts of people have asked themselves this question. It's obvious that it feels strange to suddenly be part of the cohort asking but I assure you it's not new. And the answer hasn't changed much since.
And like to anyone else who hints that “automation creates better jobs”, I have to add: but not for us. Maybe for the next or the generation after that.
Industrial and technological progress has birthed better conditions overall, but at a cost of locally worse ones. Mine workers that got displaced didn’t end up being machine operators - most of them landed on benefits or sporadic gig work. Only the next generation was able to be properly trained and educated to be able to benefit from the technological advancement en masse. And we might see that happening again.
This piece circles, without naming it, around the concept of “deontic scorekeeping” central to the work of Robert Brandom on semantics. The idea that our ability to create and sustain conceptual systems depends on the give and take of reasons within a social setting. Brandom has been front of mind for me lately because elements of his theory both explain why LLMs should work in principle, and where they are bound to be radically deficient. An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time.
Worth reading: Robert Brandom, “Making It Explicit: Reasoning, Representing, and Discursive Commitment”
I mean, many companies operate within particular domains but don't have much skin in the domain itself in a way that is meaningful to other participants there -- like Oracle builds software for healthcare, ostensibly, but any actual user of their products will tell you they are nightmarish with regard to usability, and research shows that patients are often harmed as a result. So healthcare isn't their game, it's selling healthcare software.
Likewise OpenAI doesn't have "skin" of any shape or value in e.g. the mathematics community or even in mathematics research per se. In my cynical view, they are exploiting the exposure of mathematical research to automation in an effort to create a case study of their product obsoleting a highly visible and well-leveraged and relatively small profession. Regardless, I doubt even they would say they have durable skin in mathematics in any sense, certainly not in either of the senses I mentioned above. But their output inhabits the same space as mathematicians, who have to contend with the consequences
What a coincidence, I've also picked up inferentialism but never really got into it.
I'm interested in the reversal that Sellars proposes - it seems clear to me that "representation" is not prior to the space of reasons, despite how unintuitive it is.
> An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time.
I see no reason why this can't be the case in the future, even though I think inferentialist-based theories are generally strong. Can't you force LLM's (or whatever AI architecture will exist in a decade) to stake durable commitments itself, then? They're at least autonomous enough to run computers. I agree that that is a core part to true meaning & autonomy, but nobody just lets them yet. I don't think inferentialism is a consciousness-based argument, either, so that escape hatch isn't available. I also don't think this is a necessary condition to engage in the space of reasons (but maybe then I'm misunderstanding it, or retreating to a more Sellarsian understanding). Could you explain on this more?
Though again, I only have the book sitting on my desk, and I haven't cracked it open...
I actually agree with you. LLMs could become participants in the future, but this would require (1) durability of real awareness over time (an architecture change from the current fixed-weights + transient context architecture) and (2) that humans grant them the status of equal participants (probably not a terribly high bar given how people already treat these things). I'm not aware of any real progress toward (1), and all the stand-ins people have developed live in the context layer or textual artifacts, which are poor stand-ins for durable memory.
And yeah, consciousness based arguments are bunk IMO. It's clear that LLMs are in a basic sense "aware", and even to some extent "sapient" (in Brandom's usage), i.e. they can justify claims and object to things at least locally. I follow Rorty on the question of consciousness, which is to say that consciousness has no deeper meaning in practice beyond "are you awake", and in philosophical discussion it's largely a proxy for "are you one of us" in some amorphous sense.
Well that's too bad, since Rorty completely misses the point on consciousness.
Consciousness, the interesting part anyway, is qualia, or the "it is like something to be me" as Nagel put it.
Intention, as Dennett used it in his book "The Intentional Stance" is the "are you one of us" angle, and is distinct from consciousness because as the book title suggests, it is a stance taken with respect to some other system (person, cat, dog, turtle, LLM) rather than a description of subjective experience.
So I think it is your (and Rorty's) positions that are bunk. It is very, very far from clear that LLM's are in any basic sense "aware" let alone "sapient". They are extraordinarily able to manipulate language in a way that leads to text generation that has traditionally been assumed to indicate consciousness and/or intelligence. But we have no way of knowing if it is like anything to be an LLM, even though most of us are busy taking the Intentional Stance towards them.
Brandom wrote a shorter version of the book, called "Articulating Reasons", which is available in full on his faculty page [1], or from booksellers. He's a very wordy writer (kind of exhausting to read, even for someone who enjoys philosophy), but if you get ahold of Making It Explicit, chapters 2 and 3 have the meat of the ideas I'm talking about here.
Edit: One of my ways of benchmarking new AI models is actually to type a version of this prompt in and see how sophisticated the response is: "Talk to me about the concept of deontic scorekeeping in the context of llms". You'll get good mileage out of that.
Humans change over time due to what they experience. It’s different from waking up from a ten-year coma and having access to a record of what happened to yourself in an alternative timeline where you didn’t fall into the coma.
I think in future, each company will built its own universe of mathematics consisting of prized discoveries. Maybe one Mathematical Universe per Company in the multiverse of mathematics.
Mathematicians always define their terms exactly, in order to begin their discussion. Philosophers never define their terms exactly, because then they would have nothing to discuss.
Because language is mimetic, and people are consuming huge quantities of AI-generated text. I.e. saying that an LLM can't be an equal participant in our language games isn't saying that it can't play by the rules. In fact that's what LLMs are trained to be best at.
What an LLM can't do (at least with the current architecture) is sustain a commitment that it can be held accountable for later. It doesn't have durable "perspective". It can't update its priors. Maybe a new architecture will come along that gives LLMs memory plasticity, at which point they will shift into being individuated quasi-persons, but that's not what we've got now.
Recursive self improvement is a bulk process that shapes the weights of the next model. The weights are still frozen. Each individual "agent" would need to able to durably update its own dispositions to get to what I'm talking about.
I'm not suggesting mathematics and language are the same thing, but I am saying (which shouldn't be controversial) that mathematics as a discipline exists within the medium of language, and that mathematical reasoning, discovery, and proof happen via people proposing, justifying, testing, and objecting to formulations in language. This isn't a metaphysical claim about whether math is real or captures inherent structures of the universe etc.
Ok, then what is an agent that provides a 'thinking' or reasoning loop around said model?
You ended your first post with: "An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time."
And so if there is an agent, a thinking loop, that can recursively adjust over time...how does your statement hold up? I'm particularly talking about 'staking durable commitments or changing its dispositions over time'. Recursive self improvement is all about these 2 things, especially when it's the 'outer thinking loop' doing the improvement.
But you're right, Mathematics exists as a medium within Language. But then Language is just a transfer of ideas from one mind to another.
This principle is the heart of what the article is talking about: a transfer of logical mathematical ideas passed from a human to another. And the sense of 'shared understanding' that comes with it. It has nothing to do with keeping score.
It's about getting a 'sense' for why someone thought or rationalized an idea in order to connect some other idea. You get an 'ah-ha' moment, and some of those moments are gone, or a different path is taken to reach the moments now. That is what the 'weeping' is about (not that I agree with the article. I think anyone can spend however they want. Math doesn't have to change, it's that people want it to, apparently, because it's 'easier' to do something different, or for some other reason I don't know about).
It would only be true if you consider Mathematics and Language to be the same thing.
Both depend on Logic, which is where "deontic scorekeeping" comes in. You can only establish something (score) is true and believable by 'keeping score' and having some level of understanding about the language or math you are reading.
The article is mostly referring to the connection that comes from shared understanding between humans, particularly mathematicians, as they build new shared understanding, and realize there are limits to what they can know and 'leave behind' logic for others to pick up and carry on.
That connection has been severed, or strained a bit, but I'm sure new ones will be created. It just might be of the same flavor that mathematicians prefer, therefore they weep.
And if I understand "deontic scorekeeping" correctly, these forums are a better representation of the concept. You will lend some amount of belief to what is said/read based on what you know.
Ideas are contagious and AI is our most powerful vector yet.
I suppose we would see some interaction with AI in that sense, but it'll take place over the course of learn cycles and when AI starts ingesting its own ideas it typically goes wrong somewhere down the line.
I think Thompson has no understanding of endeavors like pure math or the theoretical sciences. In the words of Einstein, "I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts; the rest [is] just details."
I think mathematicians aren't bemoaning their lost sunk costs. They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_. Their voyages of discovery, which give life meaning, may never leave dry dock again.
It is strange, because in a sense, when you start learning math, you never explore, you are being taught.
Now mathematicians were able to exercise curiosity. That is going to change. Back to the ranks of eternal learners if you will.
The fun was in the research. Now I think it will leave the door open toward more Applied math. What can people do with all the discoveries. The curiosity will be there.
I think it is better that way.
It will also put a cap on abstractions that overlaps. In essence, AI is less likely to create new theories, coin new terminology, etc. But it is better suited to recognize emerging patterns.
That will probably simplify mathematics.
Unless the domain of abstraction is infinite and with each new abstraction comes its own results but I doubt it. Who knows though...
> they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_
Until we can demonstrate AI consciousness, “seeing the raw truth” will be a human activity. Even now, verifying and understanding these AI proofs is a massive endeavor. Coming up with an intuitive (to humans) distillation of the finding remains an open challenging demanding expertise.
i think to certain types of people (who are probably more likely to be mathematicians), the "self" discovery aspect of it is important, they don't want to read about a new proof for a problem they were grappling with, they want to come about it through their own thoughts.
LLMs are not feeding us things, we are asking it and getting answers. This dialectic I think is super powerful and it still requires the human to ask questions and continue expanding intellectual curiosity to go down the rabbit hole and discover. LLMs are just an incredible rubber duck but the discovery is still there.
We literally had a case where OpenAI may have stolen the dialectic from a mathematician using its product and then given it to a proprietary model burning tens of millions of dollars of tokens [1].
That's such a nice way to put it! I recently stumbled into "The Last First- Winter K2"[1] and saw the same spirit along with a similar misguided effort to win without the will, nor capacity to do it — e.g. influencers taking a stab at K2 is like prompting your way to results.
Why is not like changing to a different type of vessel for the voyage? Unless and until it is all AI in closed system, could direct machines where to look etc.
> The story of human discovery and the triumph of the human spirit will soon be excised from this discipline. The Dinitz-Garg-Goemans counterexample was the most egregious demonstration. It revealed that the process of prompting novel proofs will be as auraless as ordering doordash. Watch as magic and mystery evaporate. Watch as the sun sets on our heroic age. Is there not something evil in the act of blocking all future generations of mathematicians from the experience of discovery? Forget about accuracy or even attribution. Something fundamental to the experience of mathematics is being taken.
> You are a helpless onlooker. Before you a channel through which humans have accessed the ineffable and sacred for thousands of years is being sealed for eternity.
As someone with friends in the mathematics community, they've expressed similar sentiments.
I have to wonder if this is the equivalent of teleporting back in time and finding Marco Polo or any of those early explorers who traveled for the love of the game (and fame and money), and opening up Google Maps on your phone and showing them the zoomed out world. And showing them any island or village they could name.
This is absurd and silly. Discovery doesn't go away because more new things are being discovered. This position only makes sense if you make an arbitrary cut point where some instances "don't count". If you were to go back to scientists or mathematicians several hundred years ago and tell them that one day science would be done by tens of millions of full time researchers around the globe, often working in teams, some of them might also bemoan the loss of the "hero scientist" as any commoner could now participate. But science and math have only benefited from this, and this has increased, not decreased, the beauty and wonder in these fields.
It is not the same because the act of problem solving for discovery is now to be done exclusively by machines, as humans are no longer remotely competitive.
If you read the linked article, the author goes into more detail about how doing mathematics also has been an act of communication with past and present human mathematicians. This is very much true when math and science are done by millions of human researchers, but not so when it is done by massive swarms of agents at a couple labs.
I am sure science and math will benefit in the sense of solving more problems than ever before. But you are not really understanding the agony of the humans caught in the change.
> They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance...
Not "never again", it would be extremely difficult but science and math are also built on random, trial and error, and intuitions that could not arise from AI.
That's the issue - trial and error. A human can try a couple ideas in a day, but realistically, there are not that many sane ideas.
Computer can iterate without frustration on a completely random garbage. Once in a while it stumbles upon a gem. Even if it's one in 10000, that's still hundreds of good ideas in a day (provided enough GPUs).
Your comment assumes math and science are some kind of closed systems that can mechanistically pursue any endeavour but reality (whatever it is (e.g. the universe)) is much more complex than that, and there are realities that are outside of those systems. Not saying that humans can see all those realities though.
> I am not one of those AI people who believes that hundreds of millions of jobs will be wiped clean from existence in the next five years
"Wiped clean" is the wrong phrasing, and 5 years is a short timeframe given the ability of some sectors of the economy to resist change. But yes, hundreds of millions of white collar professionals will need to rethink their careers and their business models within the foreseeable future.
Just today there was an HN article about how shady the dental industry is. In the future, you will go to a special dental imaging facility where a modestly-compensated technician images your whole mouth and feeds the results into an AI system, and when you get home you can look at the assessment and chat with the AI about it. Then you can potentially go visit a dentist, oral surgeon, etc, if you actually need work. This system will produce far better dental health outcomes at far lower cost: the diagnoses will be more accurate, and there will be no bias towards additional, unnecessary procedures.
> In the future, you will go to a special dental imaging facility where a modestly-compensated technician images your whole mouth and feeds the results into an AI system, and when you get home you can look at the assessment and chat with the AI about it. Then you can potentially go visit a dentist, oral surgeon, etc, if you actually need work. This system will produce far better dental health outcomes at far lower cost: the diagnoses will be more accurate, and there will be no bias towards additional, unnecessary procedures.
Right up until the sellers of dental supplies find a way to...
Indirectly influence model training to increase the frequency with which models recommend dental work and/or lower the bar for what they determine to be "necessary"...
or...
Directly influence model recommendations by paying model providers (who will be happy to take that money).
The point being that models (and particularly the humans that control them) are presumably just as corruptible as the humans they are replacing.
I still think mathematicians are going to be as important as ever. The LLMs are only finding what was technically possible given our current breadth of knowledge after brute force solving problems. Eventually it will run out of things that it can do with its training and the only way to get it to do more will be training it on new human found knowledge.
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
> Eventually it will run out of things that it can do with its training and the only way to get it to do more will be training it on new human found knowledge.
I don't see how its output possibilities could be infinite given a finite set of data. Taken to the extreme if you give an LLM only a single piece of information then that is going to be the only thing it can produce. Given it two pieces of information and maybe it can produce every combination of those two things. Given all of the worlds knowledge I'm sure its possible outputs are incomprehensibly large, but still not infinite. Then having its outputs match a set of really specific instructions is going to be a small subset of that.
How is this different from human brains being made up of a finite number of neurons in a finite number of configurations? I know very little about LLMs and nothing about neurology and maybe you can explain to me why one is so much more powerful than the other.
> a finite number of neurons in a finite number of configurations
Neurons and synapses change, especially synapses (the connections between neurons). Some neurons have a few connections to other neurons. Others have hundreds of thousands of connections to other neurons. These grow and change. "Estimates are between 100 trillion and 1,000 trillion neural connections" Is it finite? Depends on your definition of finite. If anything countable is finite, then it is finite but the number may be practically uncountable. Is it fixed? No.
As I understand it, the advantages of AI have not just been speed of processing.
Humans have cognitive limits. Humans hold a specific slice of all knowledge at a time and necessarily limits what correlations can be leveraged. This is similar to "context windows" in modern AI. Human minds are wildly variable in efficiency. AI is has constant inefficiency, largely controlled by the speed of light, physical RAM, and processing power, with superior (no cost) "thought" context switching. The AI also has superior accuracy without the need for "concentration" because the AI is processing on a Turing machine with the limited operations that it's superior at in terms of time and energy - eg find an element in a list of 1 million elements.
Sure, a given LLM can only produce so much (though it might be a lot), and then you'll need fresh inputs. But you contend that those have to be human, while I am arguing that they could be
- random,
- from the environment,
- from other AIs.
That increases the space considerably.
In particular, note that your argument also applies to humans: A human, being finite, can only produce finitely many things. But you add other humans, the environment, and pure chance to the mix, and it'll be pretty infinite for all practical purposes.
I would be curious to see the end result of letting it endlessly update its inputs from its own outputs. I was under the impression that eventually this would cause delusions and if you let it do this long enough and it is solving problems that no humans can verify as correct that it isn't useful.
Maybe that is the limits of my imagination, but it seems unwise to take humans completely out of the loop. Having mathematicians around that can understand what it is doing so that we can utilize that knowledge in a way that we can have some confidence in seems important.
Typical thought experiment - go back to the early years of humanity, even before we've created language itself. Communication is basic grunts and other such things, cutting edge knowledge is 'poke him with the pointy end'. Compile all of this knowledge into the training set for an LLM, let it run with infinite processing power and infinite time. It'll just continually remix the knowledge of that snapshot of time. You're certainly not getting to the Moon, discovering the secrets of the atom, or even discovering mathematics.
It sounds increasingly dumb to bring this up given how advanced models have become, but it remains true - they are still fundamentally token prediction algorithms. And that imposes hard constraints on their potential. These constraints are relatively academic in our current world because there's just so absurdly much information and no human can hold more than a negligible amount in his mind at once. So they'll certainly be able to connect many 'obvious' dots that we don't see simply for a lack of carrying capacity, but they're not going to discover concepts that do not clearly follow from the comprehensive knowledge of an era.
It seems far more likely to me that current LLMs have learned generic reasoning capabilities which will allow them to solve effectively infinite problems, rather than whatever vague limit on capabilities you seem to think there are.
Yeah, I think that's a great essay and it really helped clarify some of my own ideas.
At the same time, I think it's pretty amazing how this is the fundamental question of AI's trajectory, yet people on both sides seem so sure of their viewpoint with little actual evidence or data to back it up.
That is, it's possible that LLM-based approaches will be forever limited to this "convex hull" of current training data, and thus humans will always have a role to play (and will retain primacy when it comes to overall intelligence), because it appears that humans are not limited to this convex hull based on previous discoveries (e.g. I think basically every scientist would argue Einstein's general relativity was outside the convex hull that existed at that time).
Yet, if LLM-based approaches are eventually able to surpass humans on this "novel discovery" axis, then we as a species are basically done for when it comes to intellectual primacy - and then it becomes a very strange and scary world. And many AI researchers at the top companies clearly believe current approaches will scale and eventually (pretty soon I'll add) lead us to RSI.
I have no idea which side is right, and I'll admit I really hope LLMs eventually hit a wall. But again, I just am surprised that many seem to be putting forth their beliefs, but I would love to know if there is any good evidence one way or the other (or better yet, a more concrete and verifiable definition of the "convex hull" so that researchers could provide some falsifiable examples).
Came here to say this. What AI is doing with math is essentially fuzzing, but looking for valid inputs that solve a problem and the inputs are mathematical abstractions. It's a cool approach, but AI doesn't understand what's going on, and without understanding it won't be able to create the next generation of mathematical abstractions needed for the next generation of proofs.
aren't mathematicians needed to create the problems? Everything solved so far is a question posed by a human. Which is probably why cracking diseases is more difficult (apart from man made viruses :/)
As a software engineer it is hard for me to feel sorry for these mathematicians. Software engineers are getting laid off because of advancements made by AI. Math researchers are employed at universities, and universities aren't laying off mathematicians now that OpenAI has solved some of their puzzles. Mathematicians can still feed their families, software engineers displaced by AI can't. Yet I see far more of these blogs about the plight of mathematicians, not enough about the plight of software engineers.
When software engineers spent the last 50 years eliminating the work of clerical, secretarial, and dozens of other back-office functions, were they concerned about how those people would feed their families? Do you think anybody but other software engineers feels any sorrow for them today, now that they are facing the same fate?
What an asinine comment. Do you think I, as a software engineer, am sitting around twirling my mustache, cackling as I plot to destroy livelihoods? I'm trying to make a living like anybody else. I've had my own opportunities lost to outsourcing and H-1B's since day 1.
The economist John Keynes predicted almost 100 years ago that technological advances would lead to a 15 hour workweek. If AI now makes you 5x as productive, then why aren't you working 1 day a week for the same pay? Why didn't Keynes' vision come true.
While I mostly agree with you, there's an argument to be made that classical programming tended to eliminate the mechanical parts of work that people hate doing, while AI is removing the intellectually stimulating part.
It's not fun to think of a future where knowledge workers become irrelevant in society and we're back to just physical work and managerial elites.
I'm not really one of them, but there are many developers for whom the intellectually stimulating part is designing the system. Writing the code was boring drudgery that they hated doing. They tend to call themselves "architects" or something similar, not "programmers."
That wasn't software engineers eliminating that work. And neither is it today AI eliminating software jobs. Let's name the straw man in the room: it's humans displacing humans, and extracting the value for themselves.
Just like in past history.
Yes, it sucks, for software engineers, those in the past, and those in the future. As long as you and others fall for the straw man perhaps you and others will get more and more tricked and hurt, misplacing your aggression and hatred on each other rather than those receiving most of the extracted value.
Yes in some cases, but the reduced costs also allow lower prices which benefits all consumers of whatever product is being produced. At least for those products where there is a competitive market.
There are orders of magnitude fewer mathematicians with full time academic positions than there are software engineers. The economics are different and consequently academia tends to be more slow moving in reacting to market trends. It doesn't mean it isn't coming, but it will look somewhat different
I don't personally grieve for the likes of Strogatz or Tao, it seems likely both of them will be fine however this pans out. But many more mathematicians have been toiling away in precarity and obscurity and without tenure for years and years. And of course many mathematicians went into private sector roles as software engineers, actuaries, analysts, ML engineers and similar, and have been displaced there, too.
And highly visible blog posts written by famous mathematicians with large audiences and closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, nor that software engineers aren't also writing about their plight or ending up on the front page as well.
To me this goes in the same direction as people not feeling sorry for software developers because our job is supposedly automating the job of other people (which I don't think describes the profession accurately as a whole at all).
Neither sits right with me. Can't we just all collectively acknowledge that we have to grapple with this new piece of technology that either is already or at least seems to be going to be hurtful to a lot of individuals?
Instead of looking at the in comparison limited group of people currently pushing this technology and asking ourselves whether we should be on board with their doing, we look to one another and are happy that someone else is now suffering just the same as we are. What a sad state of affairs.
100% agree. The comment you are responding to is basically playing "victim Olympics".
AI is going to suck hard for lots of professions, software engineers and mathematicians included. I think it's much more productive for folks in these professions to show solidarity with each other given the way AI will disrupt their livelihoods, rather than showing disdain based on who you think may have it slightly better.
As a software engineer? The career whose very reason, largely, for existing in this market is to automate jobs, with few notable exceptions? That one is somehow deserving of sympathy and that of mathematicians is not? Come off it. The notion is undignified.
Are phones an "automation of existing jobs"? Maybe couriers (??), but most of what people use them for goes far beyond that.
What about the software used to drive trains or autopilot planes? We still have conductors and pilots, but now the outcomes are safer on average and more efficient.
Or something like Google Maps -- all that replaced was the paper booklet people used to keep in their cars, it's not like we used to employ 'navigators' to go out on a road trip.
Or something like Intuit QuickBooks: there's still an accountant in the loop, and if anything more accountants today than there were a few decades ago.
Certainly some software is essentially automatory in nature. But to characterize 'nearly all' as being such just betrays a lack of awareness for the rest of the field.
> That one is somehow deserving of sympathy and that of mathematicians is not
He didn't say that mathematicians aren't deserving, he was griping that people said this about SWEs. Do you think mathematicians are deserving but SWEs aren't?
> Software engineers are getting laid off because of advancements made by AI.
The bean counters laying off software engineers ought to take notes from the frontier labs' own hiring practices. They're still hiring lots of humans for business and engineering roles even when they would be better positioned than anyone to automate away those jobs with their world-class models (https://openai.com/careers/search/).
What's your source for "Software engineers are getting laid off because of advancements made by AI". I haven't experienced that in my field and can't find any data to support that notion.
It's not about universities, it's about grant funding over the next few years. It is very apt to collapse if AI is more useful than people. Why pay people to find this when tokens will do instead.
I'll let you in on a secret: In the US, most math professors don't seek grants. In most universities, I don't think grants are even a factor in their tenure application. It's quite different from engineering.
In my undergrad math department, only 2-3 faculty members out of a dozen bothered with grants.
Who will continue to develop neural nets if the mathematics training pipeline dries up? Will we see the frontier labs relinquish AI research to the machines themselves while their humans apply for unemployment benefits?
Currently math research serves both as a training pipeline and as a math-production pipeline, and its funding is set based on those two outputs. If it is "just" a training pipeline, do we need as many mathematicians?
Who has been funding grants, and do you really think the grants are going to stop? There are infinite number of puzzles in Mathematics. The grants are not from companies like Boeing and Walmart who urgently need solutions for the problems, if they were I can understand why they might stop.
Software engineers are getting laid off because of the end of zero interest rates, wars started by Putin and Trump, and a bit because of pandemic over hiring. The part that is due to AI is less hiring of juniors. Know your enemy before starting a fight.
The difference is it takes great intelligence to be a mathematician, whereas anyone can be trained to write code. It’s like the difference between an automotive engineer and a mechanic. I would argue writing code takes less skill than carpentry.
Do you write much code? Do you design software? It sounds like you don't. The challenge with software is managing complexity. This is unique to this field. Mathematicians are humans.
> Software engineers are getting laid off because of advancements made by AI.
This is said by a lot of CEOs trying to make layoffs look good, but I haven’t seen anything that suggests that it’s true.
> Yet I see far more of these blogs about the plight of mathematicians, not enough about the plight of software engineers.
Really?!? We’ve been living through 3 years of blog posts, LinkedIn hot takes, and podcasts talking about the plight of software engineers in the era of AI. There isn’t a week that goes by without an HN post about it.
I can feel empathy for the practitioners in a field that may have been profoundly changed, the same way I can feel empathy toward software engineers who are struggling with the changes in their own field.
In the end, we’re all trying to figure out where this leads. And how this will affect our lives and our work.
The idea that a junior software engineer who can't get a software job _and also can't get any other kind of job or move somewhere cheaper to live_ to the point that they can't afford to feed their families is what's unrealistic.
It's not like the options are write software or starve. Billions of people find jobs and can feed their families without writing software.
I also don't often meet junior software engineers who actually have families to feed. Most juniors work in the industry for a few years before deciding to get married and have kids.
I think your expectations of who gets to do math is uncalibrated. One famous math researcher who solved a major open problem was working at Subway while still doing math on the side.
A very small fraction of people who get math degrees actually continue to do math in their careers. They usually have to get other jobs in order to survive (actuary, teacher, finance, etc.). Academic math funding was already drying up for last few years, and now AI will probably cause more cuts. Not to mention that academic math positions have never paid particularly well.
I feel bad for anyone who can't find a job, but the software industry as a whole has been the cushiest industry for decades, and the current turbulence seems more temporary (and driven by corporate greed) than a systematic destruction of the trade.
Unfortunately this often means moving away from family. What are you going to say to the kid whose parents toiled to get him through college on the expectation that he would be able to take care of them? "Sorry Mom, I have to move to North Dakota to work on the oilfields"?
This current moment we are in feels like something out of the Remembrance of Earth's Past trilogy, bit instead of humanity becoming super depressed and hopeless about a future alien invasion we are super depressed and hopeless about LLMs destroying all our hopes and dreams.
>Yes, some are crying about bruised egos, the feeling of wasted years, a creeping sense of status obliteration, the frustration of an unfair competitor, the indignation of feeling cheated and mistreated, and uncertainty about the future. But they are also mourning...
This nails it, however IMHO its almost all bruised egos and feeling of wasted time. I don't know the ratio of A:B but I also don't know anyone that is in the latter category of feeling doom and mourning that their craft is about to regress.
I don't know what's happening exactly, but I am genuinely astonished how little people seem to care about people losing something real, dismissing it as "bruised egos", using petty terms like "whining" and "crying", or calling them some insult for the crime of being angry or sad for having a big chunk of their life pulled out from under them. I'm referring to the big picture of common talking points, not just this case.
I guess I'm not astonished that people are so bad to each other in general, but more that in the case of genAI it's so prevalent in places that seemed more elevated previously.
Part of me wonders if this is actually a form of self-defense. The misery of others can provoke sympathy or the opposite: Angry pushback to protect oneself from dwelling on their misery.
I saw something similar on Twitter responding to 45yo software engineers making comments of depair in that HN thread about the increased suicide rate of middle-aged men.
For some reason I'm stuck in a real depressing, doomer algorithm / homepage on Twitter. But everyone on my homepage seems to have a take on the HNer comments along the lines of "see, this is why you don't make your job into your identity".
But that's such an antihuman response. The only reason you can put decades into a field to grind and build expertise is because you have an identity-level interest in a subject.
It's also not a good thing if the optimal way to live going forward is to have no passion for anything lest it changes so that we won't feel bad. I don't think that's possible unless you remove the human part of our brains or make life so horrible that we're happy just to survive another day.
Source? There has not been a statistically-significant increase in middle-aged male suicide rates between 2023 and 2024 confirmed data [1]. (2025 breakouts aren’t out yet, but top-line data show decreases.)
In 2025 in the UK men age 45–64 had a suicide rate of about 24 per 100,000, which is the highest it has been in the past half century, and is higher than other age categories. In the mid 2000s, the rate was like 17 per 100,000.
From your link, in the USA the overall rate for men of the same age is about 30 per 100,000, but varies dramatically between states.
Similarly, I got into software because I like working with computers and solving problems for others. I see TONS of similar sentiment where people are almost joyously exclaiming “Software is solved! Sorry!!! It’s been a long time coming, you all deserved it, get fucked!”
And I can’t imagine feeling the same about any group of people. It’s been odd, to me. I’m just trying to support myself and the people in my life, and now there’s a looming fear that I can’t do that anymore… business owners are drooling over that, and other sectors are laughing.
Lots of people have lost their jobs and had to overhaul their lives due to layoffs or technological advances or political choices or factories moving overseas or whatever.
They are showing as much care for mathematicians as they received themselves, which is not much.
i think a big part of the backlash isn't about math per se and it's about what 'work' or 'a job' are supposed to be.
when mathematicians complaining about losing the part of the job that they love, people think "if you love doing it, why is anybody paying you? you're describing a hobby."
Because we don’t see it as something for them to be legitimately upset about, except that it’s going to disturb their ivory tower unserious profession.
If AI got significantly better at performing surgery overnight and doctors started crying about how they were going to be replaced, what do you think the public response would be? Non-doctors want the best possible care; they aren’t interested in protecting an industry. The same will be said for pilots and lawyers, too.
People dislike self-serving whingeing, end of story, but that’s doubly true when it comes out of a profession (theoretical mathematics) that is mostly practically useless.
The doom and mourning is that it's no longer their craft. Their involvement is on the threshold of no longer being useful. What does it mean for humans when the best their involvement accomplish is slowing down progress?
This is a fundamental human need and it's being taken from everyone eventually, by design. It will take a generation to turn over and find new ways of being useful. Those who ran into this wall and could not safely reduce their income and retire/pivot to other fields, will be the coal miner oxy crisis of this generation.
Mourning is fine if it is temporary, however no man should dread their own future if they still have control of their life. This is the idea of unalienable rights and was enshrined hundreds of years ago. It seems to me that anyone dreading the future of their field failed to take a page out of their retirement strategy and diversify their own interests, i.e. https://en.wikipedia.org/wiki/Polymath
Ok, so if you really believe that losing one's vocation at 25 is the same as a 75 year old losing their spouse, that paper suggests you should wait at least 6 months before you start being a jerk about it.
I don't see what point you are trying to make. At 25 losing your vocation gives you more than plenty of time to transition into another lifestyle. Many people will consider this the very beginning of their career. At 75, retirement is near. Your legacy is known but not final. 6 months is less than 1% of your lived life, and you have a lifetime of memories to reflect and enjoy.
I was talking to a mathematician friend about this, and she was telling me that a lot of the proofs that have been produced in the past couple weeks don't have an application.
To me it begs the question: in a theoretical world where we don't have human mathematicians anymore, what is the point of these proofs if there's no human who actually understands it?
If the point of a lot of this math is only to expand the boundaries of human knowledge, it all seems kind of pointless.
Often, we don't know the applications of new math. For a long period of time we had "useless", "purely theoretical" mathematics that eventually turned into relativity and quantum mechanics.
Proofs are somewhat like legos. A bigger toolbox of them can only help in solving other, possibly practical, problems.
As far as the utility of a human being involved -- In a non-theoretical world where we don't have feline mathematicians, what is the point of these proofs if there is no cat which actually understands it? The cats can benefit from, for example, advances to optimziation algorithms that reduce costs for cat food delivery, of course.
Is AI at the stage that it can also point out all interesting things to study and then solve them? Otherwise humans would still be able and needed for progress.
Good question. I'm not a professional mathematician, but I would be interested in seeing what results the mathematicians get from trying to prompt it to come up with new and interesting problems.
My intuition is that it'll be at 'smart undergrad' levels today, though as the cryptographers say, attacks always get better.
None of them have pointed to any of the solutions and said "this is real innovation" - because it's all been mining existing ideas and applying them elsewhere.
Imagine you spend years working on a solution to one of these problems. Only to realize after you publish that more than half your answer already existed in another branch of mathematics and you spent a bunch of time re-inventing it.
Yes the first big solve by OAI was "stolen" and that is tragic, and pretty bad. But it looks like this new batch, the one people are crying about, has none of that stink.
Hacker News is so depressing these days. One doomer post per day to keep the valuations up.
Nothing has changed in math. Math is not solved nor has the human been kicked out of the loop. Same with programming.
*I said nothing really changed because LLMs becoming superhuman at deduction was priced in with o3 and neither the peer review, training nor publishing methods will get a revamp beyond what could already be done with SQLite and a website.
I'm no mathematician, but my impression as someone who at least does a lot of applied work with maths is that the main thing that's changed is that the yardstick by which academics earn recognition is being re-assessed.
But from my perspective proofs have never been the most interesting part of maths. What really interests me is the intuition that leads to new applications, and to new questions. Newton, for example, gets more credit for calculus than Leibniz because he's the one who demonstrated how darned useful it is. Erdos is arguably more famous for asking interesting questions than for answering them.
I still don't see LLMs seriously contributing to that facet of mathematics any time soon. Every so often I ask one to suggest a good binomial confidence interval for a particular application, and it still tends to just suggest one of the subpar options that everyone learns in a first year stats course.
Proving theorems is one of the main ways that mathematicians turn math into money.
The recent barf-out done by LLM companies is useful if what are you are interested in is an unreadable mess and someone giving you the final answer. You might be able to extract some new "aha!" moments out of it, but we will have to wait and see what happens once people go through it. I would hypothesize the LLM output will be good at hinting at some non-obvious relationships and patterns, but I doubt it will yield anything of substance in its own right.
Historically, proving difficult theorems required mathematicians to sometimes invent new fields, new ways of looking at problems, the discovery of which itself yielded incalculable contributions to both mathematics and other fields. It is this that is the greater contribution of and to mathematics.
> Proving theorems is one of the main ways that mathematicians turn math into money.
Mathematicians working at universities are paid to teach, to engage in the politics and business of government contracting, and only in very rare circumstances to play prestige games on famous problems.
It is unlikely that Congress will decide to slash budget for NSF's MPS directorate on account of AI getting good at proving theorems. That's just not how Congress works.
It is also unlikely that LLMs will be able to do, in the near future, do the sort of applied mathematics that happens in the context of occasional NIH or DoD funding that flows into Mathematics departments, for a variety of complex sociological reasons I'm happy to expound upon.
And it's unlikely Engineering degree programs will stop requiring calculus sequences, since being able to do the computation was has not been the actual point of teaching calc since he late 20th century (if ever).
So, the good news is that I doubt any of this will have much of an effect on the job market for Mathematicians who want to prove theorems for a living. The bad news, of course, is that the job market for Mathematicians who want to prove theorems for a living was already pretty horrendous.
I’m on your side on this overall, I think. And I suspect we’d agree more than disagree on nuances. But saying that ‘nothing has changed’ is very obviously wrong.
I guess I chose the words "nothing has changed" because that's true relative to all the subtext of content I'm seeing online claiming that "math is solved"
It was, but the comments on that post were insanely depressing to read. I'm a mathematician, and find myself largely hopeful and excited for its future, but being online this last week has been incredibly brutal due to the surrounding vitriol. It's an avalanche of negativity, and I'm largely not talking about that of my peers (though indeed, some of my peers). Most mathematicians I've spoken have been reasonable / positive, perhaps an effect of my field.
I really need to just stay off social media for like a month and keep talking IRL. Longer, if I know what's good for me.
I agree with "nothing has changed" in practical terms. If you take a look around most things rely on an undergraduate level of math than whatever is at the frontier. The proofs may be important, but they are really remote to people's lives.
This is like saying WW2 didnt happen while you were living in a Soviet village in 1940s, and you were doing the same thing, and nothing seemed to change
ZIRP is over but rates are not especially high and yet I don’t remember job market being that bad. Maybe employers are taking wait and see approach and avoid hiring developers they expect to layoff in a year or two if models will continue to improve and becoming cheaper at the current pace.
I think that models will improve and get cheaper. I think we'll see Opus 5.5 tier models open weights in six months.
You are probably right that some companies are factoring AI into headcount but I'd imagine that the interest rate and energy crisis are bigger concerns
Not that it explains all job market weirdness but you do have a problem on the hiring side with having to deal with the flood of AI generated applications. I assume that’s going to have a slowing effect on the typical apply/interview/hire process.
It was long predicted that the sign that AI is here in macroeconomics is rising interest rates, because investors can get MUCH higher rates of return doing AI investments than borrowing governments, why would I lend money to Greece when I can lend it to Anthropic?
And how! All the “nothing has changed, stop whining posts” are neglecting that they haven’t had to go look for a job. My previous company became quite toxic about LLMs and employee usage. It’s not “move over to the paradigm or get left behind” instead it was “jump on the hype-wagon and sing LLM’s praises all day, every day or you’re out”.
I own my company and directly participate hiring. What’s changed among me and my peers is that we’re on incredibly precarious economic grounds with no telling what’s going to happen next month.
LLMs haven’t done much in the way of informing me or others I know regarding “who and how many”.
I would wager that most of them are AI generated. The cost of generating a neat looking LaTeX resume and adding vibe-projects to one's GitHub is very low...
The doom posts will continue until profits are up.
Jokes aside, its like working for a company, individually you can lift mountains and someone else will take credit. When you use LLMs for a single bit, all credit goes to LLMs lol
This was the top comments when the submission disappeared from the front page.
Now the thread has been cleaned up and a pro-defeatism comment is the top comment and the submission is on the front page again (I'm not alleging moderator intervention, user mechanisms are sufficient).
You use the word "already" as if it already happened, but this is confusing speculation with reality. Market prices are a summary of speculation. Plenty of things are "priced in" that haven't happened yet, and maybe won't if the market is wrong.
Anticipating that something will happen is not the same as evidence that it's happened.
I was on Twitter around 2024-2025 and showed both Daniel and my advisor at UCSD sota results I created in group theory using Gemini 2.5 (edited) Pro in Q2 2025.
A lot of us knew what was coming. Profs I speak to these days say it's the same old except they need to pick a different kind of problem for grad students
the above, a "sorting" machine is the primary usage of hyperscalers currently, they're just trying to find new uses to boot for extra money/legitimation.
the browser industry
the phone industry
the CAs
JavaScript
it's all paid for by those wanting to sort humanity into whatever bucket the can fear monger the peasantry into for aweek or however long it takes the classification system to sort out.
gentrification works, but we chose forcible displacement now we have to live with the forever consequences.
would you give guns and bombs to the displaced native americans who taste blood over their beads and trinkets?
we've been inside the event horizon of the singularity for years, the tax bill will only get worse unless we recognize it for the tick that it is.
> One doomer post per day to keep the valuations up.
Yes, outsiders (investors, journalists) are given a false impression while insiders (software engineers) are supposed to give up. Double win for the agitprop machine.
It's probably because with the release of each model it is becoming more and more difficult to see how a person's livelihood and way of life continues. Uncertainty stacked on uncertainty.
How will it pan out, no one really knows. The leading frontier labs are continuing to hire aggressively. But who knows for how long or for long or near-term goals.
The open ai math dump was actually what got me off the singularity wagon.
There were mistakes that could easily be seen with a diagram rendering three big results wrong, exposition is terrible, no coherent underlying theory generated from solving so many problems, as Thomas Bloom pointed out even duplicate proofs of the same statement in a single paper.
It clicked for me, "this is slop but slop can be superhuman and useful!". Similar to programming where it can generate as many criticisms of your codebase but you have to weed them out.
If anything, that makes the case that math is fucked even stronger. Nobody had any idea of how to prove quasi-Riemann. OpenAI produced three proofs, one of which was just a lemma in solving another problem. They have a machine that is better than every human being alive at math that solves problems humans cannot even when working inefficiently.
Math was never only about deduction. It's also about data curation.
I was taking to my friend in OA who was really surprised that the proof of L(F_2) = L(F_3) could be done in the 1980s. We just didn't have a superhuman deducer back then.
yeah nothing changed in math. mathematicians are weeping for some strange reason (maybe paid by OpenAI to weep?). And Terry Tao is posting blogs on AI + Mathematics because he was bored (or because he was also paid by OpenAI).
I don't get the argument - if we follow what you say, they're not _overreacting_, they are reacting appropriately but should have done so earlier (when o3 was released) rather than now?
My claim is that if Bob, a mathematician, believes that he is rendered useless by an LLM then he did not play with o3 and all the other models between now and then to realize that, yes, they are superhuman at details and deduction but not superhuman at math
> I think I have been underrating the pace of model improvements. In March 2025 I made a bet with Tamay Besiroglu, cofounder of RL environment company Mechanize, that AI tools would not be able to autonomously produce papers I judge to be at a level comparable to that of the best few papers published in 2025, at comparable cost to human experts, by 2030. I gave him 3:1 odds at the time; I now expect to lose this bet.
“I’ve slowly updated my timelines over the past year…”
and
“I think I have been underrating the pace of model improvements. … I was not correctly calibrated as to the capabilities of existing models, let alone near-future models.”
Sometimes you think you’ve been accused of everything you could be accused of. Wonders never cease!
> The "moderation by less", as well as the guidelines, are both farcical in nature. They've given way to ruination of an otherwise decent tech discussion forum
The guidelines have been constant (with minor updates) for most of the two decades HN has existed. Dan’s a moderator for 14 years and I’ve been one for several. Both of us have been active participants almost since the beginning. When did the ruination begin?
Your comment seems a generic vent, largely unrelated to the parent comment but if you have any actionable suggestions you’re welcome to email us.
> Your comment seems a generic vent, largely unrelated to the parent comment
There it is, the "off topic" play. Well done, Tom.
If you'd put anywhere near the amount of attention in moderating the site for over all quality that you put into my "largely unrelated" comment, this entire comment thread would not exist. Think it over.
Please don’t insinuate that I’m “playing”. It’s a slimy tactic, not an earnest contribution to a conversation. You opened this subthread with an accusation that we’re putting our thumb on the scale for the CCP. Yes, it breaks the guidelines, along with basic decency. The only reason this site still exists for people to bemoan that it’s not as good as it used to be (which people have been saying since about three months after it started) is that we have guidelines and uphold them in a way that people can trust, often against pressure from many different people with all kinds of agendas. As I said, if you have any actionable suggestions you’re welcome to email them but all I see is someone complaining about quality whilst having no concern for the quality of their own contributions here. If you don’t like the guidelines you should take your own advice and find a site that’s more to your liking.
What I was aiming for was to point out the oddity of dang selecting the one odd ball thread to tell everyone to play nice, in what is otherwise a site that is daily filled with AI doomer posts, as per the opening comment of this thread to which I responded. And I did mention that I found it amusing - because I doubt either of you are actually shilling for CCP. This wasn't even the main point of what I was after.
That neither of you are at the very least bothering to steer the greater discourse towards some higher ground is a lack of balance that I am highlighting.
To remark my comment as off topic in the context of the thread opener is to dismiss what I am saying using a very lazy tactic that I've seen used countless times before. No, it is not off topic. It is very much on topic and relevant.
And if you have a problem with my comment, feel free to email me.
I happen to be (re)reading Strogatz' book "Nonlinear Dynamics and Chaos" right now. It's beautiful thing, and nothing in the "age of AI" threatens to equal it or in any way diminish my enjoyment of it.
I think the point is that in the "age of AI" virtually nobody will have the opportunity to follow a career and produce works like Strogatz was able to do.
I'm not disagreeing with the post. My personal opinion is that LLM "thinking" is qualitatively different to human thinking, that the "convex hull of ideas" idea is probably right in some sense, that the social structures we have built to allow and encourage human intellectual exploration are not obsolete and that there is a high risk of catastrophic damage being done to them by those who fail to see this.
> Today, the mathematicians are weeping, because the machine smashed their tower first. But tomorrow, it may be the physicists, the economists, the illustrators, or the writers who weep over their fallen blocks.
Isn't it extraordinary that these models still can't write well? I mean, they write passably well, but they all have a highly characteristic style that you can spot from a mile away. These language models can crack the toughest open problems in math, but they haven't yet cracked human-like writing, especially long-form writing, without exposing themselves. This is very very odd, IMO.
Writing is a very slippery thing. “Good” writing from 200 years ago reads as unbelievably dense and overwrought to most people today. So even if you made an LLM that was “good” at writing, how long would it stay that way? AI systems can put out more writing per day than all of humanity combined, meaning it can also generate and beat to death cliches much more efficiently.
Or, just maybe, they share a key property with the mounds of popular writing, journalism and random internet accretions they were trained on: they seem total rubbish on anything you know about deeply, but brilliant on everything else.
Their math is as just as good as their rambling writing and their Ghiblified poster art. Most people don't seem to realize that.
I think it is. Why is it that the only people in any field I'm aware of that think the AI output in their field is high quality are either the ones that are carefully crafting the output themselves or were producing/consuming slop themselves before all this started? (Outsiders pretty uniformly like the output, which is why I drew the parallel to Gell-Mann amnesia.)
The difference here obviously being that the part that you mention is more embedded in the proofs (long and difficult and near-hallucinatory) but the results that matter are that the proofs are correct and validated. So I think you're failing to account for that, the problem for math is that the journey matters less than the destination.
Hard disagree. If we send someone out exploring and they discover something (maybe?) but their account of their journey is impossible for anyone else to follow and contains obvious hallucinations, what have we gained?
Language models don't have a characteristic style you can spot from a mile away. They haven't had it since before ChatGPT.
What is true, is that chat models (and by extension agents) have a very characteristic style after their LLM went through post-training. But the pre-trained language model doesn't have that style.
So if you want to write well with an LLM, you could and it is a well understood problem. It is more a matter of that not being of much interest, as it competes with having the model be good for chat interfaces.
How to have a well-aligned, RL'ed, safe or thinking model, which also writes well in long-form, is a bit an open problem. Though presumably agents could do it when they have access to a pretrained model.
Why is writing in the style of a corporate marketing department a requirement of being good for chat interfaces? Why can't they tune them to sound more like a normal human?
You can just tell them to adopt a different style. To make sure, add another pass with an agent that flags and/or fixes LLM tics. Humans typically do several passes over writings that they intend to publish, why are we expecting agents to do it in one shot? Just like the superpowers skill for software development does a spec phase, planning phase, several review rounds, etc., if you do the same with writing you get very passable results.
Math and programming languages are formal. Meaning they don't have any ambiguity in them. Every statement is what it is. That means they are very rigid and there's not a lot of variance. Natural languages are more diffuse and a written piece is more the reflection of the author than anything else.
That is why it's so disturbing. After several paragraphs, you realize there's nothing human there even when the actual information is present. People that do create AI piece are OK with it because they already have the context, but for the reader, it's always the uncanny valley.
There's no money in it. There's money in programming, and math is a good target to give the models superhuman reasoning abilities, but it already writes well enough for middle managers to write all of their emails.
Article refers to Hugo Duminil-Copin, who also did a podcast with Brady Haran [1] about this subject, for him it isn't case of bruised ego, or gatekeeping. He realized that the way things were done were going to change, and it made him emotional, he is not pessimistic or against AI.
I need to do some more research on this. Because I've always been told that AI, more specifically LLMs, are "glorified autocompletes". Yes they have huge data sets but ultimately they can only provide answers based on data that they were trained on.
So how can they possibly solve problems that humans have worked for decades or centuries on without being able to solve? How did they find something new? Is it that they were able to deduce the solution by examining all current data sets? Or simply brute force it until the produced solution passed all necessary tests?
The following certainly does not describe all mathematics or all LLM operations, but its my mental model for why LLMs are so effective in several fields.
Lots of mathematics entails recognizing that a tool/techniques that works in one area can be adapted to a completely different problem. For a human to do this requires having a robust mental model of the technique and the problem itself, and probably having just the "right" mental model to see how they fit together. And we are talking about extremely hard/sophisticated techniques and extremely hard/sophisticated problems, so the ability to deeply appreciate either can require years of study. And on top of that, even if the mathematician has sufficient understanding to develop the intuition that the technique might work, they will need profound fortitude, skill, and patience to see the solution through.
Unlike human mathematicians, who will develop a deep understanding of only a relative handful of techniques and problems in their lifetime, LLMs have ALL written techniques, problems, solutions, etc stored in their internal representations. So when they ably match a problem to a technique, we can imagine the operation as a supercharged autocomplete, or even an extremely proficient search engine. Their stroke of genius is really a consequence of capacity, moreso than cleverness.
They have access to a much larger corpus of information than any single human can manage in his one brain. No human mathematician reads all the papers and has perfect recall on them. The answers have always been there, but no individual has been able to make all the right connections to pull them together and formalize a new discovery or proof.
> Is it that they were able to deduce the solution by examining all current data sets? Or simply brute force it until the produced solution passed all necessary tests?
Yes, both of these + an infinite token/compute budget and SOTA+ models. It's not like some hobbyist out in the woods with a GPU running Qwen 27B can do this.
I am not quite saying "if you can't beat 'em, join 'em", but I know more math now than in any point in my life because I want to understand how LLMs work.
I understand there are many types of math and the mathematicians don't all want to sit around and do KV cache and gradient descent things, but surely a percentage are as interested as I am and can contribute to this new emerging field? I would wager that Xl+1=Bl Xl+Cl ℱl (Al Xl) makes much more sense in their mind than mine.
This is the best attitude to have about the current state. Unless you have some dramatically different sensible solution (and you probably don't when it comes to technology, because it seems to spread for reasons that would eliminate other sensible solutions) that will catch on and take over and replace AI: it's going to continue to mature as long as it's mostly useful to everyone. And AI isn't even a new industry, it has been maturing for quite a while, which adds more weight to the argument that having an attitude that adapts to technology (unless you wish to go solo) is a 'better' fit.
The dramatic solution can never be: 'we should all just want to do it this way because it felt better to me'. That never seems to work, from what I've seen. So there is a lot of public discourse, arguing, to determine if 'doing things the old way' is perhaps more better. And if not, maybe we just shed a tear and move on (to look for a better fit).
As usual the author is ending on a completely unrealistic positive note: "humans may come to value more highly our capacity to relate and care for one another".
Does relating to someone pay my bills? People will use the informational tools to improve their social status and resource accumulation, there is no doubt about this.
I'm convinced the people who do not see what Mathematicians see simply have not considered that their jobs are just as vulnerable. The day when OpenAI replaces their own AI researchers with GPT will be upon us, and the response from the Mathematicians will be "First time?"
One of the driving forces of math achievement is an internal award (yes, friggin business speak).
The vanity, fame, self-improvement, it's very selfish as everyone does.
Now the fame coming from proving things like Riemann Hypothesis is taken away.
Self-improvement? relying on AIs make you stupid. It will be lost.
Vanity? Who else don't know how to use AIs? It cannot fill your void.
Now also the most important thing is the communication.
There will be less communications amongst mathematicians at least in person. On paper? maybe but mostly via AIs.
I don't think it's the communication that's lost, it's the motivation. People love to collaborate, but they don't always want to waste time doing it.
It's the same reason you see 'no AI' repo labels: only by forcing some standard on the community can the 'old way of collaborating' continue to exist.
There will for sure be new ways of collaborating, and walled off gardens like you suggest, where communication stops and everyone just shares some final product.
But, in some cases the product must be understood (or demonstrated) before value can be derived, and so collaboration will still exist.
Desire, and the 'shape' of collaboration has changed greatly though. Why collaboration has changed, is a completely separate issue related to economy and how each of us spends our time.
Desire and motivation are factors to consider. Would you want to invest 5 years of effort into solving the Hypothesis 'the old way', knowing someone is probably working on it right now with AI?
And then once it's solved by AI: do you want to churn through the proof to understand it? What if it takes you 5 years to churn through the proof, and it turns out someone made a mistake with AI (I have no idea what would be realistic amounts of time, but the idea is still worth considering).
The issue is very complex, and you will always be hungry.
For sure, I just wanted to correct the impression that it has been solved. There are a lot of people going around pretending LLMs have solved everything and human maths is over, but what has been achieved with them so far, while impressive, is a very, very long way short of that.
If I were a mathematician working on the Riemann Hypothesis, I'd probably be rather pissed off right now but continuing my work, i.e. the same as I am as a software developer.
I get you. What people are doing now is questioning value: in themselves, and what they can create for others. I hate to always oversimplify things but we're pretty simple things to begin with:
Social creatures that share a common space, with finite time that nobody wants to waste.
The author mixes "Science" and "Mathematics". Mathematics is not a science. There is nothing empirical about it. By mixing the two concepts, a reader might think that AI is on the verge of solving all of science. Until AI gets good at digging large circular holes in the in the ground, I think Experimental Physics is safe.
Maybe math is more like a science now, though? It's as if ancient astronomers saw the results from a modern telescope. "Why even look at the sky anymore," they might ask. "And we don't even own the telescope!"
Maybe the answer is to look into how Big Science works? There's still plenty of work to be done figuring out what to do with the outputs from these new math-observing instruments.
I had visions of large automated warehouses full of chemical and biological components hooked up to science machines to do everything from mixing, boiling and printing to spectrograph and robotic assembly. Smart computers and humans would pick the experiments to brute force with exact billing.
We are seeing many fields being impacted. Makes me happy to see things like artcraft coming out that directly impacts the big tech companies themselves.
Programmers, artists, anyone who used to create any form of documentation, translators, there are literally so many.
Either these mathematicians thought it would never come for their jobs, because all of these other jobs were simpler or they've been living under a rock.
Either way, I don't feel for them any more than I do for all of humanity.
As a mathematician, I will never understand how my colleagues had never foreseen this. Okay, maybe you can believe in a plateau but at least accept as a possibility that there won't be one. This applies to every other human endeavour.
I am also sad, but my sadness is, in a way, priced in.
It's not really a profound insight. Back in the 1980s when I first started writing BASIC programs I remember thinking "well, if someone invents a program that can write programs, there will be no more work for programmers"
It's easy to have that thought, and eventually you'll be correct. One thing about technology is that it only improves. It's always building on top of what already exists. The only uncertainty is the exact timing, not the ultimate outcome.
The people struggling right now - they were told. 30 years ago. They really should have come to terms with it by now.
But these are also the people who refused to believe it, for whatever reason. Their heads were in the sand. So I do feel bad for them... but... this is somewhat self inflicted.
It was really quick. I stumbled across a comment from KConrad on MathOverflow on how useless AI was for research. That comment was from 2024. When it disproved the unit distance conjecture in May, the solution involved a breath of knowledge of the literature that it made sense it took a computer to make the connection. It only took 5 months for it to advance to the point that it was better than humans at almost everything. Even if you expected it, the mind boggles at how fast it was.
Also, it's impossible to really know how you're going to react to something until it happens to you. When ChatGPT came out, I already thought "in the long run they're going to automate almost everything humans love to do". Despite having 4 years to brood about it, I did not really know what it would feel like until it happened to me directly.
Even before LLMs it was feeling like the design of society wasn't really for people any longer, instead it's more and more designed for corporations and their convenience. In the US at least. Same with how the internet has stopped most people with socializing the same way they did in the past.
Now we have a new layer that will be optimized for these digital entities. We see it in writing all over the internet. There will be tons of other places they show up and doing things that don't make sense to us.
I don't see how this is possible. There are constraints on the speed at which information can move and the number of steps required to compete a given task. The improvement cannot continue, let alone accelerate, indefinitely without bounds.
Okay, how can we be certain even about that? It sounds just as plausible to me that the improvements will become asymptotic and boring, not exponential or inconceivable -- and how can we make any confident prediction at all about the heights these models will reach? The technology those heights require doesn't exist, and its existence isn't guaranteed, even if it is possible.
I think what makes it hard is that it's quick, but not sudden. I understand constant-rate improvement. I understand what it's like to be in a car crash. What I can't understand, emotionally, is the constant acceleration. Even now, if I look at an OpenAI solution in isolation, I can understand the big picture, so if things froze where they are I could adjust. Intellectually I know I'm not going to get that chance, but emotionally I don't.
I object to a few of the assertions made by maths folk in the article- 1st being that Google Translate taught us nothing about linguistics. If you use google translate you learn less about linguistics than if you had to experience learning the languages first hand, maybe, but you can learn form just that output if you are determined to, ad, more importantly, the folks who built it and are still building it are still learning a huge amount about linguistics.
What are the relationships between many languages that become apparent, including code as a language that were not obvious before llms? Translation is fairly solved. The study of how and why languages, not at all.
When anyone can push a button on a machine and out comes a math result, it still doesn't become theirs or anyone else's until they can internalize it and make it part of their thinking.
"I can’t solve these things, but maybe you people in the future can stand on my shoulders."
Seeing AI being lauded for solving problems like this makes me feel... uncomfortable.
We are feeding all works of the giants that we have all stood on into a huge vat, in the hope to generate something meaningful.
If we can't understand the output, internalize it, or build from the time and experience that a human would have gained from solving the same problem, it feels like a dead end.
When all the problems have been "solved" by AI, what's next? If humans no longer struggle to solve the problems that the previous generation have left behind, how do we progress?
I remember the same doom cycle during my PhD when GPT 4 came out [1,2]. It seemed like everyone in NLP was freaking out except me. A few years later and new CS PhDs are still graduating and joining academia and industry. Much ado about nothing.
Considering I currently live in Ithaca and have a friend doing a Math PhD, so I've heard from him some of the discussions in the department. I think the biggest shock for people is that individuals spent significant portions of their time on some of the problems that OpenAI supposedly solved (I say supposedly because all of the proofs have yet to be independently vetted). I understand that it's a shock, but I'm confident that in time it will be no more of a blip than it was for NLP.
A blip for NLP? What bespoke NLP research is about anything other than LLMs these days? How many companies are handcrafting bespoke NLP models instead of sending a LLM request? Really confused here.
My friend, who is a math professor, told me that they weep because they are about to become just like us developers: prompt writers and AI output reviewers.
> My friend, who is a math professor, told me that they weep because they are about to become just like us developers: prompt writers and AI output reviewers.
If it was about understanding interesting proofs that some AI came up with, and extracting their essence, I don't think the situation would be so bad.
I see the much larger problem in the now existing career prospects of non-tenured researchers in mathematics. Everybody know how precarious the career prospects in academia and how precarious often the non-tenured positions in academia already are. With the new AI breakthroughs in math, these have in my opinion even worsened a lot.
Mathematicians are grieving the birth of something that is, in a very real sense, the crowning achievement of mathematical ingenuity.
I never appreciated hard math much because my brain just can't get there. I thought so much of math was much ado about nothing, but now I see the art in math...not in the inscrutable formulas, but in the creation of AI.
Well done, mathematicians. You can now rest from your labors.
A hypothetical... suppose AI "solves" (for your preferred definition of "solve") your field and what you used to do becomes useless or near-useless. But you still enjoy doing it and you also get UBI that provides for comfortable lifestyle regardless of what you choose to do.
Questions:
(1) Do you still weep for what has transpired?
(2) Do you continue to do what you used to do (with optional AI assistance)?
For me: (1) no, (2) yes and I think the same would be true for most people. So I can't help but believe that most of the anguish about AI is far more about a direct economic hit to people's livelihoods than it is about the impact to their respective fields. Which is more than reasonable. But then why not frame the conversation that way instead of beating around the bush?
I’d be okay with UBI and hobby intellectual work for the rest of my life. But I’m not a mathematician. Many of them probably have more of their identities tied up with their cognitive abilities and social standing.
For many people, the answer to 1 is yes. You maybe happy with our future where we putter around aimlessly as consumers, but some people want to live in a world where they can at least try to do something that matters. Virtually every professional mathematician is motivated by personally making a permanent contribution to human knowledge, no matter how small.
I love that we have new ways to solve problems. And it's been hard to accept that my own unique intelligence—which I've spent decades cultivating—just isn't as important as it used to be. I am developing new ways of thinking to better adapt to an AI-enhanced world, but I'm not done with the mourning process. We're all finding our way through this.
Mathematicians should web search the arguments when artists were hit by the wave. Scientists in general and people that think humans know better.
This is probably the first time in history deep thinking is being replaced by a machine, but the overall arguments are the same in all cases. Graphical artists saw it first, then programmers, now mathematicians.
No, there is not stopping the wave. No, society won't probably be able to support the same number of mathematicians as before. But yes, there will still exist mathematicians after the wave break, just probably completely different than the old way.
And yes, some people will still try to do artisanal mathematics and say it's better, it probably is, if the artisanal mathematician in question is doing deep creative and out of the distribution work.
My take is that it is an exciting time to be a mathematician since the frontier for interesting math problems is about to explode, and without prior art or references, it's green field for both AI and human. Think of all the new discoveries we'll make.
OpenAI didn't have to mass publish these solutions. They did it to make themselves look good. They are ostensibly making a tool for people, to better humanity. Instead, they chose hubris and self-interest.
Letting mathemeticians use these tools to reach the same conclusions would have been far less destructive, and potentially, even exciting. Shame on OpenAI.
Mathematicians are smart enough to have figured out which way is up. You can debate the stuff outside someone's field not knowing the details but the insiders know what is happening. Ai may not be better than someone with very specific knowledge at this point but it is certainly better than the net. Once it gets optimized for every little super human knowledge, it can do better.
These guys know because they looked at it. Denying it is useless. But maybe some of these guys can figure something new using it and asking it to look for it.
I'm wondering if mathematicians are sort of going through what programmers have been going through recently, really questioning whether their craft can continue. But now it feels like, in the software world, at least from my seat, people can handle much larger scope and work on much more complex problems. If anything, my job has gotten a lot _more_ interesting.
So I wonder if mathematics will go through that too? A period of chaos and doubt, but finding new and more effective ways of working.
This is such an insidious propaganda targeted at the demoralization of entire professions.
Strogatz is an AI booster who "wept". Totally representative!
How much do they pay you? Does OpenAI have bulk subscriptions to your Substack?
Those of us who loved programming have already been through this.
I hate programming these days - back in the day, the cubicle-hell nature of "popular" frameworks was at least offset by being able to think through and solve interesting problems.
These days most of us are stuck in the "endless-review" loop with LLMs. You can't afford to not use it given the inflated expectations. As with all of modernity, productivity doesn't yield leisure - it just proportionally increases your workload.
Hardly surprising that the other side of the Curry-Howard correspondence is now getting hit with this. Math was one of those depts. where slow/deep-thinking was possible (CS was already insane 10 years back - now it's just absurd) - now even this fortress will be broken. Tragic.
I think they might find comfort in knowing it's not just mathematicians - this is coming for all of us. Computers putting us out of work has been coming for a long long time.... and now it's here.
The beginning of this article is decent, the end sounds like a tobacco lobbyist touting the health benefits of nicotine.
> If intelligence becomes less uniquely human, we may come to value more highly what remains uniquely human: our capacity to relate and to care for one another.
Lol. How does the author think relations between people work? (At least those outside the family). Relationships require something that fills them with meaning - a reason why you would want to have that relationship in the first place. Without meaning, no relationship.
Getting those fields wiped just shows how unnecessary those fields where in the first place. I'm a programmer. I am the adapter between a stakeholder and a machine. I am just needed because the stakeholder lacks the knowledge to tell the machine what he wants. If he can use this new fancy adapter called Agentic AI now I happily quit my job and go on finding something that makes more sense in the first place.
The same goes for math.
Let's find some things that bring value other than just the price of a stock.
Broken take, with out this trail of mathematics that lead us here we'd have never reached this place. You think multi dimensional matrix math comes natively to humans?
At worst its time is past, but even that is unlikely.
I wonder how much this is like a tremendous telescope being invented which can see new worlds with utter clarity. We could verify that a planet was habitable... but it wouldn't bring us any closer to visiting it.
> "Earlier this year, Shanmu Jin, a Chinese medical resident, used ChatGPT to solve a problem called Crouzeix’s conjecture, which professional mathematicians had failed to solve for decades."
I note that that these conjectures being solved by AI are named after people, minds knowledgeable and and brilliant enough to come up with the question in the first place and recognize its value. What we have in these AI math solving systems is the equivalent of the chess and go software that can beat humans: something that can adhere to a set of rigid rules to reach a win state once given a starting point. But, as Pablo Picasso said, “What good are computers? They can only give you answers.” These AIs are a magnificent achievement and will change mathematics and coding but can they ask earthshaking questions? Could an AI identify conjectures that mathematicians recognize as a worthy question that will lead to new insights? Where is HAL9000's theorem or the M5 Multitronic's conjecture? Maybe they can someday but I don't see any immediate prospects for it.
Please spare us the "AI will surely keep getting better forever" (unlikely and don't call me Shirley), "moving the goalposts" (I myself haven't set any), etc. non-arguments.
I still remain hopeful that this is a step change in capability and capacity that we can adopt and adapt towards our own purposes. What was taking decades for us to do has been reduced to days and dollars. So while we’re witnessing a forest fire consuming entire fields of open problems in math, the best upside would be finding new problems that come from learning how to work with the new tools.
This is what it seems like so far for software. The speed limit has changed. It’s interesting to explore what that means. Extending the analogy, long ago you could be a race car driver part time; that would be pretty laughable for an F1 driver. It’s a very specialized skill and the optimal athlete is quite different for driving a car than for running, for example. That feels like what I’m seeing in software.
The most effective folks are much faster and better with these tools than average. It’s a different skill set.
I think that formal verification makes Math much closer to code than many other fields. But I’m eager to see the first mathematicians that are dramatically more proficient with the new tools than average.
These guys are still in the early stages of grief. They should look at coders; we've already been there. Coders don't assume coding is going to remain a profession. Why should any other profession be exempt from disruption?
Honestly, there are much bigger fish to fry, like how will everyone pay their bills, and how will we prevent catastrophic AI.
I strongly feel most angst is because Mathematics has become yet another capital intensive game to play. Rather than a noble, purely intellectual practice.
> Think about a world where non-mathematicians leapfrog the field after a few AI prompts. It would be a world with more knowledge. But it might be a world with less understanding.
This seems like a good summary of the article, and I think the answer here is obvious.
So what?
News flash folks: we do not have the knowledge to survive on our own. If a solar flare deletes the electric grid, the first thing that happens is 8 billion people die in the next year.
We survive on abstractions others have built, and we have a global dependency web.
AI abstracting knowledge is neither new or dangerous; if it is dangerous, this certainly isnt the argument to prove it.
>I wanted to talk to one of the mourners to understand their technological grief. I wanted to know if theirs was a familiar case of bruised ego or disappointment—akin to, say, a boy who spends an hour building a tower out of blocks and watches his big brother smash the thing to smithereens—or something stranger and more profound.
I'll be honest. The response to mathematicians, even this one, makes me concerned about the lack of empathy and honestly just theory of mind of many people in tech. It's not a mystery why people are upset that their field, for many the singular passion to which they've devoted their entire lives, is being annihilated so that a massive company can boost its IPO valuation. It's not "bruised ego" ffs.
Isn’t it deeply exciting that the proofs look so alien?
Isn’t that in itself the new frontier for human understanding?
I would have thought that mathematicians would have found alien forms of maths to be astonishingly compelling, must learn, must know, must understand.
Instead there seems to be a sort of shoulder shrugging lament “we don’t understand it”.
I would barely be able to sleep with excitement at the potential for where this could lead. Like finding an ancient tomb full of answers to our deepest questions along with the promise of more.
How deep does maths go? Is it “solved” or have we just been given tools to delve ever deeper?
Where is their curiosity - don’t the want to find the bottom?
The interesting answer is we don't know. Many of the math problems that make our computers efficient were developed hundreds of years ago with nothing we could do with them.
It is mostly impossible to figure out what we find when we solve these problems. But occasionally they'll lead to real world efficiency in algorithms we use and it changes the world.
I have little sympathy, since I think it is a result of many decades of complacency when it comes to thinking about why want to people do what they do and instead just enjoying being the ones with the results and money. People who love the process and see the human as inherently valuable won't have a problem. I'm more shocked that there are so many brilliant people who are so results-oriented and don't even have a concept of value outside of that. I'm kind of disgusted by the tears actually
This is exactly my perspective as well. Seeing humans as inherently valuable is the key. It's shocking to me that so many people seem to have been reducing humans to the results they are able to produce and now that the results appear to be drying up, their perception of their own human value is going down with it.
I’m fully STEM: software developer with a physics PhD with a mechanical engineer wife, but this is certainly just deserts for the STEM people, who mocked the humanities and especially philosophy for centuries (literally, this started back with Kant even) for spending time thinking about these questions. STEM people are not at all spiritually prepared for it, and this is the main disappointment for me. I spent many years struggling with publish or perish in physics but all those around me claimed they simply loved doing physics and that that’s what mattered. Now as soon as their exclusive ability to give results is slightly threatened the love of physics/maths/coding is no longer spoken about. I get maybe they weren’t the same people, but I thought more people loved the process than it seems today. If anything these new developments make it even clearer for me what I love about this kind of work. I’m so happy it has made me not have to defend based on results, a razor sharp contrast that makes it so clear really why humans do things
> I have little sympathy, since I think it is a result of many decades of complacency when it comes to thinking about why want to people do what they do and instead just enjoying being the ones with the results and money.
It's not clear from your comment: Are you talking about math professors?
If so, what money? They make a living, but it's not that great. I just checked the salary of two associate professors at my university: $80-85K.
And keep in mind they often start their careers quite late. Often multiple postdocs after PhD. Starting a tenure track position in your mid 30's is not common.
> I'm more shocked that there are so many brilliant people who are so results-oriented and don't even have a concept of value outside of that. I'm kind of disgusted by the tears actually
The whole point of the article is that the person crying is because he loves the process and is worried the human connection will be gone.
Anyone who would replace me with a robot never loved me anyway. If that happened I would go and seek out the humans who really do care, and take solace in the fact that Christ will always love me
Handle what situation? Why would people who love me ever replace me with a robot? It’s a random posed situation that no one discussed and doesn’t make any sense lol
Beyond just making you redundant in your job, the whole architecture of your existence, the thousands of hours of struggle, the sacrifice of putting off social games or personal enjoyment are now rendered moot in hindsight. You are made one step closer to complete worthlessness, which will surely continue as AI becomes a more satisfying personal companion, a more worthwhile friend, lover, etc.
How is one to feel safe in the progress of the future when the only hints of the wonderful post-scarcity utopia we can quantify so far is the removal of all human leverage via their labor? All it tells us is we will be bargaining with superintelligence with nothing to stand on, only a trust that the 5000 lab executives and researchers solved the most important research problem of all time on the first try.
I recently thought about this and fear that AI may further drive us humans apart.
Instead of working with humans, I increasingly work with a fleet of agents.
When you talk with machines, you "outsource" that central human society-building element.
But machines never socialize back in any meaningful way. You gradually lose yourself.
I have not totally abandoned the hope that a machine could be someone. LLMs aren't that, though.
There are billions of real-life humans already there with you. Why do you need different ones exactly?
I presume, you don't like those already around. Fair point, they have many flaws for sure.
But that's the reason you interact with them in the first place? To learn and make not only other's flaws go away, but also your own?
I'm sure the Telegraph operators, human calculators, mine workers and all sorts of people have asked themselves this question. It's obvious that it feels strange to suddenly be part of the cohort asking but I assure you it's not new. And the answer hasn't changed much since.
Industrial and technological progress has birthed better conditions overall, but at a cost of locally worse ones. Mine workers that got displaced didn’t end up being machine operators - most of them landed on benefits or sporadic gig work. Only the next generation was able to be properly trained and educated to be able to benefit from the technological advancement en masse. And we might see that happening again.
Worth reading: Robert Brandom, “Making It Explicit: Reasoning, Representing, and Discursive Commitment”
The participant is not an LLM, the participant is a company. The company learns. It adapts. It has a trillion dollars of skin in the game.
Likewise OpenAI doesn't have "skin" of any shape or value in e.g. the mathematics community or even in mathematics research per se. In my cynical view, they are exploiting the exposure of mathematical research to automation in an effort to create a case study of their product obsoleting a highly visible and well-leveraged and relatively small profession. Regardless, I doubt even they would say they have durable skin in mathematics in any sense, certainly not in either of the senses I mentioned above. But their output inhabits the same space as mathematicians, who have to contend with the consequences
They hire math and physics grads and good command of math is very useful in computer science, machine learning and AI.
And how do you see these qualities changing over, say, the next decade?
I'm interested in the reversal that Sellars proposes - it seems clear to me that "representation" is not prior to the space of reasons, despite how unintuitive it is.
> An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time.
I see no reason why this can't be the case in the future, even though I think inferentialist-based theories are generally strong. Can't you force LLM's (or whatever AI architecture will exist in a decade) to stake durable commitments itself, then? They're at least autonomous enough to run computers. I agree that that is a core part to true meaning & autonomy, but nobody just lets them yet. I don't think inferentialism is a consciousness-based argument, either, so that escape hatch isn't available. I also don't think this is a necessary condition to engage in the space of reasons (but maybe then I'm misunderstanding it, or retreating to a more Sellarsian understanding). Could you explain on this more?
Though again, I only have the book sitting on my desk, and I haven't cracked it open...
And yeah, consciousness based arguments are bunk IMO. It's clear that LLMs are in a basic sense "aware", and even to some extent "sapient" (in Brandom's usage), i.e. they can justify claims and object to things at least locally. I follow Rorty on the question of consciousness, which is to say that consciousness has no deeper meaning in practice beyond "are you awake", and in philosophical discussion it's largely a proxy for "are you one of us" in some amorphous sense.
Consciousness, the interesting part anyway, is qualia, or the "it is like something to be me" as Nagel put it.
Intention, as Dennett used it in his book "The Intentional Stance" is the "are you one of us" angle, and is distinct from consciousness because as the book title suggests, it is a stance taken with respect to some other system (person, cat, dog, turtle, LLM) rather than a description of subjective experience.
So I think it is your (and Rorty's) positions that are bunk. It is very, very far from clear that LLM's are in any basic sense "aware" let alone "sapient". They are extraordinarily able to manipulate language in a way that leads to text generation that has traditionally been assumed to indicate consciousness and/or intelligence. But we have no way of knowing if it is like anything to be an LLM, even though most of us are busy taking the Intentional Stance towards them.
[1] https://sites.pitt.edu/~rbrandom/Courses/2022%20Phil%20of%20...
Edit: One of my ways of benchmarking new AI models is actually to type a version of this prompt in and see how sophisticated the response is: "Talk to me about the concept of deontic scorekeeping in the context of llms". You'll get good mileage out of that.
Deontology - `normative ethical theory that the morality of an action should be based on whether that action itself is right or wrong`
What an LLM can't do (at least with the current architecture) is sustain a commitment that it can be held accountable for later. It doesn't have durable "perspective". It can't update its priors. Maybe a new architecture will come along that gives LLMs memory plasticity, at which point they will shift into being individuated quasi-persons, but that's not what we've got now.
I've written some about this here, if you're interested: https://elliotmilco.substack.com/p/deontic-scorekeeping-comm...
I think you are also suggesting Mathematics and Language are the same thing.
I'm not suggesting mathematics and language are the same thing, but I am saying (which shouldn't be controversial) that mathematics as a discipline exists within the medium of language, and that mathematical reasoning, discovery, and proof happen via people proposing, justifying, testing, and objecting to formulations in language. This isn't a metaphysical claim about whether math is real or captures inherent structures of the universe etc.
You ended your first post with: "An LLM encodes the normative regularities of our linguistic/conceptual games into its weights, but it cannot be a real participant in our games because it is incapable of staking durable commitments or changing its dispositions over time."
And so if there is an agent, a thinking loop, that can recursively adjust over time...how does your statement hold up? I'm particularly talking about 'staking durable commitments or changing its dispositions over time'. Recursive self improvement is all about these 2 things, especially when it's the 'outer thinking loop' doing the improvement.
But you're right, Mathematics exists as a medium within Language. But then Language is just a transfer of ideas from one mind to another.
This principle is the heart of what the article is talking about: a transfer of logical mathematical ideas passed from a human to another. And the sense of 'shared understanding' that comes with it. It has nothing to do with keeping score.
It's about getting a 'sense' for why someone thought or rationalized an idea in order to connect some other idea. You get an 'ah-ha' moment, and some of those moments are gone, or a different path is taken to reach the moments now. That is what the 'weeping' is about (not that I agree with the article. I think anyone can spend however they want. Math doesn't have to change, it's that people want it to, apparently, because it's 'easier' to do something different, or for some other reason I don't know about).
Both depend on Logic, which is where "deontic scorekeeping" comes in. You can only establish something (score) is true and believable by 'keeping score' and having some level of understanding about the language or math you are reading.
The article is mostly referring to the connection that comes from shared understanding between humans, particularly mathematicians, as they build new shared understanding, and realize there are limits to what they can know and 'leave behind' logic for others to pick up and carry on.
That connection has been severed, or strained a bit, but I'm sure new ones will be created. It just might be of the same flavor that mathematicians prefer, therefore they weep.
And if I understand "deontic scorekeeping" correctly, these forums are a better representation of the concept. You will lend some amount of belief to what is said/read based on what you know.
I suppose we would see some interaction with AI in that sense, but it'll take place over the course of learn cycles and when AI starts ingesting its own ideas it typically goes wrong somewhere down the line.
I think mathematicians aren't bemoaning their lost sunk costs. They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_. Their voyages of discovery, which give life meaning, may never leave dry dock again.
Until we can demonstrate AI consciousness, “seeing the raw truth” will be a human activity. Even now, verifying and understanding these AI proofs is a massive endeavor. Coming up with an intuitive (to humans) distillation of the finding remains an open challenging demanding expertise.
We literally had a case where OpenAI may have stolen the dialectic from a mathematician using its product and then given it to a proprietary model burning tens of millions of dollars of tokens [1].
[1] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_priority...
1: https://en.wikipedia.org/wiki/The_Last_First:_Winter_K2
> The reaction from the math community has been a mix of indignation, astonishment, and sorrow.
Really? Not an iota of positivity or optimism? I'm not sure I can believe it.
> You are a helpless onlooker. Before you a channel through which humans have accessed the ineffable and sacred for thousands of years is being sealed for eternity.
https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...
I have to wonder if this is the equivalent of teleporting back in time and finding Marco Polo or any of those early explorers who traveled for the love of the game (and fame and money), and opening up Google Maps on your phone and showing them the zoomed out world. And showing them any island or village they could name.
If you read the linked article, the author goes into more detail about how doing mathematics also has been an act of communication with past and present human mathematicians. This is very much true when math and science are done by millions of human researchers, but not so when it is done by massive swarms of agents at a couple labs.
I am sure science and math will benefit in the sense of solving more problems than ever before. But you are not really understanding the agony of the humans caught in the change.
Not "never again", it would be extremely difficult but science and math are also built on random, trial and error, and intuitions that could not arise from AI.
Computer can iterate without frustration on a completely random garbage. Once in a while it stumbles upon a gem. Even if it's one in 10000, that's still hundreds of good ideas in a day (provided enough GPUs).
"Wiped clean" is the wrong phrasing, and 5 years is a short timeframe given the ability of some sectors of the economy to resist change. But yes, hundreds of millions of white collar professionals will need to rethink their careers and their business models within the foreseeable future.
Just today there was an HN article about how shady the dental industry is. In the future, you will go to a special dental imaging facility where a modestly-compensated technician images your whole mouth and feeds the results into an AI system, and when you get home you can look at the assessment and chat with the AI about it. Then you can potentially go visit a dentist, oral surgeon, etc, if you actually need work. This system will produce far better dental health outcomes at far lower cost: the diagnoses will be more accurate, and there will be no bias towards additional, unnecessary procedures.
Right up until the sellers of dental supplies find a way to...
Indirectly influence model training to increase the frequency with which models recommend dental work and/or lower the bar for what they determine to be "necessary"...
or...
Directly influence model recommendations by paying model providers (who will be happy to take that money).
The point being that models (and particularly the humans that control them) are presumably just as corruptible as the humans they are replacing.
Finding that new knowledge may be exponentially more difficult, but it will be much more valuable.
How do you know this?
Neurons and synapses change, especially synapses (the connections between neurons). Some neurons have a few connections to other neurons. Others have hundreds of thousands of connections to other neurons. These grow and change. "Estimates are between 100 trillion and 1,000 trillion neural connections" Is it finite? Depends on your definition of finite. If anything countable is finite, then it is finite but the number may be practically uncountable. Is it fixed? No.
Humans have cognitive limits. Humans hold a specific slice of all knowledge at a time and necessarily limits what correlations can be leveraged. This is similar to "context windows" in modern AI. Human minds are wildly variable in efficiency. AI is has constant inefficiency, largely controlled by the speed of light, physical RAM, and processing power, with superior (no cost) "thought" context switching. The AI also has superior accuracy without the need for "concentration" because the AI is processing on a Turing machine with the limited operations that it's superior at in terms of time and energy - eg find an element in a list of 1 million elements.
- random,
- from the environment,
- from other AIs.
That increases the space considerably.
In particular, note that your argument also applies to humans: A human, being finite, can only produce finitely many things. But you add other humans, the environment, and pure chance to the mix, and it'll be pretty infinite for all practical purposes.
Maybe that is the limits of my imagination, but it seems unwise to take humans completely out of the loop. Having mathematicians around that can understand what it is doing so that we can utilize that knowledge in a way that we can have some confidence in seems important.
It sounds increasingly dumb to bring this up given how advanced models have become, but it remains true - they are still fundamentally token prediction algorithms. And that imposes hard constraints on their potential. These constraints are relatively academic in our current world because there's just so absurdly much information and no human can hold more than a negligible amount in his mind at once. So they'll certainly be able to connect many 'obvious' dots that we don't see simply for a lack of carrying capacity, but they're not going to discover concepts that do not clearly follow from the comprehensive knowledge of an era.
https://birdsnfrogs.github.io/2026/09/12/Felix_qui_potuit_re...
At the same time, I think it's pretty amazing how this is the fundamental question of AI's trajectory, yet people on both sides seem so sure of their viewpoint with little actual evidence or data to back it up.
That is, it's possible that LLM-based approaches will be forever limited to this "convex hull" of current training data, and thus humans will always have a role to play (and will retain primacy when it comes to overall intelligence), because it appears that humans are not limited to this convex hull based on previous discoveries (e.g. I think basically every scientist would argue Einstein's general relativity was outside the convex hull that existed at that time).
Yet, if LLM-based approaches are eventually able to surpass humans on this "novel discovery" axis, then we as a species are basically done for when it comes to intellectual primacy - and then it becomes a very strange and scary world. And many AI researchers at the top companies clearly believe current approaches will scale and eventually (pretty soon I'll add) lead us to RSI.
I have no idea which side is right, and I'll admit I really hope LLMs eventually hit a wall. But again, I just am surprised that many seem to be putting forth their beliefs, but I would love to know if there is any good evidence one way or the other (or better yet, a more concrete and verifiable definition of the "convex hull" so that researchers could provide some falsifiable examples).
Why?
The economist John Keynes predicted almost 100 years ago that technological advances would lead to a 15 hour workweek. If AI now makes you 5x as productive, then why aren't you working 1 day a week for the same pay? Why didn't Keynes' vision come true.
governments implemented (and still implement) keynesian economics, and it has turned out to be a very bad idea and he was very very wrong.
It's not fun to think of a future where knowledge workers become irrelevant in society and we're back to just physical work and managerial elites.
Just like in past history.
Yes, it sucks, for software engineers, those in the past, and those in the future. As long as you and others fall for the straw man perhaps you and others will get more and more tricked and hurt, misplacing your aggression and hatred on each other rather than those receiving most of the extracted value.
Yes in some cases, but the reduced costs also allow lower prices which benefits all consumers of whatever product is being produced. At least for those products where there is a competitive market.
I don't personally grieve for the likes of Strogatz or Tao, it seems likely both of them will be fine however this pans out. But many more mathematicians have been toiling away in precarity and obscurity and without tenure for years and years. And of course many mathematicians went into private sector roles as software engineers, actuaries, analysts, ML engineers and similar, and have been displaced there, too.
And highly visible blog posts written by famous mathematicians with large audiences and closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, nor that software engineers aren't also writing about their plight or ending up on the front page as well.
Neither sits right with me. Can't we just all collectively acknowledge that we have to grapple with this new piece of technology that either is already or at least seems to be going to be hurtful to a lot of individuals?
Instead of looking at the in comparison limited group of people currently pushing this technology and asking ourselves whether we should be on board with their doing, we look to one another and are happy that someone else is now suffering just the same as we are. What a sad state of affairs.
AI is going to suck hard for lots of professions, software engineers and mathematicians included. I think it's much more productive for folks in these professions to show solidarity with each other given the way AI will disrupt their livelihoods, rather than showing disdain based on who you think may have it slightly better.
Are phones an "automation of existing jobs"? Maybe couriers (??), but most of what people use them for goes far beyond that.
What about the software used to drive trains or autopilot planes? We still have conductors and pilots, but now the outcomes are safer on average and more efficient.
Or something like Google Maps -- all that replaced was the paper booklet people used to keep in their cars, it's not like we used to employ 'navigators' to go out on a road trip.
Or something like Intuit QuickBooks: there's still an accountant in the loop, and if anything more accountants today than there were a few decades ago.
Certainly some software is essentially automatory in nature. But to characterize 'nearly all' as being such just betrays a lack of awareness for the rest of the field.
> That one is somehow deserving of sympathy and that of mathematicians is not
He didn't say that mathematicians aren't deserving, he was griping that people said this about SWEs. Do you think mathematicians are deserving but SWEs aren't?
The bean counters laying off software engineers ought to take notes from the frontier labs' own hiring practices. They're still hiring lots of humans for business and engineering roles even when they would be better positioned than anyone to automate away those jobs with their world-class models (https://openai.com/careers/search/).
Generalization fallacy, survivorship bias, etc.
Say you have a friend who likes making music (not professionally - just a hobby).
If an invention came out tomorrow that took the joy completely out of making music, would you respond with "It's hard for me to feel sorry about you."
Just because things suck for you doesn't mean it can't suck for others (in different ways).
In my undergrad math department, only 2-3 faculty members out of a dozen bothered with grants.
This is said by a lot of CEOs trying to make layoffs look good, but I haven’t seen anything that suggests that it’s true.
> Yet I see far more of these blogs about the plight of mathematicians, not enough about the plight of software engineers.
Really?!? We’ve been living through 3 years of blog posts, LinkedIn hot takes, and podcasts talking about the plight of software engineers in the era of AI. There isn’t a week that goes by without an HN post about it.
I can feel empathy for the practitioners in a field that may have been profoundly changed, the same way I can feel empathy toward software engineers who are struggling with the changes in their own field.
In the end, we’re all trying to figure out where this leads. And how this will affect our lives and our work.
It's not like the options are write software or starve. Billions of people find jobs and can feed their families without writing software.
I also don't often meet junior software engineers who actually have families to feed. Most juniors work in the industry for a few years before deciding to get married and have kids.
At that point they won't be software engineers
A very small fraction of people who get math degrees actually continue to do math in their careers. They usually have to get other jobs in order to survive (actuary, teacher, finance, etc.). Academic math funding was already drying up for last few years, and now AI will probably cause more cuts. Not to mention that academic math positions have never paid particularly well.
I feel bad for anyone who can't find a job, but the software industry as a whole has been the cushiest industry for decades, and the current turbulence seems more temporary (and driven by corporate greed) than a systematic destruction of the trade.
Unfortunately this often means moving away from family. What are you going to say to the kid whose parents toiled to get him through college on the expectation that he would be able to take care of them? "Sorry Mom, I have to move to North Dakota to work on the oilfields"?
This nails it, however IMHO its almost all bruised egos and feeling of wasted time. I don't know the ratio of A:B but I also don't know anyone that is in the latter category of feeling doom and mourning that their craft is about to regress.
I guess I'm not astonished that people are so bad to each other in general, but more that in the case of genAI it's so prevalent in places that seemed more elevated previously.
Part of me wonders if this is actually a form of self-defense. The misery of others can provoke sympathy or the opposite: Angry pushback to protect oneself from dwelling on their misery.
For some reason I'm stuck in a real depressing, doomer algorithm / homepage on Twitter. But everyone on my homepage seems to have a take on the HNer comments along the lines of "see, this is why you don't make your job into your identity".
But that's such an antihuman response. The only reason you can put decades into a field to grind and build expertise is because you have an identity-level interest in a subject.
It's also not a good thing if the optimal way to live going forward is to have no passion for anything lest it changes so that we won't feel bad. I don't think that's possible unless you remove the human part of our brains or make life so horrible that we're happy just to survive another day.
Source? There has not been a statistically-significant increase in middle-aged male suicide rates between 2023 and 2024 confirmed data [1]. (2025 breakouts aren’t out yet, but top-line data show decreases.)
[1] https://www.cdc.gov/nchs/products/databriefs/db572.htm
In 2025 in the UK men age 45–64 had a suicide rate of about 24 per 100,000, which is the highest it has been in the past half century, and is higher than other age categories. In the mid 2000s, the rate was like 17 per 100,000.
From your link, in the USA the overall rate for men of the same age is about 30 per 100,000, but varies dramatically between states.
And I can’t imagine feeling the same about any group of people. It’s been odd, to me. I’m just trying to support myself and the people in my life, and now there’s a looming fear that I can’t do that anymore… business owners are drooling over that, and other sectors are laughing.
Hard times, I guess.
They are showing as much care for mathematicians as they received themselves, which is not much.
when mathematicians complaining about losing the part of the job that they love, people think "if you love doing it, why is anybody paying you? you're describing a hobby."
If AI got significantly better at performing surgery overnight and doctors started crying about how they were going to be replaced, what do you think the public response would be? Non-doctors want the best possible care; they aren’t interested in protecting an industry. The same will be said for pilots and lawyers, too.
People dislike self-serving whingeing, end of story, but that’s doubly true when it comes out of a profession (theoretical mathematics) that is mostly practically useless.
https://en.wikipedia.org/wiki/Life,_Liberty_and_the_pursuit_...
To me it begs the question: in a theoretical world where we don't have human mathematicians anymore, what is the point of these proofs if there's no human who actually understands it?
If the point of a lot of this math is only to expand the boundaries of human knowledge, it all seems kind of pointless.
Proofs are somewhat like legos. A bigger toolbox of them can only help in solving other, possibly practical, problems.
As far as the utility of a human being involved -- In a non-theoretical world where we don't have feline mathematicians, what is the point of these proofs if there is no cat which actually understands it? The cats can benefit from, for example, advances to optimziation algorithms that reduce costs for cat food delivery, of course.
My intuition is that it'll be at 'smart undergrad' levels today, though as the cryptographers say, attacks always get better.
None of them have pointed to any of the solutions and said "this is real innovation" - because it's all been mining existing ideas and applying them elsewhere.
Imagine you spend years working on a solution to one of these problems. Only to realize after you publish that more than half your answer already existed in another branch of mathematics and you spent a bunch of time re-inventing it.
Yes the first big solve by OAI was "stolen" and that is tragic, and pretty bad. But it looks like this new batch, the one people are crying about, has none of that stink.
Nothing has changed in math. Math is not solved nor has the human been kicked out of the loop. Same with programming.
*I said nothing really changed because LLMs becoming superhuman at deduction was priced in with o3 and neither the peer review, training nor publishing methods will get a revamp beyond what could already be done with SQLite and a website.
But from my perspective proofs have never been the most interesting part of maths. What really interests me is the intuition that leads to new applications, and to new questions. Newton, for example, gets more credit for calculus than Leibniz because he's the one who demonstrated how darned useful it is. Erdos is arguably more famous for asking interesting questions than for answering them.
I still don't see LLMs seriously contributing to that facet of mathematics any time soon. Every so often I ask one to suggest a good binomial confidence interval for a particular application, and it still tends to just suggest one of the subpar options that everyone learns in a first year stats course.
The recent barf-out done by LLM companies is useful if what are you are interested in is an unreadable mess and someone giving you the final answer. You might be able to extract some new "aha!" moments out of it, but we will have to wait and see what happens once people go through it. I would hypothesize the LLM output will be good at hinting at some non-obvious relationships and patterns, but I doubt it will yield anything of substance in its own right.
Historically, proving difficult theorems required mathematicians to sometimes invent new fields, new ways of looking at problems, the discovery of which itself yielded incalculable contributions to both mathematics and other fields. It is this that is the greater contribution of and to mathematics.
Mathematicians working at universities are paid to teach, to engage in the politics and business of government contracting, and only in very rare circumstances to play prestige games on famous problems.
It is unlikely that Congress will decide to slash budget for NSF's MPS directorate on account of AI getting good at proving theorems. That's just not how Congress works.
It is also unlikely that LLMs will be able to do, in the near future, do the sort of applied mathematics that happens in the context of occasional NIH or DoD funding that flows into Mathematics departments, for a variety of complex sociological reasons I'm happy to expound upon.
And it's unlikely Engineering degree programs will stop requiring calculus sequences, since being able to do the computation was has not been the actual point of teaching calc since he late 20th century (if ever).
So, the good news is that I doubt any of this will have much of an effect on the job market for Mathematicians who want to prove theorems for a living. The bad news, of course, is that the job market for Mathematicians who want to prove theorems for a living was already pretty horrendous.
I really need to just stay off social media for like a month and keep talking IRL. Longer, if I know what's good for me.
And this is only the beginning.
You are probably right that some companies are factoring AI into headcount but I'd imagine that the interest rate and energy crisis are bigger concerns
It was long predicted that the sign that AI is here in macroeconomics is rising interest rates, because investors can get MUCH higher rates of return doing AI investments than borrowing governments, why would I lend money to Greece when I can lend it to Anthropic?
LLMs haven’t done much in the way of informing me or others I know regarding “who and how many”.
I’ve worked in tech for 20+ years and I’ve never seen it like this. Sure there are job openings, but sooo many applicants it seems.
(This is Sweden, YMMV.)
But many people perceive this very differently, see link below. And perception is reality after all.
https://news.ycombinator.com/item?id=50093180
Is it like Chess and Go? There are still plenty of people playing for fun, but the machines are better at it than we are.
Jokes aside, its like working for a company, individually you can lift mountains and someone else will take credit. When you use LLMs for a single bit, all credit goes to LLMs lol
Now the thread has been cleaned up and a pro-defeatism comment is the top comment and the submission is on the front page again (I'm not alleging moderator intervention, user mechanisms are sufficient).
Sure, there are people who overstate things. But that isn't an excuse to keep your head in the sand.
Anticipating that something will happen is not the same as evidence that it's happened.
A lot of us knew what was coming. Profs I speak to these days say it's the same old except they need to pick a different kind of problem for grad students
https://en.wikipedia.org/wiki/IBM_and_World_War_II
the above, a "sorting" machine is the primary usage of hyperscalers currently, they're just trying to find new uses to boot for extra money/legitimation.
the browser industry the phone industry the CAs JavaScript
it's all paid for by those wanting to sort humanity into whatever bucket the can fear monger the peasantry into for aweek or however long it takes the classification system to sort out.
gentrification works, but we chose forcible displacement now we have to live with the forever consequences.
would you give guns and bombs to the displaced native americans who taste blood over their beads and trinkets?
we've been inside the event horizon of the singularity for years, the tax bill will only get worse unless we recognize it for the tick that it is.
Yes, outsiders (investors, journalists) are given a false impression while insiders (software engineers) are supposed to give up. Double win for the agitprop machine.
How will it pan out, no one really knows. The leading frontier labs are continuing to hire aggressively. But who knows for how long or for long or near-term goals.
There were mistakes that could easily be seen with a diagram rendering three big results wrong, exposition is terrible, no coherent underlying theory generated from solving so many problems, as Thomas Bloom pointed out even duplicate proofs of the same statement in a single paper.
It clicked for me, "this is slop but slop can be superhuman and useful!". Similar to programming where it can generate as many criticisms of your codebase but you have to weed them out.
I was taking to my friend in OA who was really surprised that the proof of L(F_2) = L(F_3) could be done in the 1980s. We just didn't have a superhuman deducer back then.
Special relativity which Einstein got a Nobel for is now taught in high-school.
"Of course if you move a magnet in a piece of copper you will generate a current, it's extremely obvious it should be so"
> I think I have been underrating the pace of model improvements. In March 2025 I made a bet with Tamay Besiroglu, cofounder of RL environment company Mechanize, that AI tools would not be able to autonomously produce papers I judge to be at a level comparable to that of the best few papers published in 2025, at comparable cost to human experts, by 2030. I gave him 3:1 odds at the time; I now expect to lose this bet.
https://www.daniellitt.com/blog/2026/2/20/mathematics-in-the...
“I’ve slowly updated my timelines over the past year…”
and
“I think I have been underrating the pace of model improvements. … I was not correctly calibrated as to the capabilities of existing models, let alone near-future models.”
Sometimes you think you’ve been accused of everything you could be accused of. Wonders never cease!
> The "moderation by less", as well as the guidelines, are both farcical in nature. They've given way to ruination of an otherwise decent tech discussion forum
The guidelines have been constant (with minor updates) for most of the two decades HN has existed. Dan’s a moderator for 14 years and I’ve been one for several. Both of us have been active participants almost since the beginning. When did the ruination begin?
Your comment seems a generic vent, largely unrelated to the parent comment but if you have any actionable suggestions you’re welcome to email us.
There it is, the "off topic" play. Well done, Tom.
If you'd put anywhere near the amount of attention in moderating the site for over all quality that you put into my "largely unrelated" comment, this entire comment thread would not exist. Think it over.
That neither of you are at the very least bothering to steer the greater discourse towards some higher ground is a lack of balance that I am highlighting.
To remark my comment as off topic in the context of the thread opener is to dismiss what I am saying using a very lazy tactic that I've seen used countless times before. No, it is not off topic. It is very much on topic and relevant.
And if you have a problem with my comment, feel free to email me.
Never been invited, but I've also never felt smart enough for that community. I'm glad I can read it though!
> Today, the mathematicians are weeping, because the machine smashed their tower first. But tomorrow, it may be the physicists, the economists, the illustrators, or the writers who weep over their fallen blocks.
Isn't it extraordinary that these models still can't write well? I mean, they write passably well, but they all have a highly characteristic style that you can spot from a mile away. These language models can crack the toughest open problems in math, but they haven't yet cracked human-like writing, especially long-form writing, without exposing themselves. This is very very odd, IMO.
Their math is as just as good as their rambling writing and their Ghiblified poster art. Most people don't seem to realize that.
"Some subset of this collection is valid, therefore they all are" is not a valid inference. It's more like what we call "proof by intimidation".
I think it is. Why is it that the only people in any field I'm aware of that think the AI output in their field is high quality are either the ones that are carefully crafting the output themselves or were producing/consuming slop themselves before all this started? (Outsiders pretty uniformly like the output, which is why I drew the parallel to Gell-Mann amnesia.)
I read this passage and thought, "has Derek even talked to software developers"?
That feels to me like the first discipline to go through this, where their daily activities are massively changed by GenAI.
Maybe visual artists/photographers were impacted before then?
Anyone have a timeline of this stuff?
What is true, is that chat models (and by extension agents) have a very characteristic style after their LLM went through post-training. But the pre-trained language model doesn't have that style.
So if you want to write well with an LLM, you could and it is a well understood problem. It is more a matter of that not being of much interest, as it competes with having the model be good for chat interfaces.
How to have a well-aligned, RL'ed, safe or thinking model, which also writes well in long-form, is a bit an open problem. Though presumably agents could do it when they have access to a pretrained model.
That is why it's so disturbing. After several paragraphs, you realize there's nothing human there even when the actual information is present. People that do create AI piece are OK with it because they already have the context, but for the reader, it's always the uncanny valley.
[1]: https://www.youtube.com/watch?v=omuJpoV-Ko4
So how can they possibly solve problems that humans have worked for decades or centuries on without being able to solve? How did they find something new? Is it that they were able to deduce the solution by examining all current data sets? Or simply brute force it until the produced solution passed all necessary tests?
Lots of mathematics entails recognizing that a tool/techniques that works in one area can be adapted to a completely different problem. For a human to do this requires having a robust mental model of the technique and the problem itself, and probably having just the "right" mental model to see how they fit together. And we are talking about extremely hard/sophisticated techniques and extremely hard/sophisticated problems, so the ability to deeply appreciate either can require years of study. And on top of that, even if the mathematician has sufficient understanding to develop the intuition that the technique might work, they will need profound fortitude, skill, and patience to see the solution through.
Unlike human mathematicians, who will develop a deep understanding of only a relative handful of techniques and problems in their lifetime, LLMs have ALL written techniques, problems, solutions, etc stored in their internal representations. So when they ably match a problem to a technique, we can imagine the operation as a supercharged autocomplete, or even an extremely proficient search engine. Their stroke of genius is really a consequence of capacity, moreso than cleverness.
Yes, both of these + an infinite token/compute budget and SOTA+ models. It's not like some hobbyist out in the woods with a GPU running Qwen 27B can do this.
Newton was possibly just taking a dig at his small-statured rival, Hooke. Newton was brilliant, but a shit.
I understand there are many types of math and the mathematicians don't all want to sit around and do KV cache and gradient descent things, but surely a percentage are as interested as I am and can contribute to this new emerging field? I would wager that Xl+1=Bl Xl+Cl ℱl (Al Xl) makes much more sense in their mind than mine.
The dramatic solution can never be: 'we should all just want to do it this way because it felt better to me'. That never seems to work, from what I've seen. So there is a lot of public discourse, arguing, to determine if 'doing things the old way' is perhaps more better. And if not, maybe we just shed a tear and move on (to look for a better fit).
The implication here is that you wasted your time learning that math, and the fact you learned that will not actually help you contribute to anything.
Now maybe you are closer to understanding the feelings expressed in the article?
Does relating to someone pay my bills? People will use the informational tools to improve their social status and resource accumulation, there is no doubt about this.
The vanity, fame, self-improvement, it's very selfish as everyone does.
Now the fame coming from proving things like Riemann Hypothesis is taken away. Self-improvement? relying on AIs make you stupid. It will be lost. Vanity? Who else don't know how to use AIs? It cannot fill your void.
Now also the most important thing is the communication.
There will be less communications amongst mathematicians at least in person. On paper? maybe but mostly via AIs.
It's the same reason you see 'no AI' repo labels: only by forcing some standard on the community can the 'old way of collaborating' continue to exist.
There will for sure be new ways of collaborating, and walled off gardens like you suggest, where communication stops and everyone just shares some final product.
But, in some cases the product must be understood (or demonstrated) before value can be derived, and so collaboration will still exist.
Desire, and the 'shape' of collaboration has changed greatly though. Why collaboration has changed, is a completely separate issue related to economy and how each of us spends our time.
> There will for sure be new ways of collaborating
I am not smart enough to know what the new ways will be but there should be one to adapt to changes.
And then once it's solved by AI: do you want to churn through the proof to understand it? What if it takes you 5 years to churn through the proof, and it turns out someone made a mistake with AI (I have no idea what would be realistic amounts of time, but the idea is still worth considering).
The issue is very complex, and you will always be hungry.
If I were a mathematician working on the Riemann Hypothesis, I'd probably be rather pissed off right now but continuing my work, i.e. the same as I am as a software developer.
Social creatures that share a common space, with finite time that nobody wants to waste.
Every analogy works "only" at a certain abstraction level. No need to disregard oversimplification. This spawned the debates so all good.
Maybe the answer is to look into how Big Science works? There's still plenty of work to be done figuring out what to do with the outputs from these new math-observing instruments.
Either these mathematicians thought it would never come for their jobs, because all of these other jobs were simpler or they've been living under a rock.
Either way, I don't feel for them any more than I do for all of humanity.
I am also sad, but my sadness is, in a way, priced in.
I just had a chance to flinch first.
It's easy to have that thought, and eventually you'll be correct. One thing about technology is that it only improves. It's always building on top of what already exists. The only uncertainty is the exact timing, not the ultimate outcome.
The people struggling right now - they were told. 30 years ago. They really should have come to terms with it by now.
But these are also the people who refused to believe it, for whatever reason. Their heads were in the sand. So I do feel bad for them... but... this is somewhat self inflicted.
Also, it's impossible to really know how you're going to react to something until it happens to you. When ChatGPT came out, I already thought "in the long run they're going to automate almost everything humans love to do". Despite having 4 years to brood about it, I did not really know what it would feel like until it happened to me directly.
That's how the singularity works. It's going to keep getting quicker, incomprehensibly so.
Even before LLMs it was feeling like the design of society wasn't really for people any longer, instead it's more and more designed for corporations and their convenience. In the US at least. Same with how the internet has stopped most people with socializing the same way they did in the past.
Now we have a new layer that will be optimized for these digital entities. We see it in writing all over the internet. There will be tons of other places they show up and doing things that don't make sense to us.
But it can continue to inconceivable levels before it gets to that point.
Certain of predictions? I think that's an unreasonable ask.
And I'm comfortable with my prediction. Rather than argue about it - let's wait a year and see what happens, and then we can discuss it.
Oh, good point! I misread your comment. Sorry for that!
> Rather than argue about it - let's wait a year and see what happens, and then we can discuss it.
Deal!
What are the relationships between many languages that become apparent, including code as a language that were not obvious before llms? Translation is fairly solved. The study of how and why languages, not at all.
Seeing AI being lauded for solving problems like this makes me feel... uncomfortable.
We are feeding all works of the giants that we have all stood on into a huge vat, in the hope to generate something meaningful.
If we can't understand the output, internalize it, or build from the time and experience that a human would have gained from solving the same problem, it feels like a dead end.
When all the problems have been "solved" by AI, what's next? If humans no longer struggle to solve the problems that the previous generation have left behind, how do we progress?
Considering I currently live in Ithaca and have a friend doing a Math PhD, so I've heard from him some of the discussions in the department. I think the biggest shock for people is that individuals spent significant portions of their time on some of the problems that OpenAI supposedly solved (I say supposedly because all of the proofs have yet to be independently vetted). I understand that it's a shock, but I'm confident that in time it will be no more of a blip than it was for NLP.
[1]: https://xxcancel.com/mayhewsw/status/1636476184098643968
[2]: https://xxcancel.com/andriy_mulyar/status/163613925780582809...
If it was about understanding interesting proofs that some AI came up with, and extracting their essence, I don't think the situation would be so bad.
I see the much larger problem in the now existing career prospects of non-tenured researchers in mathematics. Everybody know how precarious the career prospects in academia and how precarious often the non-tenured positions in academia already are. With the new AI breakthroughs in math, these have in my opinion even worsened a lot.
UPDATE: For a related point, see also pixl97's post: https://news.ycombinator.com/item?id=50104145
I never appreciated hard math much because my brain just can't get there. I thought so much of math was much ado about nothing, but now I see the art in math...not in the inscrutable formulas, but in the creation of AI.
Well done, mathematicians. You can now rest from your labors.
Questions: (1) Do you still weep for what has transpired? (2) Do you continue to do what you used to do (with optional AI assistance)?
For me: (1) no, (2) yes and I think the same would be true for most people. So I can't help but believe that most of the anguish about AI is far more about a direct economic hit to people's livelihoods than it is about the impact to their respective fields. Which is more than reasonable. But then why not frame the conversation that way instead of beating around the bush?
heck, we have the resources to that now but we don't do it.
This is probably the first time in history deep thinking is being replaced by a machine, but the overall arguments are the same in all cases. Graphical artists saw it first, then programmers, now mathematicians.
No, there is not stopping the wave. No, society won't probably be able to support the same number of mathematicians as before. But yes, there will still exist mathematicians after the wave break, just probably completely different than the old way.
And yes, some people will still try to do artisanal mathematics and say it's better, it probably is, if the artisanal mathematician in question is doing deep creative and out of the distribution work.
Letting mathemeticians use these tools to reach the same conclusions would have been far less destructive, and potentially, even exciting. Shame on OpenAI.
Well, you accidentally described a top mathematician before age of 41.
These guys know because they looked at it. Denying it is useless. But maybe some of these guys can figure something new using it and asking it to look for it.
So I wonder if mathematics will go through that too? A period of chaos and doubt, but finding new and more effective ways of working.
How much do they pay you? Does OpenAI have bulk subscriptions to your Substack?
I hate programming these days - back in the day, the cubicle-hell nature of "popular" frameworks was at least offset by being able to think through and solve interesting problems.
These days most of us are stuck in the "endless-review" loop with LLMs. You can't afford to not use it given the inflated expectations. As with all of modernity, productivity doesn't yield leisure - it just proportionally increases your workload.
Hardly surprising that the other side of the Curry-Howard correspondence is now getting hit with this. Math was one of those depts. where slow/deep-thinking was possible (CS was already insane 10 years back - now it's just absurd) - now even this fortress will be broken. Tragic.
I think they might find comfort in knowing it's not just mathematicians - this is coming for all of us. Computers putting us out of work has been coming for a long long time.... and now it's here.
> If intelligence becomes less uniquely human, we may come to value more highly what remains uniquely human: our capacity to relate and to care for one another.
Lol. How does the author think relations between people work? (At least those outside the family). Relationships require something that fills them with meaning - a reason why you would want to have that relationship in the first place. Without meaning, no relationship.
I recommended reading this other post that was on HN earlier today: https://thetheorygirlie.substack.com/p/ai-was-great-until-it...
It describes in pretty grim words what happens to collaboration once you have nothing anymore to collaborate on.
> Mathematicians may still teach proofs, argue over what they mean, translate alien logic into human insight, and pass that understanding to students.
This would people to have time to understand and dissect those proofs - it doesn't work if there is a new breakthrough proof every week.
Are there any mathematicians who are genuinely excited about this tremendous leap forward in mathematical knowledge? Where are those articles?
The same goes for math.
Let's find some things that bring value other than just the price of a stock.
At worst its time is past, but even that is unlikely.
I note that that these conjectures being solved by AI are named after people, minds knowledgeable and and brilliant enough to come up with the question in the first place and recognize its value. What we have in these AI math solving systems is the equivalent of the chess and go software that can beat humans: something that can adhere to a set of rigid rules to reach a win state once given a starting point. But, as Pablo Picasso said, “What good are computers? They can only give you answers.” These AIs are a magnificent achievement and will change mathematics and coding but can they ask earthshaking questions? Could an AI identify conjectures that mathematicians recognize as a worthy question that will lead to new insights? Where is HAL9000's theorem or the M5 Multitronic's conjecture? Maybe they can someday but I don't see any immediate prospects for it.
Please spare us the "AI will surely keep getting better forever" (unlikely and don't call me Shirley), "moving the goalposts" (I myself haven't set any), etc. non-arguments.
This is what it seems like so far for software. The speed limit has changed. It’s interesting to explore what that means. Extending the analogy, long ago you could be a race car driver part time; that would be pretty laughable for an F1 driver. It’s a very specialized skill and the optimal athlete is quite different for driving a car than for running, for example. That feels like what I’m seeing in software.
The most effective folks are much faster and better with these tools than average. It’s a different skill set.
I think that formal verification makes Math much closer to code than many other fields. But I’m eager to see the first mathematicians that are dramatically more proficient with the new tools than average.
Honestly, there are much bigger fish to fry, like how will everyone pay their bills, and how will we prevent catastrophic AI.
This seems like a good summary of the article, and I think the answer here is obvious.
So what?
News flash folks: we do not have the knowledge to survive on our own. If a solar flare deletes the electric grid, the first thing that happens is 8 billion people die in the next year.
We survive on abstractions others have built, and we have a global dependency web.
AI abstracting knowledge is neither new or dangerous; if it is dangerous, this certainly isnt the argument to prove it.
I'll be honest. The response to mathematicians, even this one, makes me concerned about the lack of empathy and honestly just theory of mind of many people in tech. It's not a mystery why people are upset that their field, for many the singular passion to which they've devoted their entire lives, is being annihilated so that a massive company can boost its IPO valuation. It's not "bruised ego" ffs.
Isn’t that in itself the new frontier for human understanding?
I would have thought that mathematicians would have found alien forms of maths to be astonishingly compelling, must learn, must know, must understand.
Instead there seems to be a sort of shoulder shrugging lament “we don’t understand it”.
I would barely be able to sleep with excitement at the potential for where this could lead. Like finding an ancient tomb full of answers to our deepest questions along with the promise of more.
How deep does maths go? Is it “solved” or have we just been given tools to delve ever deeper?
Where is their curiosity - don’t the want to find the bottom?
Where or what do solving these math problems lead to?
Is there some suggestion that they lead to deeper understanding about something else? Do they solve physics problems?
What’s the benefit? What’s the point?
It is mostly impossible to figure out what we find when we solve these problems. But occasionally they'll lead to real world efficiency in algorithms we use and it changes the world.
It's not clear from your comment: Are you talking about math professors?
If so, what money? They make a living, but it's not that great. I just checked the salary of two associate professors at my university: $80-85K.
And keep in mind they often start their careers quite late. Often multiple postdocs after PhD. Starting a tenure track position in your mid 30's is not common.
> I'm more shocked that there are so many brilliant people who are so results-oriented and don't even have a concept of value outside of that. I'm kind of disgusted by the tears actually
The whole point of the article is that the person crying is because he loves the process and is worried the human connection will be gone.
Still disgusted?
Ever heard of sour grapes?
This is the lie you tell yourself to handle the situation.
Why would one who loves someone, ever love another?
...under capitalism...
Sure we will...