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.
I found it amusing the one time that I've seen dang recently steer a thread and actively participate was in a complete one-off on Sino cultural standards (and the perception thereof). To me it almost seemed like he was issuing a threat because, amusingly, I thought, Xi's minions are watching.
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 (or news aggregator, or YC propaganda machine or whatever you want to call it).
If you want actual discussion around things, lobsters, awful or even 4chan are better than HN.
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"
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 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”.
> 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.
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
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.”
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 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.
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.
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 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.
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.
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.
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.
Visible blog posts written by famous mathematicians closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, or that software engineers aren't writing about it or ending up on the front page
> 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/).
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.
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.
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.
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.
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 :/)
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.
> 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 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.
> 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.
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.
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.
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.
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.
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.
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.
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?"
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.
> 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.
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 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.
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?
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.
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.
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.
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 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.
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.
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 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.
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?
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.
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.
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.
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.
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.
> "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.
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?
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.
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
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
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.
I found it amusing the one time that I've seen dang recently steer a thread and actively participate was in a complete one-off on Sino cultural standards (and the perception thereof). To me it almost seemed like he was issuing a threat because, amusingly, I thought, Xi's minions are watching.
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 (or news aggregator, or YC propaganda machine or whatever you want to call it).
If you want actual discussion around things, lobsters, awful or even 4chan are better than HN.
> lobsters
Never been invited, but I've also never felt smart enough for that community. I'm glad I can read it though!
TBH I come to HN to understand US silicon valley mindset. difficult to get a more distilled version of that in other places.
Am, this is 80% Indians with most of them from India.
not sure what is the source for this. I'm just a latino posting from Ireland tho.
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"
I think the https://news.ycombinator.com/item?id=50043026 Terence Tao post was much more hopeful and along the lines you're suggesting.
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
Re depression: Seems like it is not just HN... You say nothing changed. Maybe that's even true.
But many people perceive this very differently, see link below. And perception is reality after all.
https://news.ycombinator.com/item?id=50093180
Yes I take issue with all the anti-human propaganda coming out. I think that there will be a future we're essentially replaced but it's not now
> Math is not solved nor has the human been kicked out of the loop. Same with programming.
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.
Go apply for some jobs. You’ll quickly come to the realization that something has changed.
And this is only the beginning.
Yes, interest rates are higher than ever and consumer sentiment makes business wary
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 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”.
The fear is the sales pitch. AI has some uses but nowhere near enough to justify the price tag, so we need something more to sell it.
Fear and FOMO mainly.
> 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.
I'm sorry, but "nothing has changed in math" is a truly ridiculous statement.
Sure, there are people who overstate things. But that isn't an excuse to keep your head in the sand.
o3 already had this priced in amongst many mathematicians I talked to at conferences
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.
You have an earned an upvote from Long Term Capital Management!
Doesn't seem to be the case here: https://www.daniellitt.com/blog/2026/2/20/mathematics-in-the...
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
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).
They are overreacting imo. A lot of mathematicians stuck their head in the sand with o3 but this was the logical outcome; superhuman deduction
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
Disagree, there are in fact documented cases.
> 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.”
Fair enough. But after the distinct distances result if you did not price it in, that's on you haha
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 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.
tbf naming something "deontic" is not helpful
The irony of complaining about an academic jargon word in a thread about mathematicians.
I don't think that's true. Why is it that I see more people using "shaped" and "load bearing"?
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.
I've written some about this here, if you're interested: https://elliotmilco.substack.com/p/deontic-scorekeeping-comm...
You don't consider recursive self-improvement a step towards 'updating a perspective'?
I think you are also suggesting Mathematics and Language are the same thing.
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.
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 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.
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.
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.
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.
Visible blog posts written by famous mathematicians closely aligned with the news and hype cycles getting frontpaged on HN doesn't mean that mathematicians are disproportionately whiney, or that software engineers aren't writing about it or ending up on the front page
> 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/).
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.
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.
Software engineers still can feed their families. The notion that software engineers can not feed families is not consistent with reality.
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.
How do you know this?
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.
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.
Well humans do that and you expect them to continue to do that - why can't AI models do it as well?
Perhaps they could some day. I'm basing my understanding on the current day capabilities. Once that changes I will update what I think.
The set of data will increase as it outputs
this is assuming that humans can be original in ways llms won't be, which I doubt will hold true
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 :/)
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.
> 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.
https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...
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.
Even if this was overly long and mostly things I've seen before, I'm just very thankful that it wasn't yet another claude piece.
There was an interesting passage in the article:
> 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.
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.
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.
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.
> Today, the mathematicians are weeping, because the machine smashed their tower first.
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.
No, tech writers have it much worse.
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.
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.
Makes me wonder whether it's a fundamental limitation of the technology or more like missing a good set of tasks in the training pipeline
Might be that the vast majority of their training data is poor writing.
Gemini's (at least for Flash 3.6 - 3.8) writing feels quite "human" to me
Recently a Canadian immigrant won a bunch of the highest French literature prizes for his novel, which then turned out to be an LLM fabrication.
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.
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.
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?"
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.
> 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.
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?
There is no reality in which everyone gets their basic needs (food, roof, health) without a job.
heck, we have the resources to that now but we don't do it.
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 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.
[1]: https://xxcancel.com/mayhewsw/status/1636476184098643968
[2]: https://xxcancel.com/andriy_mulyar/status/163613925780582809...
I’m not sure I’m following… because as I understand it NLP is basically solved now (with transformer LLMs). No?
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?
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.
I saw it coming since reading Kurzweil in high school and it's still heavy.
I just had a chance to flinch first.
This is it.
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.
> It was really quick.
That's how the singularity works. It's going to keep getting quicker, incomprehensibly so.
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.
I like to call it the great incoherence.
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 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.
As a programmer I’ve been ‘weeping’ for a few years now.
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.
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.
What new ways of thinking are you developing?
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.
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?
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.
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.
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.
UPDATE: For a related point, see also pixl97's post: https://news.ycombinator.com/item?id=50104145
If understanding is so important and AI systems can only produce knowledge. Why can't mathematicians continue their work on better understanding?
> “They have annihilated my field of research.”
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.
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.
> "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.
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?
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 know now why you cry." - Terminator
I am curious.
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?
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
Your loved ones have replaced you with more agreeable robots. Now no one cares whether you live or die.
Still disgusted?
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
ahem
I weep because the money was bad.