Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence.

I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.

As a software engineer, I myself have only recently recovered from it. So, it’s really interesting to watch a prominent figure in their industry publicly go through “purpose death” and the related grief. It’ll be a useful case study to re-read his written meditations through this cycle.

I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet.

However, soon as the goalposts keep falling, I think like most humans he will accept, retool, and come out of this grief with renewed purpose with larger expectations of himself and mathematics. This recent post even starts towards some of that - but sadly is slightly off the mark.

“The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.”

He still thinks there is controlling AI. AI will run and trample anything that stays in front of it. He needs to one day find acceptance in letting AI run while he learns how to suggest it minor course corrections which it may or may not accept, and when it doesn’t accept quickly learn from the AI why he was right or wrong.

I maybe wrong, but I think this is the cycle of “purpose death” we will all have to contend with in our own time.

The sports comparison is wrong here because general public never paid for the specific match results. The value was always in the show, the advertising and betting around it, the health and educational value of doing sports, etc. And the sport mostly lives on what it earns, not on public funding.

Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions? Should we increase their number to handle the speedup brought by AI? Or decrease because they're being replaced? Should we pay more to those using AI to do their research, or to those explaining and exploring the AI-generated results?

Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet, you're about to have a rude awakening. We've gone from high school, to university math, to Euler problems all the way to Millennium problems in a time frame most people couldn't even do a PhD. If you start any math research now with a horizon beyond the next two years, I'd be terrified of the current rate of progress.

Regarding AI getting better than humans, in some ways it may be more like the invention of the microscope - instead of worrying about it reducing demand for people with good eyes it may open up new discoveries.

One example I'm kind of excited for is that I've long suspected that the inability to combine quantum mechanics with general relativity is because the maths gets too hard for humans. I mean Navier Stokes on singularities in fluid flow in euclidean space is hard enough. Particles may be singularities in quantum fields in relativistic space time which is probably mathematically far harder. But it would be interesting to know how that works.

For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.

This is not something that's just true on its own; it's on us as a species to make sure that it remains that way, for the sake of our dignity.

However, this position will be extremely difficult to defend, against the economic value of not caring.

That’s where the future of mathematicians lies.

This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathematics and we just have to worry on making it so LLMs can digest these proofs.

>Nevertheless, if it turns out that what OpenAI has provided is a mere answer

It has a proof attached. Saying that it "doesn't provide understanding" does not invalidate that there is a formal proof. It fundamentally is trying to expand the requirements of proof to be something more than is required.

  In mathematics, it is more natural to treat AI as an assistant rather than as a competitor. As Jeremy Avigad (2026) puts it, “We should keep in mind that AI is nothing more than technology, designed to serve our purposes. It is misguided to think of mathematicians as competing with AI; when we drive a car, we aren’t competing to see who can go faster, and when we use a phone, we aren’t competing to see who can speak louder.”

It will take probably a while before we will get a translation into something that than will actually have a positive impact.

That could be either a second proof or a streamlined version of the AI one.

> If, instead, mathematicians treat AI as a technology for advancing its long-standing and centrally human purposes, the technology may come to contribute to an accelerated flourishing and enrichment of the discipline.

For the longest time, people who conducted research (not just math) ranked and measured their peers (albeit quasi-subjectively) by 1.) their ability to solve difficult problems, 2.) the cleverness of their solutions, and 3.) the clarity of their explanations.

With the advent of these models, we're understandably worried because #1 and maybe #2 may be gone (maybe even #3).

Are researchers going to shift the ranking/measuring of their peers over to ... "so-and-so is a world-class explainer of AI proofs"?

If you go around telling people, "no no no. You don't understand. The important part of our intellectual work is now going to be <something that was never weighted highly>", well, then it feels like you're handing me a participation trophy and telling me I came in 1st place.

I have no idea how the next 5 years will shake out, but I think that's why there's a lot of anxiety at the moment.

- Disproof of the Jacobian conjecture by example

- Construction of a non-sofic group

- Existence of singularity in Navier-Stokes

Mathematical conjectures tend to be universally quantified, especially those conjectures that are used as building blocks (e.g. RH). If anything, AI models are currently performing a useful service by disproving false conjectures, a kind of mathematical weeding.

The good news from the last couple of years of coding agents is that while models have become more persistent and knowledgable, their creativity (defined as being able to escape their training distribution and synthesize completely novel ideas) is improving at a much slower rate.

AI will only become a threat to mathematics if/when it develops the capability for creative big-picture problem solving. If that happens, the impact on mathematics will be a footnote compared to the impacts on society at large, since creativity unlocks a host of new economic capabilities.

This subjective attitude turns mathematics into nothing more than number-poetry.

That would reduce mathematics to something very pathetic.

Focus instead on attribution. Yes, OpenAI took the last tiny step in the process of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! For many theorems, I can still recall which exposition was the one that "sank in" for me (often not the first one!) a decade after grad school.

In my mind, this makes current LLMs unfit to deserve any credit at all -- they cannot give credit to others, so they and their owners deserve no credit themselves. OpenAI's LLM took the last tiny step, but not any of the important ones.

Chess and Go have most definitely not been solved. In AI research when we say that a game (and usually we mean a traditional board game) has been "solved", what we mean is that we can correctly predict the outcome of any game instance from any board position provided both players play perfectly [1]. This can mean we have an algorithm that chooses the perfect play for each player in any position or that we have mapped the entire game tree for that game: every move in every game, from start to finish.

There are games that have been solved this way: tic-tac-toe; connect four; nim; othello, checkers. But not chess and Go.

Rather, what we have for chess and Go are super-human engines, i.e. computer players that no human has ever beaten in the full game. So for example a chess engine like Stockfish can always choose what move to make in order to win against a human player in any board position. However, that is still not the same as knowing how to play perfectly in any board position. Like the old joke with the two guys trying to outrun a bear, a chess engine doesn't have to play perfect chess to be super-human: it just has to play better than any human.

To the extent that chess and Go are games it could be said that winning is the whole point of AI game-playing [2]. But the article above suggests that there is no point of "winning" in maths. In AI chess it is unfortunate that the development of super-human chess engines has ended all research in using AI chess to understand the way that human players play chess (which is to say: not by alpha-beta minimax, or Monte Carlo Tree Search, or anything like that) which was the original reason that luminaries of the field such as Shannon, Minsky, McCarthy, Michie, and even Turing himself were interested in the question in the first place. The concern then for mathematics is that AI "winning" at maths will kill mathematics research and replace it with ... as McCarthy would have it "very fast fruit flies" [3].

_______________

[1] https://en.wikipedia.org/wiki/Solved_game

[2] Then again see John McCarthy's criticism of that idea written in the wake of DeepBlue vs Kasparov: https://www-formal.stanford.edu/jmc/newborn/newborn.html

[3] ibid.

I thought the reason we were encouraging people to go into STEM, and providing clever people with large salaries, was that mathematical results were of practical value to the wider human race. In which case, it’s surely very good news that AI can get those results.

Isn’t all this handwringing just the equivalent of Hackney cab drivers bemoaning the advent of the motor car? Phrased in much fancier language, of course, because the people involved are cleverer and more articulate.

25 Field Medalist and 5000+ mathematicians from leading institutions around the world endorsed an open letter expressing concerns about the impact of AI on mathematics:

https://www.mathandai.org/

More than 1,900+ mathematicians have also shown concern over the Caltech Mathathon:

https://docs.google.com/document/d/1IL0b2oG2KvvSnxn_DuXsNxuH...

James Maynard, a Fields Medalist, has also publicly expressed concerns about the implications of AI for mathematics:

https://www.youtube.com/shorts/R9VQnNv5SoI

A lot of people seem to believe that with more time and training, LLMs will surpass human intelligence. But they are fundamentally not like human intelligence. They do not reason, learn, conceptualize, think creatively or abstractly, even though we have some hacks to mimic these behaviors.

I posit that treating LLMs like GPU-powered brains that will eventually surpass us in most fields is pure science fiction if you know anything about how they work. I think they will remain astronomically powerful in some areas (pertaining to fuzzy deep search and recombining existing knowledge) and hilariously bad in others.

If you ask it to then prove its assertion, it will then certainly output the tokens that look like a plausible proof. It has to, as it is programmed too.

This "proof" might even be thousands of pages of very technical looking and professional sounding jargon.

It's not a real proof though, and as an artifact it is 100% useless to both the field of mathematics and humanity.

[1]: https://en.wikipedia.org/wiki/God_of_the_gaps

Nope, introspecting motivation is useful. There have been similar posts made about people using bots in PvP competitive online gaming: some people play to enjoy the game, and hopefully get better until they reach their skill ceiling. Others play (just)to win, and are open to buying aimbot hardware and software

It's not about moving goalposts. What you're not understanding is that, even if for you is crystal clear that AI will be 100x smarter tomorrow, those in charge cannot simply bet all on that. Right now AI cannot really replace the core sauce of mathematicians (all the "understanting" and "asking the real questions" stuff), so it'd be unwise for, say, countries to start making decisions as if AI is capable of that.

If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wow, they couldn't have pulled that off before". All the vibecoded "Show HN" projects seem to be half-broken and then abandoned before being finished.

It feels like we've gotten less ambitious, not more. Because yes, you can prototype more easily, but this means less commitment to what we create.

Mathematics is probably the same way. There's a short-term rush when you pull the lever, but there's less desire to get invested in what comes out.

Maybe this is a one-off, or maybe in a few weeks we'll figure out how to get AI to explain the proof in terms we can understand. Then math research will accelerate. But maybe it's not a one-off, and by this time next year we will have an oracle that just answers all of our questions, but in such a way that we don't even know what questions to ask anymore. Then AI will just mop up the existing and the subject will end.

Formal proof only emerged early in the 20th century, and the standard became that in theory a proof should be formalizable to answer any skepticism, but the real goal in Euclid's time and ours has been to communicate why a theorem is true to your fellow humans. There were a few theorems that are only known via computer proof, like the Four Color Theorem, but this has always been regarded as disappointing or even controversial, and the fact that there hasn't been any conceptual breakthrough has meant that we didn't learn anything other than the sheer fact that the Four Color Theorem is true. Theorems that produce understanding, on the other hand, typically produce many new ideas that lead to more theorems.

The purpose of scholarship is understanding. This is just as true for science as it is for math. If AI produces a unified theory of fundamental physics, but it's just an opaque blob, physicists will find it just as unsatisfying.

Yes I fear a lot of doom and gloom around AI is unearned and only really serves to prop up the valuation of AI companies. It's still very much unclear how much work OpenAI actually did versus just copying the nearly complete homework of someone 5 minutes earlier.

I don't think you understood the point. The point applies to all of basic science. You of course want some explanation supporting the raw answer, so you can use that insight in other contexts.

The impact of mathematics on other disciplines goes much further than specific results. Just as important, if not even more so, are the language and ways of thinking that typically come out of the process of establishing those results. Results without the accompanying conceptual understanding are about as useful as a mere oracle for math theorems.

Another point that seems to be frequently missed or mischaracterized is that mathematicians are not opposed to computational tools as a matter of principle and in fact do use them when they help their research. The current controversy is not about a hypothetical future where mathematicians have easy access to open-source, open-weight, auditable natural-language assistants to help them internalize a new result or search for counterexamples. It's primarily about the recent behavior of certain for-profit companies suddenly trying to disrupt mathematics by caricaturing it in the public eye as a game they can "solve" or "beat" for headlines and valuation.