YHK - yet another hacker news clone

The whole point of the letter was that if we adopt this gradient search strategy the humanity might get stuck in a local maximum forever.

Tokens want to be paid for

Yes, and here towards the bottom the author gets to the reason he didn’t sign with the other medalists:

> I felt that there was nothing to be gained from criticizing AI companies for generating too many solutions too quickly.

> Under the circumstances, I think the best we can do is recognise the changes that are coming and try to work out the least unsatisfactory way of dealing with them.

Basically let’s make it a short-term problem and deal with it. Groups of people can deal with short term emergencies. Don’t turn it into a structural issue.

And in my view what’s the alternative in the letter exactly? The tools exist. Is there going to be drama every time somebody decides to use them?

I don't understand this logic.

Ok, so unresolved math problems are often something people discover while trying to solve a different math problem.

However, math problems are really there to solve a real world problem. We have unlimited real world problems no matter how smart AI gets. Therefore, we will always have unresolved math problems.

Yeah. It's interesting how many commenters here can (regretfully) no longer justify humanity's existence. Trolling or not, that's becoming familiar.

Prediction: In a hundred years, some humans will survive. Hopefully 8 billion or more. But among the survivors, actively anti-human attitudes and behavior will become unpopular [1].

[1] I mean really very, very unpopular.

Why? Why should a government invest money into this? Here you see human understanding as an ends, while historically in society it has been applied as a means to ends like social power, resource accumulation, etc.

Now these means are generated. If the proof yields some improvement somewhere, it can be used and there needs to be no human in the loop

I agree with your argument of expected societal shift, but it's important to keep in mind that this is largely a developed country issue. It'll be a while before child-staffed cobalt mines or whatever is superseded. A significant amount of poverty could be alleviated through improved resource distribution and policy, without really needing improved productivity/increased resource production.

"And maybe I could have tried to gain that respect in a different way, such as thinking very hard about an area of mathematics until I was able to demonstrate to others just how well I understood it. But I’m not sure how motivating that would have been for me. I very much hope that there is a pool of young people for whom it will be a powerful motivation, because I think the survival of a human mathematical tradition may well depend on it. [...] Thus, the primary risk, as I see it, is that a lot of people who would have done a PhD in mathematics and gone on to become custodians of the mathematical tradition will no longer wish to do so. Those of us who have PhD students, including me, need to try as hard as we can to come up with imaginative ways for them to use their time productively (in consultation with the students themselves, obviously)."

When I read this I'm trmpted to read "imaginary" instead of imaginative - that is: in the sense lacanian psychoanalysis uses the term imaginary in contrast to symbolic - the latter of which would mean that it's having consequences within the symbolic social order. From their own, quite selfhonest evaluation the author assumes that without those they would most likely not have persued the mathematical profession. Which also relates to:

"A related risk is that the perception among policy-makers will be that mathematicians are no longer needed and that funding will become much harder to come by: we urgently need to come up with good ways of explaining the value of having a large pool of human mathematical experts, even if it is no longer part of their role to find new proofs of theorems."

Note that there isn't any attempt to establish a possible horizon as to how that coule happen.

It seems to me that the end of the article has a strong tendency to a somewhat stoic attitude of one might phrase as: it is going to happen anyways - the systemic context in which these corporations act makes it inevitable ("However much we might regret that, there is no chance that the impact of such models on mathematics will persuade AI companies to stop their release, though perhaps concerns about safety will lead to some delay and give us a bit more time to work out how to adapt. Assuming that they are released, there will be a flood of new results, whether we like it or not, and it will no longer be the AI companies producing them, though perhaps the pattern will continue that the AI companies will have access to more powerful models and so will obtain more than their fair share of headline results.") - which makes me kind of wonder if it is not some sort of cognitive dissonance within the authors view of the situation to not also think 'it's not going to happen' in regard to their stated requirements (students that don't need to be motivated by a desire to be symbolically valuated as explorers of the mathematical frontier, and policy makers that acknowledge the value of funding the social "production" of human mathematical experts /enable such a community through funding).

So basically they see the same problems as the authors of the letter (which they also state in their letter - their should be no room for a misrepresentation of that fact: "I felt that I could not sign the letter, despite agreeing with much of what it said. Instead, it seemed better to do what I did with the Leiden Declaration and set out my own position in a blog post. But it should be understood that by doing that I am not setting myself up as a member of some opposing camp: indeed one of my worries at the moment is that the mathematical community might become bitterly divided, something I would very much like to avoid.")

So what stays is mostly their disagreement on that conceptual understanding is more important than the solving of problems for all mathematicians. - which kind of makes the problemfield of ai in mathematics somehow more urgent, as far as I have thought it through. And I'm not really convinced that the displacement of the problem into some sort of pedagogy (and it should be appreciated that the author implicate themselves in the responsibility to establish it) instead of finding solutions in the realm of policy and regulation. Seems realistic though, that they see that as an effort unlikely to succeed in a meaningful way.

Can someone argue against that reading? Am I missing something? My conclusion as such is that not only are they not opposing the authors of the fields medalist letter, but also that their evaluation of the situation is much more dire without them giving in to resignation.

> what do people do when their labour is not required any longer

I don't think this is the main issue (if at all) discussed here or in the field medalist letter. If anything, the majority of pure mathematics graduates are absorbed from the industry and a lot of exodus happens along the different scales of academia to there (though industry is also dealing with this issue but that's not what's concerned here). The issue discussed is what mathematics itself will be, which is much deeper. AI finding proofs to open problems does not solve at all the question of how to produce new problems, and there is no indication imo that there is way to go with that with AI.

Pure mathematics is not like applied sciences, as it is only tangentially influenced by external applications. Deciding which problems to tackle is a social process and a matter of taste/aesthetics, and is built largely through the exact friction that is more and more removed with AI. This is what makes it unclear how one can find problems without this friction, and none of these posts/letters have an answer really. Each one seems to describe just different standpoints than concrete, practical ideas.

   Coasean Ceiling: organizational size limit where the internal friction of managing a firm consumes all of its energy, leaving nothing left for actual production

Did you even read the open letter? Mathematicians are annoyed because the proof is only meaningful if people understand it and came to it. I mean I’m basically just summarising it now but it’s annoying you didn’t read it or can’t comprehend its nuance.

> that AI can do everything economically necessary

Who gets to define this? Those with power are famously bad at understanding long-term implications, how things work, and what matters - especially when it comes to funding things like research.

The Machine Stops by E. M. Forester is basically this world.

>that AI can do everything economically necessary

This is practically impossible, because the "economically necessary" things to do are never fixed but instead are in a state of constant fluctuation.

Furthermore, a chain is only strong as it's weakest link. AI alone is not sufficient to do all the "economically necessary" things. We would need vast numbers of highly advanced robots to do the rest of the work going on in the world (which is >> than the work currently done by AI). So if we restrict the definition of "economically necessary" to mean the subset of all possible tasks that we currently need to do, then we are sorely lacking in the required infrastructure. We may never get there either.

In the meantime, the labor shock knowledge workers experience could lead to large unemployment. Even those that find work doing non-knowledge work, the decrease in pay and benefits may be substantial.

I think these realities are worth understanding to help ground these pie in the sky ideas about what the future will be like. Not to be mean, but your idea of the future is basically a fantasy.

I somewhat disagree. we still need humans to provide direction and context and expanded the concept of... well everything. But we will certainly need less of them. AI will afford the ability to more quickly disseminate state-of-the-art. As soon as a breakthrough is discovered, you no longer need to read 300 whitepapers to hopefully stumble upon it, AI will identify relevancy quicker.

AI didnt break through stavier-nokes until a human set the initial direction. That's not going to change.

> Everything therefore becomes a hobby or a game. People do things because they enjoy them for their own sake, or because they are endeavours used as vehicles to socialise and enjoy others’ company, or because a shared social belief exists and is cultivated such that doing such and such a thing confers social status.

There is actually a big leap in logic you’re doing here that it seems you are naive to. The world looks the way it does today because human societies, businesses and individuals are fundamentally in competition with one another for scarce resources, and having more resources leads to more capacity to survive, so there is always an incentive to acquire more. If you can no longer compete, you can and will be exploited. You don’t have to look very hard, far or back in time to realize that this is what society looks like. If everyone is incapable of competing except those who can afford to run a datacenter, that will not end up in socialist utopia.

>Everything therefore becomes a hobby or a game.

Already predicted. How much Whuffie you got?

https://www.gutenberg.org/ebooks/8086

Just to add that the Dedekind cut example seems to stand beyond any RL policy used in chess or go, AlphaZero or AlphaProof. In the classical RL there is an state-action space. If the solution requires jumping to a totally difference action space (that must be created) the local policy stalls. Dedekind cut is an example of a out-of-distribution state-space generation.

A cynical could say that AI could not interpolate the Dedekind cut but it could extrapolate to create a lot of money but just using an imaginary extra point.

The ironic part is that generating a joke like this requires jumping across three distant fields: real analysis, machine learning limits, and VC market cynicism. For an AI to discover that specific overlap through statistical search, the combinatorial space is absurdly huge. Yet a human brain connects them in a fraction of a second. This tiny joke is a micro-proof of the macro-argument: human conceptual leaps routinely bypass exponential search spaces.

> I can not fathom a LLM could conceive from scratch concepts like the real numbers by Dedekind.

What stops you? I can fathom it alright.

I am always suspicious of these arguments like "a machine won't do thing x which humans can". These always basically pre-suppose that humans aren't machines. If that's what you're arguing for, say it outright.

Your position is compatible with the letter.

[I have not read Gower's article. It's only that your response is prompting me to share what i've been thinking recently]

>the stepping stones required for human growth are disappearing.

Actually only in an institutional sense, imho. Maybe I'm exaggerating, but reddit.com/r/math* or even mathstackexchange will be so back with users analyzing and distilling proofs with AI. Maybe in 5 years (when lean attains 10% popularity of rust, and/or gpt7 level models cost ~USD5 on average, per month, inflation adjusted or not) this types of submissions will make those sites as fun/educational as mathoverflow [has always been for me]. One dreams that by that time openAI and Anthropic will have taken down your ethno-cultural "compatriot" Masayoshi with them.. (I prefer his brother whom he did not regret giving a physical beating to. Only purely on principle) so that they can't acquire these sites

Such forums can then replace math grad school, if the profs/alpoges who drop by get into the habit of constructive criticism (as they do on mathSE already). It's already starting, I see personally interesting 1 AI-aided submissions every 1.5-3 weeks starting 2 months ago

It would be like rust discussions on HN for you I bet.

This seems unlikely when s/math/physics/, or s/Reddit/HN/ because HN hates AI-aided posts so ideologically (sorry mods, I don't mean you guys). MO is also not as welcoming to outsiders/lay, congruent to academia (only online) PhysicsSE/overflow had become dumb and arrogant last decade

HN, even pg seem anti-intellectual in effect tbh whenever they sneer at AI _writing_ (again sorry mods, you will figure this out soon I believe, do you or do you not want HN to end up as a reservation for meatbrains), though I mostly am on their coder side with regards to this fields medallist letter

> proving to inventing new theories and finding new conjectures with the help of AI

This is exactly the activity Tao and others worry will be hollowed out by instant "true/false" responses to novel questions.

Well, we can reduce every human activity to 0 value and take it from there: if there’s no value in understanding there’s no place for humans in the process, we can just go back to worshipping stones and let the AIs burn tokens deluding themselves chasing their hallucinations

Depends. Do you think human mathematicians will be entirely useless for any kind of input into the act of doing mathematics? If not then we'd be advised, imo, to keep funding which is inherently just a training pipeline.

The person who might have made a mathematics breakthrough that results in some miraculous medical or other discovery will likely have decided it's not economically prudent to pursue a career (pure math academia) that the tech sages, in their all encompassing wisdom (exclusively over the next 1 to 2 financial quarters), have deemed worthless, and that instead he or she should just respond to that pesky Big Four recruiter who keeps dangling a cushy six figure internship.

Real mathematicians will continue their research, whether they receive funding or not.

Math professor here.

Different academic disciplines are very different, and most don't engage in the same kind of black-and-white problem solving that mathematicians do, where you either have solved a problem or you haven't.

But all insist that you engage in some sort of outwardly visible production in your field: books, articles, conference presentations, public lectures, exhibitions, performances, something.

We haven't yet figured out what that should be, but I presume that everyone would agree that this should continue. As one possible model, check out this blog post of Terry Tao's, where he gives his own perspective on the recently proved Jacobian conjecture.

https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the...

When computers can solve the underlying actual problem, this sort of work seems likely to rise in value, and be something which a greater number of mathematicians engage in.

I don't think that the main issue either discussed by Gowers or the others who have signed the letter is simply that mathematicians should be paid "for merely understanding things". The main issue is outsourcing, laziness, and learned helplessness.

Outsourcing understanding, teaching, and proving maths to LLMs is just as dumb as outsourcing food production, manufacturing, or entertainment to a foreign power. It's not that we haven't already done most of those things in the pursuit of temporary profit optimization, but each of them has obviously bad impacts on both the individuals in society who perform those tasks, and on risks to everyone when that outsourcing fails for any reason.

As described, using LLMs is like navigating with GPS. It's fine when you're using it to optimize a path due to traffic conditions, but it can be deadly if you're flying a plane and suddenly don't have it, or any training to deal with that situation. That is where we're headed. I don't really have a take on signing the letter in particular, because as mentioned it seems a bit pointless. At the same time it also seems a bit pointless to spend $10s of millions proving a conjecture a few months sooner than a group of mathematicians already were. I don't imagine they were going to make millions doing it. The definition of material waste.

Perhaps it serves a temporary marketing win for OpenAI, or a medium term improvement in LLM performance on some productive output, but longer term it certainly risks ceding whole swaths of human endeavor to a tool we may not always have. Just as falling demand for farmers, or skilled machinists, or writers, or artists is not an immediate crisis, in the long term there is no one left to transfer the knowledge to the next generation, if something goes wrong.

This is meant to be a funny, stylized comment. If you can't bother to read to the end, just ask a chatbot to explain it to you.

Most people do not use any math after school in their lives. All of their real problems are political. Kids spend significant time in school being told that math teaches them "problem solving" and then leave school and discover, since math solves no political problems, math doesn't solve problems at all. In other places around the world, where by many measures people are much more numerate than Americans, people are actually poorer and live under more authoritarian governments. In industry, math has been reduced to a shibboleth for a neurodivergent lack of ethics, which is why mathematics PhDs go into banking, and never politics - and we imagine lawyers to lack ethics, and nearly all of our best presidents and congressmen were lawyers. Even the academic environment that supports mathematicians and the STEM community generally - all of that concentrated neurodivergence and lack of people skills has led to less political power, which means less funding and less new students, which has been much more threatening to mathematics than automated proofs.

I love math, but my honest POV is, the value of theoretical math cannot get much lower. The crisis is insurmountable. The community made its deal with the devil (Jim Simons) long ago, it thought it was a STEM discipline like bio and it's really a philanthropic humanities discipline like opera. I don't think Greg Brockman's wife can shed enough tears to convince him to donate enough money to save math departments and throttle Astra access.

Read “the feel of power” by Asimov. Written 1958. Very prescient.