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Comment by piker | Hacker News Reader

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians.

Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on the other hand it seems like an exciting time to go even deeper for in various specialties of math by deciding where to focus these powerful tools. For every conjecture defeated some seven or eight new ideas open up. Our path through that combination will be set by creative and curious human mathematicians.

[edit: deleted a distracting comparison to Chess]

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The old way of establishing career credibility is being destroyed, for better or worse. Accomplishments that used to be career-defining are hard to distinguish from AI, and correlate more with access to compute. Think about Bill Gates's math paper he wrote in college. That kind of thing is gone now as a path to credibility. There's still competitions and grades, but the diversity of paths is going away. Maybe new ones will open up. This is a competitive advantage for old people who have credible pre-2025 accomplishments they can point to.

If accomplishments can't be distinguished between talented people and untalented people with compute, is there really a point in trying? I suppose one can hope that talented people given compute will be more effective than untalented people with compute, but I despair that that may not be true for much longer.

Knowledgable people can confirm what the AI produces is correct. I could make ChatGPT produce a result on an open question and I would have zero way to verify its actual correctness.

Which is less interesting work. And you probably need to do the hard grunt work by hand first to develop the skills and intuition to be able to verify an AI-generated result. So you can’t outsource everything to AI without loss of skill.

I mean there were problems with the "old way" as well. Not clear if this change is net positive or negative in my opinion.

I find this whole way of looking at things weird. Did maths exist just to entertain and employ mathematicians? Surely maths is, like, useful? Not immediately, not predictably, but in the long run? In which case, whether mathematicians feel bad about it is mostly irrelevant - it's like complaining about the railway because it may put coaching inns out of business.

Absolutely not the same! People need jobs to bring in income. I don't believe those who profit off of this will share it with the world. The power is all concentrated in the few hands that decide whether or not the rest get any semblance of income in the long run. I don't believe UBS until it happens.

It sounds like you think no technological advances will make the world richer in the long run. I politely suggest that the past century of economic growth shows problems with this argument. I also think that, while jobs are important for prosperity, the jobs of mathematicians are a minuscule fraction of a percent of the total.

So, you're arguing that just because mathematicians are a minuscule, it doesn't matter for prosperity? Because, if so, that is an insane take honestly.

Really? "The benefit to all of humanity from advances in mathematics outweighs the lost jobs of research mathematicians". That's an insane take?

It is the very humanity that is absent in all of this. The power is still in the hands of a very few. I feel you're dismissing this with a grandeur vision of AI developement.

Given that we were nowhere near this state even two years ago, I think it’s a question of velocity more so than just distance.

The chess analogy is awful. If you simply want to know the answer to a chess problem, give it to the engine. Chess only lives on because it's a competition between humans to test their skill (just like bicycles, cars, trains didn't eliminate foot races) ... the computer is largely factored out, but not entirely -- people train with the computer, use it to check whether they played correctly, ... and they cheat. A lot. Thus there are more and more sophisticated mechanisms to detect and prevent cheating.

If you translate that to math, then all you get is math competitions, not math as a career. Of course the translation isn't nearly exact ... there's a lot more room for professional mathematicians because the math space is far more vast than the chess space and can't generally be cranked out mechanically (we have proof).

P.S. The response is nonsense ... I explained exactly why it's awful (others have too) and the response doesn't in any way refute the explanation ... rather it offers up a ridiculous strawman.

I’ve deleted it but no it’s not awful anymore than saying “we survived WWII, we can survive this.” The point was that change happens but humans find a way forward.

Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess, maybe a few hundred more can sustain a meager lifestyle with coaching gigs. I shudder to imagine what will happen to the tens of thousands of non-Fields medalist caliber mathematicians if math goes the way of chess. Perhaps Terence Tao and a few other famous mathematicians will be funded by Peter Thiel to report on how well humanity can keep up with the machines? How do you expect any mathematician to be optimistic about this comparison.

>Only ~30 top professionals actually make enough money to have a full career playing chess, maybe a few hundred more can sustain a meager lifestyle with coaching gigs.

Was this different before chess computers were invented?

Fully agreed. As someone who both loves chess and works on chess engines... these comparisons to chess needs to stop.

The distinction is mathematician vs mathematics. Mathematics is going to reach new heights beyond the wildest dreams of contemporary mathematicians. But perhaps without the participation of many paid mathematicians.

Just sounds dystopian,

Another noteworthy difference is that Stockfish is also gpl.

If there was any real money in it Stockfish would not be the best chess engine.

Thats not the point, if there were a better proprietary engine stockfish would still be there as a baseline. Anyone can access an engine as good as stockfish to practice against. Are any open models touting mathematical breakthroughs?

There is money in this, so of course the closed models are far ahead. The open models will likely catch up a bit at some point, just as Stockfish caught up to AlphaZero. That being said, there are already a couple. It seems Deepseek has a claimed proof to the "Ziegler's Cross-Polytope Conjecture" [0], but I can't speak to the significance of the result.

[0] https://arxiv.org/abs/2606.31640

Do mathematicians have the right to say "no AI PRs please, the volume is too much" just like how some open source maintainers do it? I guess they feel a loss of control, there is no way to turn the hose off.

Thinking of this a little bit with the perspective of every new proof as a burden, dumped for review by actual mathematicians.

i think i agree, we are going to have /more/ math and now need /more/ mathematicians (we are seeing https://vibemathed.com/)

these LLMs are great are generating arguments but they don't ask questions, we will need mathematicians to shepherd them into more discoveries

i really want to see open weight models crack some breakthroughs

> LLMs don't ask questions

Why don't they? That sounds like an important problem to solve.

Along with the fact that they can't learn anything (after the training stops).

As in chess and go and also coding for the past ~year there are two groups of people: the disappointed and the enthusiastic. The disappointed are sad that they lost their advantage and that the craft they honed for years or decades has rapidly lost its value; the enthusiastic are excited about the future and what computers can bring to their domain and how it will evolve. I’m a bit of both if it comes to programming, more enthusiastic than disappointed, but also more than a bit terrified about the pace of it all. I imagine that’s how Kasparov felt back then, that’s how Lee Sedol felt and now that’s how Terry Tao feels.

The most disappointed folks will simply drop out, but the enthusiastic ones will keep going and with luck make up for the ones who decided to quit. Chess and go certainly went this way.

A fundamental difference being that no one was actually paid to find good moves in chess and go like they are to solve math problems and write code. You're comparing the digital camera and the automobile.

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