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A misalignment of AI in mathematics

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Re: A misalignment of AI in mathematics

#571

Post by scotty79 »

david-gpu wrote: post #141

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…

Photography vs painting is the first thing that comes to my mind when I listen to AI critics.

Re: A misalignment of AI in mathematics

#573

Post by citizenpaul »

tmhn2 wrote: post #200

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

I've met a few Ph.D Mathematicians in Academia socially. My unfortunate experience was that they were insufferable,borderline hostile people. I tried to genuinely engage with them too. I've met one Ph.D Mathematician that left the industry whom was very enjoyable to talk to. I have a feeling that my experience was not unique and the Math world is mostly a bunch of too good for everyone on their high horse a-holes that are now being knocked down a peg. They don't like it obviously.

I'm not a fan of knocking down things that work, however I also find it hard to be against death of the gatekeeping old guard of any industry.

I think math is just gonna have to suck it up like every other industry now. Math productivity is longer out of reach of the average grad student. Like every other industry they are no longer untouchable and are gonna have to adjust to the new way of things or market forces will do what they always do which is refuse to fund ineffectiveness.

I've had to accept that tech/IT will never be the same. Just how it is. You can thrash against it all you want.

Re: A misalignment of AI in mathematics

#574

Post by paulhebert »

pred_ wrote: post #308
jrflo wrote: post #276

Earlier quoted context omitted.

That doesn't seem to be true. The OpenAI NS paper was 166 pages. Wiles-Taylor proof of Fermat's last theorem is 129 pages. The length is not unprecedented for a difficult unsolved problem. To be honest, I feel like the difficulty of reading AI proofs is due to the fact that we are on the verge of being beyond human comprehension. This is a demonstrable fact as no human has figured this out despite the problem being o…

> To be honest, I feel like the difficulty of reading AI proofs is due to the fact that we are on the verge of being beyond human comprehension. I can see where that's coming from, but I really don't think it's the case. Even with Astra, the proofs you get are just off in a way that doesn't signal superhuman comprehension. As 9question1 says, a common theme is that they dwell on insignificant steps. Another one is th…

That matches my experience with AI writing in software engineering so I’m not surprised

Re: A misalignment of AI in mathematics

#575

Post by rdevilla »

jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

[dead]

Re: A misalignment of AI in mathematics

#576

Post by david-gpu »

beepbooptheory wrote: post #488
david-gpu wrote: post #455

Earlier quoted context omitted.

I am very specifically addressing what I have read Terrence Tao say on AI and mathematics, as that is the subject of this submission. Are we on the same page?

It's not about whether the conjectures themselves are interesting or not, or whether people simply have enough time. It's that a bare proof made by a machine doesn't actually do much for us. There is not some set of problems that, once finished, will amount to some kind of final, correct system and we can call it a day and, like, utilize it. "Mathematics" is the people doing it (the "mathematical community" Tao refer…

You have expressed a few different ideas, so I will address them separately.

> It's not about whether the conjectures themselves are interesting or not, or whether people simply have enough time.

Tao seems to think otherwise, if I am reading him correctly:

I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce [0]

Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions. [1]

> It's that a bare proof made by a machine doesn't actually do much for us.

I get it, and I think the same can be said about all sorts of human endeavors.

> There is not some set of problems that, once finished, will amount to some kind of final, correct system and we can call it a day and, like, utilize it.

Sure. Although there are certainly practical applications to be found along the way. E.g. proving P=NP would be potentially very significant in the real world. I think we agree.

> "Mathematics" is the people doing it (the "mathematical community" Tao references below)

Sure. And the same can be said again about all sort of human endeavors. But I don't see how that is a reason to stop using AI in those fields, either. It doesn't subtract anything, in the same way that chess engines didn't destroy the love of the game for chess.

And just like in chess, these AIs can be used to gain a deeper understanding. Including, but not limited to, explaining to humans the proof they just came up with.

[0] https://mathstodon.xyz/@tao/117237320796901560

[1] https://terrytao.wordpress.com/2026/09/11/a-severe-misalignm...

Re: A misalignment of AI in mathematics

#577

Post by esafak »

moralestapia wrote: post #540

There's massive cope and then there's this. I've never been a fan of Tao et. al, so I'm glad he's being wiped out. He'll do fine anyway, doing conferences, etc. Also funny they deliver that on vibecoded site, lol.

Which mathematician's take on AI do you like? Do you think mathematics should no longer be an intellectual pursuit?

Re: A misalignment of AI in mathematics

#578

Post by esafak »

pixelesque wrote: post #138

Other than the fact it's mathematicians signing it, why is mathematics special in this regard: surely this generally applies to a lot of different industries and sectors of research / academia? Mathematics is being used as a benchmark because there are some high-profile awards in this area I guess, and possibly because 2/3 years ago LLMs were pretty atrocious at it so the level of improvement has been significant.

What's interesting is that these are the smartest people in the world, and AI is eating their lunch. You do the math -- pun intended.

Re: A misalignment of AI in mathematics

#579

Post by TheOtherHobbes »

mb7733 wrote: post #541
fidotron wrote: post #473

Earlier quoted context omitted.

> It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding th…

> But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. What is the purpose of that? Its like art being produced for AI to consume. What is gained from that?

It's going to be hard to compete with something that has access to all of math at once and can find connections between elements that appear unrelated to humans.

And at some point AI will start suggesting - or doing - physical experiments.

Re: A misalignment of AI in mathematics

#580

Post by subroutine »

lbrito wrote: post #385
pllbnk wrote: post #275

Earlier quoted context omitted.

I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it. Where he is critical has a lot of merit. One of the points I clearly remember him saying that having AI be able to solve many of the open problems, regardless of how important there are (there are many open problems that are not that important) greatly reduces the probl…

>I have listened quite a few interviews with Tao and I see him being very careful about criticizing AI. He very often emphasizes the usefulness of it. This is tiresome. People should be able to flat-out criticize AI without the implied need to justify themselves all the time or "be careful". Its almost like AI has a trillion-dollar agenda backing it, to the point that you have to add a careful "its really great! But…

Based on the amount of low-effort criticisms out there, clearly nobody is afraid of "big AI". Tao seems careful about his critiques of AI because low-effort off-the-cuff criticism can lead to all sorts of future problems/hypocracy.
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