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A misalignment of AI in mathematics

mathandai.org

871–877 of 877 posts

Re: A misalignment of AI in mathematics

#871

Earlier quoted context omitted.

> Would he say no? And that’s the issue the article is trying to explain.

My thought experiment was trying to extract the issue from the zeitgeist around AI, so not really

There’s answer for you there if you’re willing to see it, whether you agree with it or not. So there’s that.

Re: A misalignment of AI in mathematics

#872

Earlier quoted context omitted.

Of course there's a meaningful analogy. The poster wants to make Tao sound unreasonable and against "progress" while ignoring the very real concerns Tao has. It's what fanatics do when they want to enforce their view on the world, they have to attack anyone with a reasonable viewpoint because they can't imagine a world where someone tells them they don't like what they're doing.

I do not want to make him sound unreasonable. He is a brilliant man. But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development, so I wanted to highlight some historical similarities, imperfect as they can only be. As for the rest of your comment, I hope you have a great day.

Tao is quite the opposite of what you describe. He's had an ongoing dialogue intellectually with the challenges created by ai for mathematicians for some time (years) now and his viewpoint is quite balanced. He is not alarmist but rather correctly addresses the real problems ai advances create for mathematicians traditional way of working.

Re: A misalignment of AI in mathematics

#874
Perhaps all these fields medalists are just worried that AI mitigates their competitive advantages over a mediocre professional mathematician like me. Their main advantages are a kind of penetrating clear thinking that not all of us have and an ability to work obsessively without tiring or losing focus while retaining with a clear head a great number of facts - AI removed these advantages - as Tao has written it shifts the focus to asking good questions and using available tools to address them - and the traditional elite may not be better than I am at that part - they were just better at the solving the problems part ...

Re: A misalignment of AI in mathematics

#875

Earlier quoted context omitted.

Not if it's lean-verified.

"Lean-verified" is not some magical incantation that makes a supposed proof irrefutable. Even disregarding potential bugs in the kernel as others have said. Say that AI gives you a Lean proof and says it proves Theorem X . It could just as easily give you the same proof but claim that it proves (not X ). How would you know the difference? Nothing can really be considered proven unless a human expert can read the Lean…

The thing is that there is a standard format where the definition of the theorem is split from the proof, and verifying that the definition matches the mathematical concept is a LOT less work then reading the proof, especially if you're willing to assume that definitions in Mathlib are correct.

Re: A misalignment of AI in mathematics

#876
post #853

I was watching a talk by Terence Tao a couple of days ago, and I noticed a shift in his attitude towards AI. His enthusiasm seemed to have waned; he was becoming more dismissive of it, and I was wondering why. “A Severe Misalignment of AI in Mathematics,” with a list of important mathematicians. This post makes it clear that, to put it bluntly, they’re psychologically butt-hurt. They talk about misalignment, but this…

I think their point is more on the fact that just proving something is only half the work. Intermediate results and proofs are often also of immense value. Right now the output is sloppy proofs and LEAN code. This is useful, but a large part of the effort still lies ahead. And if you are a mathematician you'd rather be working on hard problems than fixing slop.

The main ideas for solving Navier Stoking have been exposed, it's not something buried in slop. And if it were, you could have AI write up the big ideas that actually mattered in these said slop proofs.

I think they're more afraid of the current status quo. Distilling, writing textbooks, teaching, ...

And currently, I could be wrong but, I see them being blind to the possibilities it brings. AI could very well be distilling maths, spreading it, and nurturing the ecosystem way better than the few elite mathematicians ever could.

Re: A misalignment of AI in mathematics

#877
post #720

Earlier quoted context omitted.

> Many graduate students (I know) are having a crisis if any of their research worth it? If AI can (or will) do everything, what's the point of doing experiments and all? This will eventually deter a whole generation of curious minded students from research. Those who think it's me or the machine will fail. Those who realize how much you can accelerate your research with the help of AI will succeed.

> Those who think it's me or the machine will fail. > Those who realize how much you can accelerate your research with the help of AI will succeed. This is only true up until a point. If I treat a mid-sized model (say, Qwen3.8 Flash Next) like a pair programmer, then yes, it accelerates my work. But I can already see the next stage with Fable: If I give it a couple of paragraphs of spec and $50, then I can just leave…

> But I can already see the next stage with Fable: If I give it a couple of paragraphs of spec and $50, then I can just leave the room and go wash the dishes. I learn nothing, I participate in nothing, and I bring nothing to the process. I am no longer succeeding at all. Fable's succeeding without me.

The people that uses Adobe Photoshop also did not learn anything about brushes. We are just going to operate at a much higher level of abstractions. You have to think about the question, "If I just prompted this solution, why didn't they?". This question can even be asked now, why do I even bother paying someone to do my taxes? To write my webpage? To host my website? To manage my network?

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