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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#791

Post by tmhn2 »

Shaptse wrote: post #418
reasonableklout wrote: post #187

Earlier quoted context omitted.

Tao’s key point is that the way people are using AI today does disrupt that. Because people and companies are valuing the results over understanding. So we’re getting slop results rushed out that are automatically verified. Moreover in the past, discussion and idea sharing would happen naturally to overcome the friction of the process. But now when OpenAI is stuck on a particular part of NS for example, they can just…

I won’t speak for Tao. But it is not “people” who have valued the result over understanding. “People” are a bit impressed that the machines are as good or better than the priests who have been praying at the inscrutable altar of pure mathematics. But it is mathematicians—I am speaking as a mathematician—who have adopted a culture of valuing results over exposition and transparency. The field has been rife with extrem…

I don't think that's entirely fair.

I think it's OK that there are some materials designed for a specialist audience, and some materials designed for a wider audience. Technical density serves a real purpose in the former (I'd like to just say "stack" without including an explanation 10 times longer than the rest of my paper about what a stack is and why we are talking about them), and some people expend a lot of effort on the latter (think lectures, lecture notes, textbooks, seminars, blogs, etc--totally appropriate to dig into the motivations here).

It's just the fact that it's a really vertical field, not some cultural failing, that results in pretty opaque stuff sometimes.

Re: A misalignment of AI in mathematics

#792

Post by demibabs »

nmeagent wrote: post #773
pvab3 wrote: post #714

Earlier quoted context omitted.

that is incredibly depressing

Yep. Perhaps humanity would be better off if we instituted and enforced the notion of "Thou shalt not make a machine in the likeness of a human mind." It's worth thinking about; just because we can build AI systems doesn't mean we should.

I think it would be depressing in its own way if this technology just ended up being regulated out of existence.

Re: A misalignment of AI in mathematics

#793

Post by lll-o-lll »

noslenwerdna wrote: post #760
lll-o-lll wrote: post #528

Earlier quoted context omitted.

> But there's still play. There's still curiosity. And there's still the drive to understand something for yourself. Yes, but think about what that implies if those are the only motivations left. Gone are the professions. Gone are the ambitious. There is plenty of space for people to work on intellectual pleasure pursuits (as there is with art and music), but the death of all intellectual based industries is still so…

Good? Those people were in the field for the wrong reasons. No reason to mourn them leaving

> in the field for the wrong reasons

It’s an interesting view-point. What are the “right reasons” to pursue an intellectual discipline? To selflessly further the total sum of knowledge?

> No reason to mourn them leaving

What field? Who’s leaving?

The conclusion has to be that human involvement in these pursuits is facing existential crisis. “Teach me, oh Oracle, the mysteries of the Universe”. “For a fee”.

Both the glory and joy of discovery now belongs to the machines (the owners of those machines). Perhaps that’s fine and well, but I read Anathem and feel the strong yearning to be the intellectual monk. And yes, to fight and debate and think; and obtain my place in history. The history of man.

Re: A misalignment of AI in mathematics

#794

Post by tmhn2 »

jrflo wrote: post #160
tmhn2 wrote: post #148

Earlier quoted context omitted.

At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.

I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.

Hopefully that's true. Instead of bypassing the community maybe it stimulates the community. I think it does disrupt things a bit, but I'm optimistic at the moment!

Re: A misalignment of AI in mathematics

#795

Post by reasonableklout »

redox99 wrote: post #754
ekidd wrote: post #720

Earlier quoted context omitted.

> 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…

Of course you're not going to get rich with the kind of software that LLMs can one shot these days. But that kind of software like to-do lists or basic CRUD have been saturated for over a decade, way before LLMs. People overestimate how much you can one shot, yeah a good prompt can get you 90% there but that 10% remaining often takes months of extra work. Software has always progressed this way, lots of devs back the…

But what does the human researcher do in this future?

If they are not needed to understand the result, then what's their role? Asking the right questions? But how will they know what questions to ask if they don't have a deep understanding of the domain earned by sweating the details themselves?

And how long will they be needed to ask the right questions, how long until AI can do that too?

> Software has always progressed this way

These platforms took on the order of a decade to mature, during which people had plenty of time to learn what's next. With LLMs we went from one-shotting functions in 2025 to entire projects just over a year later.

What do you think you will be working on in a decade?

Re: A misalignment of AI in mathematics

#796

Post by seizethecheese »

Animats wrote: post #739

This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem. So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody be…

That’s a charitable way to interpret what they’re trying to do in this letter. I would say they are trying to maintain the status quo to protect their status system.

Re: A misalignment of AI in mathematics

#797

Post by esafak »

JoshTriplett wrote: post #785
robotpepi wrote: post #447

Earlier quoted context omitted.

It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they…

> What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. There is no bound on the amibitions of AI. AI is set to replace anything done by people , and there won't be any room left for people. There isn't any task done by humans that AI won't be better at. This is not a tenable outcome. We should never have built machines with agency , rather than optimizat…

> We should never have built machines with agency...

We haven't quite crossed that bridge, but we do appear to be standing on it.

Re: A misalignment of AI in mathematics

#798

Post by visarga »

hn_throwaway_99 wrote: post #755
pks016 wrote: post #665

I never expected this many people (on this thread) arguing semantics and what not. I know that not everyone has morality and ethics, but I didn't realize it was this bad. I'm afraid of the ripple effect of the agenda pushed by AI companies will have. In future and even now, they say AI has significantly progressed math and scientific research in general. There is truth to this, but the narrative has done more damage…

I commented something similar on a bunch of other posts. The thing that scares me about a lot of the AI community in general is that their utopia is basically more frightening to me than their doom scenarios. They present this "incredible abundance" as the ultimate human endgame, but I agree, when we all end up like the humans in Wall-E, what's the purpose of it all? And then to get retorts of "it's just just rich te…

Probably the opposite of Wall-E utopia, AI will keep us busy. For one - we are becoming harder to differentiate, competence is hidden deep and surface signals don't carry anymore. Niches and specializations feel threatened by imitation. This means everyone is frantically searching for their own corner, musical chairs. This holds for both people and companies.

Second - every time we learned to transmit better from past experience we saw massive expansion in culture and economy, not shrinking. Writing, printing, computers, internet and AI are just gradations on the scale of transmission from past experience. Everything stands on this transmitted experience.

Re: A misalignment of AI in mathematics

#799

Post by sashank_1509 »

hn_throwaway_99 wrote: post #755
pks016 wrote: post #665

I never expected this many people (on this thread) arguing semantics and what not. I know that not everyone has morality and ethics, but I didn't realize it was this bad. I'm afraid of the ripple effect of the agenda pushed by AI companies will have. In future and even now, they say AI has significantly progressed math and scientific research in general. There is truth to this, but the narrative has done more damage…

I commented something similar on a bunch of other posts. The thing that scares me about a lot of the AI community in general is that their utopia is basically more frightening to me than their doom scenarios. They present this "incredible abundance" as the ultimate human endgame, but I agree, when we all end up like the humans in Wall-E, what's the purpose of it all? And then to get retorts of "it's just just rich te…

100% agree, their utopia sounds far worse than their “humans will go extinct” which still sounds implausible to me. I would rather die than live in a WallE society, and I hate that they’re getting trillions trying to force us there
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