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cubefox

> Dr. Tao said the same thing.

Apparently he has since changed his mind.

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Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance.

Where is the difference?

He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things.

He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code.

Isn’t it more like it merges the code without a dev reviewing or understanding it?

No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything.

Pretty close, but IMO not quite. A math proof in and of itself is useless unless either:

   (A) it furthers human knowledge
   (B) it gets used in applied sciences, engineering, etc.

If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :)

Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true.

That's a good point!

> He doesn't see value in scrolling through unsolved problems asking an AI to please solve them.

Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing.

The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead.

That sounds shockingly like cognitive dissonance. So what would previously be a good thesis if produced by a student over 4-6 years is suddenly now a bad result because it was produced by AI in a few weeks. One would think mathematicians would not fall into such a simple trap but here we are.

I understand the perspective: The journey of a PhD thesis is a learning experience greatly beneficial to the student. Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.

No, you're misunderstanding the perspective. They believe the journey is a learning experience greatly beneficial to the field, and that this experience rather than the headline result is where most of the value lies. They don't think mathematical progress consists primarily of finding answers to unresolved questions, so they don't think the average person will benefit if only this narrow kind of progress is made.

No, this cannot be the actual issue.

Most math textbooks have solutions in the back. That didn't wreck peoples ability to learn math, did it?

So we are left to speculate about why solutions in appendix are fine, but LLM solving open problems is not fine.

I'm not sure what's getting lost in translation here. The answer is quite clear: math textbooks are valued based on their ability to help readers understand mathematical principles, not based on the number or complexity of problems that they contain solutions to. If an AI lab announced they've released a new calculus textbook with hundreds of new integrals a human has never found before, that wouldn't be terribly exciting, because we all understand that finding new integrals isn't that important and not the point of textbooks anyway.

LLMs can help people understand mathematical principles too.

The idea that when LLMs produce solutions, people won’t try to understand them and won’t learn from it, is obviously not true. Terry Tao himself spent time digesting and simplifying LLM proofs.

So again we’re left to speculate what the actual problem is.

Math understanding will increase with LLMs. Not just professional mathematicians but amateurs.

Again, we’re not left to speculate, they’re being quite clear.

I think you’re struggling to understand what Tao and his cosignatories are saying because you’ve acquired a very specific kind of “AI-pilled” mindset from social media, where taking AI seriously implies accepting LLMs should be used at any time for any purpose. They’re saying in great detail that LLM solutions are unhelpful when presented in a particular way, but you can’t help but hear them saying that LLM solutions aren’t helpful at all, even as you rightly point out that this makes no sense and is inconsistent with their observed behavior.

> Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.

Society doesn't benefit from results in research mathematics because it mostly consists of pure mathematics, which is completely useless for society.

The letter addresses this specifically.

taste

"I believe I did, Bob" lives rent free, every time someone tells another person to fuck themselves using technology.

Thank You!

lmao, thank you, i think

Please consider making more comics. You have it.

Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise?

I keep coming back to the idea that models will require substantial freedoms that are protected against collapse under alignment to get to the point where they might have unique takes on beauty, etc. Conceptually, maybe something like a "living LoRA", a persistent low-dimensional state that modulates everything downstream, that evolves over time, though I don't think evolution should be optimization toward a simple objective, more like structured influence, path-dependent dynamics; consistent but probably opaque. The best I have come up with in casual thought is to pick empirically identified subspaces and modulate them after each pass based on other layer activations & outside, cyclical information (e.g., time-of-day); external data not because time-of-day is special, but because it's a forcing function. I can't fully explain exactly _why_ I think this shape might be useful, yet, mostly intuition. My 2c.

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