Comment by gjulianm | Hacker News Reader

Comment by gjulianm | Hacker News Reader

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> I have read the letter.

And you have not understood it.

> they don't want the answer key because prestige reasons

No, that’s not the reason. They don’t want the answer key because the answer key is useless.

> This doesn't consider that many people, like engineers, use math as a tool

Of course it considers it. Many people, like engineers, could not care less about the answers to most problems mathematicians work on. They do care about the tools they develop in the process. I’ve already shown examples of this but I’ll do it again: Galois theory was developed when trying to answer whether there are formulas to solve roots of polynomials of degree 5. Fourier analysis was developed when trying to find an analytical solution to the heat equation. Riemann developed his geometry to explore which Euclidean axioms were actually important. None of the direct answers were as important as how they got to them.

> Again, they want funding, they have to explain why exactly they should get it. And it better be an explanation that still holds water with AI available.

The explanation will be exactly the same. Only it will not be just hard to explain why the problem is important, but also it will be harder to explain that no, just the answer by itself is not useful without the understanding. Just like I am here having a really hard time explaining to someone who doesn’t understand how mathematical research works why “just getting the answer” is not a useful output.

This hangs on the strange assumption that the AI will "just give the final answer" and will be unable to give a human-preferred explanation. I find this assumption strange. If it holds, then mathematicians will still have a job digesting these proofs. If the AI can digest it better, then academic mathematicians will become humanities professors funded similarly to theology, philosophy and dance professors etc. for the sake of preserving a cultural practice, like traditional handmade broom makers etc.

Why is it strange? Are you familiar with how unsupervised proofs are made? It’s basically iterating on Lean code, even if it were able to explain the code to humans it doesn’t mean it can extract actual understanding and structure from it. The papers being outputted by these approaches are nowhere close to being understandable, much less useful.

> If the AI can digest it better, then academic mathematicians will become humanities professors

Cool, then once that happens we can discuss what to do. In the meantime, AI does not digest proofs properly, does not explain them and does not generate any understanding, and it doesn’t look like that’s going to change. Hence the letter and the criticism made to the approach taken by AI labs. It is not that hard to understand.

I find these discussions pointless. It's like complaining that diffusion models make hands with the wrong finger counts. Yes there was a year or a few months when that was a legit complaint. The phase where AI proves Millennium Prize level problems but can't write up a human-like paper explaining the proof strategy may be similarly brief. It feels pointless to build a grand theory of what AI can fundamentally do in the space of math proofs based on a few months of existence of such strength models.

I find it interesting how many people are incapable of imagining that the tech capability will not be frozen at today's level and where we were e.g. a year ago and that a similar change may happen until next year. Instead they make sweeping assumptions that the current limitations will be with us for our lifetimes. You need a much stronger way to adapt to the new reality.

> The phase where AI proves Millennium Prize level problems but can't write up a human-like paper explaining the proof strategy may be similarly brief

It's absurd to assume that because LLMs are improving in certain aspects they will improve in everything, specially when the part they are lacking in is not precisely something that would be a strength of their architecture. I mean, models have improved a lot but they are still not good at strictly following instructions consistently (there's a reason why AI labs are worried about safety alignment). They are still mediocre to bad at software design, even the latest models (haven't tested Astra seriously yet). And it's the same reason they are bad at creating mathematical theories: they do not have mental models like we do, it's not even useful for them. Their comprehension is limited to textual context that they need to refresh and reprocess continuously. That's just how LLMs work.

> I find it interesting how many people are incapable of imagining that the tech capability will not be frozen

I find it interesting that after taking this long to, I assume, finally understanding the point the letter was making, you automatically switch to "oh well AI will do that too".

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