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Comment by gjulianm | Hacker News Reader

There are no similarities whatsoever, other than them having opinions on a new tech that affects their field.

> nothing stops mathematicians from doing both of those things

Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.

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> get funding

It all comes down to this. Yes, they will need to give a good and convincing argument to the taxpayer. And at the end of the day, if the circumstances change, and you're unsuccessful in making your case in your plead, the taxpayer and their representatives may not want to keep the same level of funding and instead put that money to use elsewhere. So make a good argument why your job is still worth that cash under the new circumstances. The argument can appeal to aesthetics and art and philosophy and a kind of feeling of religious elegance and so on, it's fine. I can't say how well that will work, but it's worth a try. Taxes also fund theology and other pursuits with no tie to cold hard engineering etc. But that level of funding is not the same as for math currently. That gap may shrink.

I don’t get the argument you are making. If you want to reduce funding for mathematics research, argue for that. But wanting to make getting funding and coordination and collaboration harder in exchange for nothing other than PR for AI labs does not make sense

Is it just PR? Okay then the useful math can be done by AI and we can leave aesthetic math to human academics who will ascetically refrain from using AI and if anyone of them submits a paper and it turns out they used computers they will be treated like WADA treats Olympians on steroids or chess players with a vibrator up their ass telling them what move to take. But again the taxpayer may not foot the bill for this endeavor as much as they did while thinking it may be useful for technology, science and engineering innovation.

But did you read the letter, or are you familiar with the people signing it? Several things tell me you didn’t:

- The useful part of math is the tools, the understanding and the theories. Knowing whether the result is true or not is usually not useful. Imagine an AI that just says “cancer can be cured” but doesn’t say how: that’s what the letter is criticizing.

- Terry Tao is one of the biggest proponents of AI use in math. He’s been for quite some time and he shares a lot on his blog.

Seriously, it seems like you’re arguing about some idea you have in your head and you’re not making the effort to actually understand anything about this letter.

AI won't just say cancer can be cured without saying how. Not sure where you got this from. AI will be superhuman at writing the executive summary at any prerequisite knowledge level.

These people are concerned about internal community dynamics like tenure, chairs, PhDs, grad students, the whole ecosystem, papers, hiring, conferences, journals etc. But the wider population doesn't care about this and academics don't understand that nobody cares about this outside their bubble.

As Feynman said, "mathematicians can research what they please. If you want something else, you work it out yourself" (not verbatim). Indeed, now people can do this with AI and it makes mathematicians salty that they will have less prestige.

> AI won't just say cancer can be cured without saying how.

It was an example, an analogy to argue that answering a question might not be as important as how it arrives to that question. Hence the “imagine”.

> These people are concerned about internal community dynamics like tenure, chairs, PhDs, grad students, the whole ecosystem, papers, hiring, conferences, journals etc.

You just described most of the parts of the mathematical community.

> But the wider population doesn't care about this and academics don't understand that nobody cares about this outside their bubble.

I don’t care about the logistic system and yet I want my food to be in the market. If the population at large wants to use mathematics they will have to find a way to support a mathematical community. Now, if you don’t want mathematics, again, go argue about that.

> Indeed, now people can do this with AI and it makes mathematicians salty that they will have less prestige.

Except that they can’t. I do not know how many more times we need to explain that “answering questions” is not what mathematics is about. That if that path is followed, then mathematics will suffer as a result and the pace of mathematical development will slow down.

Honestly, I think it would be better for you to really stop attributing the arguments of mathematicians that are by no means anti AI to saltiness or other childish feelings. Try to be more humble and try to find what kind of ideas they might hold for them to argue this letter. Of course, that requires reading the letter and trying to understand it.

> You just described most of the parts of the mathematical community

Just as science (as in the scientific method) isn't the same as Science, the community social practice and logistics and tenure rules and committee compositions and journal page limits etc, mathematics is not the same as the academic mathematics community. They are not the sole producers of mathematics and not the sole users. The funding is largely in the hopes of the usefulness of the resulting math. Not all. Some funding is like art and culture funding, for propagating a cultural legacy, like folk dance also gets funding and experimental performance theater also gets some tax funding. But that's not the bulk currently in math.

I have read the letter. It's all about stuff of holding back because they don't want the answer key because prestige reasons, and how will grad students train their brain if we have too many answers. This doesn't consider that many people, like engineers, use math as a tool. They don't want to hold math back. It's fine to think that applications are too dirty. 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. They can do the aesthetic math as an art side project like an accountant can paint or sing off the clock. But generally you also don't pay everyone for their hobbies even if those hobbies are nice culturally rich endeavors.

> 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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