gjulianm

> 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".

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 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.

> 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.

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.

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

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.

> I read the article and they are all wrong

I would recommend a bit more humility and trying to better understand why 25 Fields medalists, among them people like Terence Tao (who isn't anti-AI by any means, he's even promoted a registry of AI Lean proofs), are saying this.

> Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing.

No. The point is that AI companies are using the models to solve problems in such a way that the useful part of problem-solving, i.e. the theories and tools developed during the process, is not present. And they are doing that because the companies seem to be motivated not by honest advancement of math but by marketing and publicity.

> they synthesize and solve lots of other problems nobody asked for.

No one asked Fourier to solve series representation of functions when he was studying the heat equation, and yet thanks to that we have Fourier analysis.

> if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades

The point they are making is that if AI keeps being used as "problem solver" rather than "theory understanding", replicating the proofs and getting the useful parts out of them will be far more difficult.

> Like the mathematicians working on famous problems in private

This is an extremely rare situation that practically never happens. Most mathematical research is done in the open, with partial results being published, conferences where approaches are discussed, collaborations... The Navier-Stokes solution is a great example: the approach that OpenAI ended up using was something that two mathematicians had proposed previously and was being studied and followed by several others, with different sub-paths within the same approach.

In that case a better answer would be "I'm fairly certain it does satisfy it, but in any case I asked Claude to double check for any issues and it didn't find any unsatisfied requirement". That's the information that matters, and it's probably faster anyways.

I try to not use AI to write text that's meant to be read by other people. I might use AI to understand and research beforehand, but the writing is mine. The most important reason is that writing allows me to check whether I actually understand what I am trying to communicate. Too many times I've started writing something and once the ideas need to be put in writing, I notice that there are concepts that I'm missing or that I don't really understand.

Second is that the LLMs are not going to have original input, they're just going to expand what I say. So at that point I might as well just send the prompt or the assorted collection of ideas and others can expand on their own. Seems more honest and efficient as I'm not just pushing a wall of slop.

I don't think you need to tear open busy streets to install fiber. In my area we got fiber (up to 10G now) and they didn't open any trench.

I am not sure how much do I trust an article about Madrid's metro that doesn't mention the fact that one of those expansions (Line 7, in San Fernando de Henares) was done with political instead of technical criteria, ending up in several hundreds losing their homes and a metro line that has to close every once in a while for repairs.

I am also heavily distrusting of the "75 percent of passengers described themselves as ‘very satisfied’". The infrastructure might be ok now, but the frequencies are getting worse (except when the pope visits, in that case they apparently have the money) and in rush hour everything is packed.

Cursor has BYOK support too. I think it also has Bedrock support.

I don’t think it’s false, much less obviously false. On one hand I have my personal experience about it, on the other you can see there’s only a small range in the “I want a conversation” scale where they want it enough to ignore the nonverbal signs that the person doesn’t want to talk but not enough to ignore the verbal ones.