robotpepi

i wonder if anyone is going to read that.

> This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!"

It's not about moving goalposts. What you're not understanding is that, even if for you is crystal clear that AI will be 100x smarter tomorrow, those in charge cannot simply bet all on that. Right now AI cannot really replace the core sauce of mathematicians (all the "understanting" and "asking the real questions" stuff), so it'd be unwise for, say, countries to start making decisions as if AI is capable of that.

Well the author of this one obtained a grant based on the work, the proof uses the same strategy as Anthropic's and even share some notation. I'm not an expert but this doesn't seem like one of those P!=NP proofs.

> Disproof of the Jacobian conjecture by example

It should be noted that there was a manuscript, available online since the beginning of 2025, with a solution to the Jacobian conjecture:

"Adrian Vasiu claims that the 7 page AI paper on the 3D Jacobian conjecture counterexample used notation and concepts from a draft of a paper jointly written with Alexander Borisov and Ofer Gabber, dated to January 14, 2025 and made publicly available on January 16, 2025."

The extract is from wikipedia, where the sources are given.

I don't think the essay was proposing that mathematicians should continue to focus on proving everything by themselves forever. It's mostly a critic of how the discussion is focusing too much on that mere "yes/no" answers is the same as makign mathematics advance.

> This subjective attitude turns mathematics into nothing more than number-poetry.

I don't think you understood the point. The point applies to all of basic science. You of course want some explanation supporting the raw answer, so you can use that insight in other contexts.

For the moment, AI is not capable of advancing mathematics _in the sense_ you're describing. AI is very bad at designing stuff, asking questions, etc. Maybe in the future you'll be able to ask the AI "cure cancer" and it'll do it, but for now we're very far away from that (this doesn't mean the current achievements aren't impressive).

> I’d say Terrance has recently left the denial phase, the anger phase

What are these comments? Tao, in particular, has been pro AI since years ago...

> Wondering how this will discourage mathematicians at all, since now they have another tool to accelerate their research.

I'm a professional mathematician and these tools are not available for me. So not happy about that!

(just to be clear, I'm not anti AI, I'm just criticising the shallowness of your comment)

I don't understand what you're proposing then. We can ask AI to solve practical problems of interest (making a computer faster for instance), but I'd say no one really believes that this is an unlimited resource. At some point we'll reach a plateau, and then AI will be an important tool but to continue advancing we'll need someone to ask the right questions.

> I thought the historical examples of photography and chess engines would be enough for people to connect the dots, but apparently not.

You're just an overconfident idiot who thinks that because there is an analogy along one dimension of a absurdly complex problem you've somehow arrived at a superior truth.

I repeat, this is an incredibly complex situation in which no one fully understands what's going on. The letter is simply asking for greater awareness of the implications of what AI companies are doing, they're not even saying that AI is bad!

agree. so many people missing the point. I don't think they even bothered to read the letter.

> I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink.

Yes, but to what point the hardware will shrink? There are several orders of magnitude of difference in what in your mind AI will become and what more conservative people believe. You take your view as granted...

so you're 100% sure that AI will solve every intellectual problem in the future, since as long as that's not the case, it's us who need to ask the questions. I don't know man, I wouldn't bet on that. What if we end up being wrong and then there is not research community?

to be honest it is difficult to discuss with someone who doesn't even try to understand the basics of basic science (and how it compares with _applied_ sicence), yet talks with so much confidence. even the solution to navier stokes won't have an immediate practical effect...

> But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development

You're locked into that idea, but provide no real argument. The dangers they describe in the letter are real.

The problem with your opinions is that you tend to state certain very quesitonable ideas with 100% confidence. Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. We don't even know how much of creative work they are able to do. We cannot make decisions that could destroy decades of progress just because of hype.

We can't be sure AI will be able to ask the questions of the future. At least right now, AI is not capable of that.

I still don't see the analogy, can you care to develop?

> Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction.

Are we really going to take what they say in public seriously?

> Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests.

I'd argue that this extremely extreme scenario is the only one in which it kind of makes sense to not have understanding. But let's be honest: no one knows if we'll be there (and it seems unlikely since everything reaches a plateau eventually). So, what happens if we allow ourselves to forget everything and then we don't reach the ideal scenario?

I don't see any meaningful analogy with your cites of Baudelaire. First of all, Baudelaire discusses art, which is very different to science. Several new forms of art have emerged, and then slowly integrated, despite the strong opinions of some. Here, Tao's letter discusses mainly practical aspect of scientific research. It is not about what a "failed mathematician" would do, or if "LLM can only record what already existed"; in fact, it ackowledges that LLM could become a central tool. If you want me to be even more precise, what they're saying (without saying it out loud) is that tech companies have too much power and are being irrespondible with it because they don't even think about the externalities.

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 don't think on the externalities.

> But complaining about the dawn of a new era of advancements seems counterproductive.

you completely misunderstood the critics. your analogy is awful. this is much closer to the industrial revolution in the uk: it brought a lot of progress, but also extreme inequality and concentration of power.

I really hate this overly condescending takes. First of all, what do you know about the internals of math research that allows you to speak with so much confidence. Second, you're not even addressing the issues raised by the letter! This is not about "oh they made a bunch of problems easier". There are huge economical interest behind: who owns and has access to models? are these companies interested in developing research or they just grind PR stunts without worrying about externalities in how research is actually conducted? Etc etc.

> It's not obvious to me that's an unethical thing to do, if it happened as they described.

What!? Even if everything OpenAI said is accurate (big hypothesis there!), it's highly unethical to rush a solution because others have jsut had success. And that's the only beginning.

> if this were true, it should be stated more clearly

stated more clearly by who? people in social media? I don't know what your feed shows you, but if you focus on what the visible people in the math community is (and have been) saying is precisely what I said.

> but right now there's no credible evidence, only claims.

since it's openAI who has the evidence (in the form of chain of thoughts, their internal processes, etc etc), it's on them to justify why they're innocent. but they've released nothing at all. we don't even know how hard they tried.

you're being naive

> We are scared of AI being smarter than us, the "human helped the AI" narrative is more psychologically comforting.

We're scared of big tech companies concentrating ridiculous amounts of power, destroying the communities that support and guide scientific research, without even thinking about the dangers and possible consequences, because a PR stunt is more important in the short term.

> They don't even claim to have had a proof, only to have been working on it.

Yeah, the guys who solved it for Euler and in the hypoviscous case, with the same technique that worked for full Navier--Stokes. They were "just" working on it.