robotpepi

You argue that it's better to be optimistic as you're a single person without power whatsoever, but your simplistic optimism is even worse. You're opinion is not new: Sartre would say you utilize your proposed insignificance to escape from the anxiety of freedom and responsability.

how naive do you have to be to believe something like that...

please tell us how you imagine things

> what if AI becomes better at humans for that as well?

The "if" is the problem. If it happens, then of course, let AI do it. For the moment AI is still bad at those type of tasks [1], so the discussion shouldn't focus on highly conjectural situations. We can't destroy the scientific ecosystem based on vague speculations.

[1] There are real reasons: it is not obvious how to optimize an LLM for doing basic science or other ill defined tasks. On the contrary, optimizing for writing a proof that passes the Lean test or code that passes the tests is a different story.

if your goal in life is proving theorems, then sure, but we don't fund mathematics to check if each conceivable theorem is true/false.

History teaches us that understanding deep problems in mathematics finds natural applications elsewhere. So, either AI completely solves mathematics (unlikely for the moment), or we use marginal amount of funding to keep the mathematical communities alive.

Research in pure mathematics is part of what we call "basic research". There are no applications in mind a priori. People instead focus on understanding, because history has taught us that understanding tough problems in mathematics finds natural applications elsewhere. It's the same as theoretical physics or theoretical computer science.

The point of the post is that what you call "AI knowledge" is not knowledge.

> If AI leads to an era of abundance, then the economic system has to change.

This is beyond naive.

Your analogy doesn't work. A "product" in research pure math is not the same as writing code.

it's incredible the amount of people who think all these recent posts in Taos blog were written by him.

> AI has largely not been trained to operate independently yet.

It's not obvious at all that it's possible to train it to operate independently. So far, AI has been succesfuly trained only for highly controlled and verifiable tasks (code generation and mathematics).

> One human needs to teach one AI system how to do one specific task. Everyone can now use this. Before you had to teach every single human having to do this task and the next generation.

We already had that before AI. The problem was precisely that it's too inefficient to make a new system for each different task. Of course, the new AI is more multimodal, etc, but up to what point? Not clear so far.

AI is very efficient when you ask them to do a specific, one-objective task. It has no independence whatsoever, that's why it cannot _replace_ humans. This is evident for anyone using AI routinely.

Of course this doesn't mean we may need less amount of humans for certain jobs, or that I'm the future AI will gain new abilities.

This doesn't make any sense. You try to explain a 28% by arguing based on edge cases.

It feels like publicity stunt. Of they really care about research, they would at least have given more reasonable citations in the Navier-Stokes paper.

> Were you, let's say 6 months ago, expecting it to resolve one of the Millennium Prize problems?

I didn't expect them to throw millions of dollars at each famous math problem. But one year ago we already had LLMs that solved IMO problems, no?

> Are you sure? (The numbers I've heard, which I admittedly have no very strong reason to trust, don't seem that way to me.)

Math has very little founding compared to other science domains. Also, if you filter mathematicians by specialization in PDE and that have worked on Navier-Stokes, then you end up with a very niche community.

> For instance, suppose you give one of today's frontier models some of those chain-of-cubes rotation puzzles. How well will it do?

I feel like this is not the correct way of thinking about it. We can also ask, for instance, how well a state-of-the-art algorithm for the salesman problem works on a particular graph topology. People do PhD thesis on topics like that, so the answer is not obvious at all. For LLMs we still don't have a curated theory that explains what they're good/bad at, and that you don't see how to extract an answer from the definitions is no surprise since this is obviously not an easy problem. But all this is normal because this is a rather new topic (models of this scale appeared when? 3 years ago? That's nothing for science).

Anthropomorphizing LLMs has added so much noise to this discussion.

> Otherwise you could just put this problem into an automated theorem prover (we've had those forever, they are actually just brute-forcing it).

There are many automatic theorem provers that do very clever stuff, just as the underlying theroy describes.

> I am shocked how people can deny that solving Navier Stokes requires some sort of intelligence.

It is absurd to waste time discussing whether it is inteligent or not. It is just an algorithm, we know how it works, and it does exactly what we expect it to do. LLMs are not magical things. The main difference is the scale: for Navier-Stokes they spent in 3 days more money that the whole mathematical community over the last 20 years easily.

By the way, I'm not saying that LLM's are useless, that I'm anti-AI or anything like that.

For me, mathematicians seem to be still having an inner discussion rather a making these essays for the more general public. In any case, I think that statements of the type "there's actually no role for human Mathematicians" are completely non-serious, so it'd sad that the discussion concentrates on that.

> In the (extremely) short run, yes. In the long run, those jobs will also be done by AI.

Let's be honest: we don't know. Maybe you're right, but for the moment it's more likely that you're not. And countries cannot bet on that vague intuition at the cost of destroying their research communities and world leadership (which takes decades if not a century to achieve).

> 1) My way of thinking, and 2) what I already know and how well I recall it in this context.

I don't think we're discussing pedagogy. Good _research_ exposition is instead related to communicate your intuition and way of seeing things. The conceptualization of a given situation or problem is what is valuable, how you connect it with other stuff, etc. It is then up to you to memorize and interiorize it.

I don't see the point. No one is proposing a complete rejection of AI tools.

You don't know what the survivorship bias is.

He later participated in Bourbaki, who were known by their overly formal style, tough.

Code has a very different purpose than math tough. The development in basic science follows a different motivation system.

I'd say this is the most optimistic scenario. there are really difficult problems to be solved in terms of access to AI.

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.