Stanford researcher discovers his head and his ass aren't the same thing.

I'm a professional mathematician. Today I proved what for me is a very solid theorem. It's something I had thought about for a few years. With a few weeks of serious use of AI I've found a proof that I am currently trying to write up, but which appears correct. The change in the workflow is enormous, but so is what one can do if one has clear what to do and how to do it.

Not every problem will receive $20M in funding to be solved by AI; for the rest, good human guidance will have to suffice. Labs only pulled this stunt because they wanted to show investors how powerful their models are on their own. But look again at the cost of that army of 10,000 SOTA agents. At the very least, I foresee a need for humans to decide when costly AI resources should be committed to a specific search plan. Grant review remains irreducibly human because it involves choosing which directions to fund and weighing opportunity costs: taking one path forecloses others.

Congratulations. You are one of those leading the way, showing how we will adapt and how the world will get better from AI.

That's not the conclusion. I started using AI after the Jacobian conjecture counterexample and have used a particular problem to learn how to use AI and to explore it's capabilities. I'm not a great mathematician but I'm full faculty with 25+ years of research experience and lots of articles and I just proved in a few weeks something that had resisted my efforts for some years.

The exploration process is much easier now. Ideas are quickly testable and multiple tests can help identify a technical obstruction. The tool requires good guidance and input but as it trains on people like me it will need those less.

At the very least our way of doing things must change. More pessimistic views seem to me defensible.

You sound a bit troubled. I was responding to the leading the way part. I'm hardly doing that. I just jumped on the bandwagon. What I do see is a tool that forces me to change behaviors learned over decades and potentially renders useless many of them while facilitating others. That's not all a rosy picture.

As for privilege, don't assume everyone lives and works in the US or gets paid lots of money to be a professor.

>full faculty with 25+ years of research experience

That sounds pretty privileged, money aside. It's always this thing with some people ... they make everything about money.

Anyway, good luck with that "wanting more" thing, it's a road that leads nowhere.

Also, https://www.youtube.com/watch?v=b8gmxT8qj8Y, particularly if any of those 25+ years were funded by public resources.

what an insane clip to reference

As a math professor, I care much more about the key idea, heuristics, and motivation than the proof. With the others in place the proof is clear, something an AI or a student can do.

Well, it's knowing when to push and when to not. You probably have an intuition for, I don't know, abstract algebra objects (I don't know your field of specialty :P), without needing to symbolically manipulate all of it, but you developed a deep intuition for them through many proofs and attempts at proofs with them.

Im glad you brought up abstract algebra—that was the one class in my math undergrad that I never developed an intuition for. I learned to do the proofs by pushing symbols around and putting bars on top of them but I never felt like I understood what was happening.

That's leaning into engineering, away from math. Heuristics aren't always accurate. Math history before proof is the history of delusion. Idea, heuristics, and motivation aren't nearly enough for correctness outside of a sandbox.

They should just make them read an old chess book like Lasker that gives low level heuristics

This is the essence of why disciplinary, authoritarian, stick based teaching of humans generally fails. It teaches succeed at any cost.

One sees this in math research. The model reports it has proved X. In fact it has given an erroneous numerical check of Y in a few atypical cases.

What makes math approachable is that the context is so well delimited (semantically) that one can guide the model with adequate correction.

Tha Jacobian conjecture is (was?) notorious for publication of false proofs. There have been many, not all by those who shouldn't have known better.

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.

Perhaps all these fields medalists are just worried that AI mitigates their competitive advantages over a mediocre professional mathematician like me. Their main advantages are a kind of penetrating clear thinking that not all of us have and an ability to work obsessively without tiring or losing focus while retaining with a clear head a great number of facts - AI removed these advantages - as Tao has written it shifts the focus to asking good questions and using available tools to address them - and the traditional elite may not be better than I am at that part - they were just better at the solving the problems part ...

Tao is quite the opposite of what you describe. He's had an ongoing dialogue intellectually with the challenges created by ai for mathematicians for some time (years) now and his viewpoint is quite balanced. He is not alarmist but rather correctly addresses the real problems ai advances create for mathematicians traditional way of working.

"I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already"

There were more than six doing that and it's essentially why it was ripe for AI to finish it off. But the finishing off was quicker than anyone expected

I'm not a mathematician, nor do I know almost anything about the discipline, but it sounds like maybe you do.

What teams of people spent an entire career working together, focused entirely on Navier-Stokes or problems they suspected were related, without any "publish or perish" concerns?

I realize tenure is a thing, but my limited understanding is that a significant amount of time is spent earning it, once you account for Ph.D. program and the years of needed to be granted it.