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.
The idea that mathematicians were not involved in actively directing the and structuring the search for solutions is absurd to any professional mathematician who has tried to prove things using these models.
What you say is true but ... This is qualitatively different than calculators or computers.
I'm a professional mathematician and all the better mathematicians I know are in crisis mode. Most of us hadn't taken this sufficiently seriously and don't know how to use these models effectively but we play with them and immediately see that the entire way we've worked all our professional lives has to change. We worry less about ourselves than about the younger folks. I've got good ideas ai still doesn't know about ... Younger folks may not get the chance.
This is the same problem for software engineers too. I am now asked: what can you do that AI cant ? The answer to this could be intangibles like taste, aesthetics, and insights which collectively fall under creativity, and often accompanies experience. And there are no shortcuts to accumulate experience and perversely the more AI is used the harder it becomes. Soon, there will be a closure of all AI generated solutions, ie all low-hanging fruits are taken. Then, experts will again become needed to guide beyond the AI knowledge closure.
Math problems are highly structured, very precisely defined, and already heavily studied and not very complicated compared to problems in engineering or finance. There's a lot of quality material on which to train and it's easy to tell quality apart from crap. The search spaces are a priori much smaller than in other areas and the people using the tools to study them are themselves good mathematicians.
Success in such problems does not automatically extrapolate to other contexts.
Finding a training algorithm that can do recurrent networks and continual learning is also a "highly structured, very precisely defined, and already heavily studied and not very complicated compared to problems in engineering or finance"
That's the thing I'm most worried about - LLMs that are super clever at coding and maths, making an actually very very dangerous model that is far more efficient, and clever in a more innate (less brute force) way.
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