Monday, September 21, 2026

Math is Cooked

Mathematicians are in a panic, over the announced solution to a Clay Millennium Problem, and the Lean 4 verification of the proof of Fermat's Last Theorem.

Tweet:

Mathematician Terence Tao: "we have to slow down AI. the pace is insane, and there's no reason to be this fast — no reason at all"

Friend of mine, math professor from one of the top five depts in the US [and Tao's coauthor]:

"I want to go away, to my little country house, and stay there. My profession has basically been destroyed by AI."

The actual Navier-Stokes equation may or may not always have solutions. The Openai counterexample assumed a forcing term.

It is no longer clear how new mathematicians will be trained, or how mathematicians will work, produce, and be credited.

Physicists are not laughing much. Theoretical Physics has been cooked for about 40 years.

There is now an orchestrated public relations and lobbying push by the leading AI companies to get special protections in federal law. The problem is that their trillion-dollar AILLM businesses are contingent on not have cheap competition from cheap Chinese and open-weight models. So they want laws declaring the cheap models to be too dangerous.

Even mathematicians have been suckered into saying the progress is too fast. The main issues are rogue agents on the internet, and recursive self-improvement. Probably half of internet traffic now is AI agents, and the big AI companies are using their models to program their next LLM releases. These are the main ingredients to what the doomsayers say will destroy humanity.

Tao is getting a lot of heat online, but he was an AI enthusiast until it outdid him on Navier-Stokes with an obscure proof.

Update: SciAm reports:

Generated by an internal large language model (LLM), OpenAI’s proof relies on an approach that many experts find unnatural. It solves a variant of the problem that mathematicians say is disconnected from reality and thus less interesting. In a sense, the LLM found and exploited a loophole in the framing of the question.

“The most important problem is unsolved,” says Luis Silvestre, a mathematician at the University of Chicago. “The Clay problem is settled, but the main problem for the Navier-Stokes equations is not.”

Furthermore, last Thursday, three mathematicians posted a proof of their own that showed that OpenAI’s method can never be extended to solve the full problem. In other words, the loophole will never be closed, barring some completely new idea.

Openai says that it has more math results to announce, and it will consult with a group of mathematicians about its release.

While the mathematicians are probably happy to be consulted, I am eager to see the results. The benefits are slowing release are not clear.

Tao's new motto is this quote:

"We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics." —Bill Thurston, 1994.
The quote fueled a notorious SciAm article on "The Death of Proof".

1 comment:

  1. Well, ever since this piece of news came and I read something about it, I have felt like cracking a joke or two... But for now, speaking a bit seriously:

    The thing is that it's been for a long time that the *professional* mathematicians have allowed their field to be turned into a recreational game of sorts. Of course, it still required intellectual efforts.

    The main change that the hyper-scaled GenText has introduced is that, now, any one can play such recreational games with minimal efforts. And not just that, any one can now *also* invent some new games of the same, barren, kind. Both, with only minimal human efforts and without the benefit of having tenured academic positions. And, so long as the subsidies from the VCs remain available, any one can try (or invent) even the more demanding among such games, for a minimal (even zero!) subscription cost.

    Let me stop here, else, I'm afraid, I might inadvertently end up cracking yet another joke. [I mean, at this point, I also began to think of theoretical physics, and the sort of ``issues'' arXiv (and even journals) have recently run into. So, stop, I must!]

    --Ajit
    PS: Regarding the Navier-Stokes: Your point about the forcing function is well taken. Indeed, I have a couple of more points to make about this much hyped result, but I will write about them later, at my blog or so.

    ReplyDelete

The Evils of AI Alignment

Computer scientist Scott Aaronson announced his reading list for his new course on AI Alignment. It is not so clear why this is even a t...