AI megathread

The “Turing machine” seems to have cracked one of the famous Millennium Problems, each of which carries a $1 million prize: https://www.nature.com/articles/d41586-026-02842-5

These problems have been among the most prestigious problems to solve in mathematics for decades.

I'm not sure to what extent this particular Problem was solved by a massive amount of computation, perhaps analogous to the huge computing resources used in weather forecasting. That's a gap in my own understanding rather than a meaningful assessment.

I'm not sure to what extent this particular Problem was solved by a massive amount of computation, perhaps analogous to the huge computing resources used in weather forecasting. That's a gap in my own understanding rather than a meaningful assessment.

There was definitely a huge amount of compute involved, as OpenAI states that 10,000 AI agents collaborated to solve the problem. It is, however, not completely clear at this point how much of the discovery was done by humans versus the AI, as OpenAI has not yet revealed the prompts they used.
I also don’t think it can really be compared to weather forecasting. Weather forecasting typically involves using enormous computing power to numerically solve a mathematical model, much like numerically solving the Schrödinger equation for a given physical system. The Millennium Problem discussed here was different - the AI had to find a single counterexample among infinitely many possible solutions to the Navier–Stokes equations. It would have been impossible to solve before the end of the universe using simple brute force.

Incidentally, words such as 'scandal' and 'controversy' have appeared in relation to that maths problem.

How OpenAI “Solving” a $1 Million Math Problem Proves Your Chats Aren’t Private

The controversy began when two mathematicians, Tristan Buckmaster, an NYU mathematics professor, and his colleague Levent Alpöge, an Anthropic researcher, spent nearly a year using OpenAI's Codex tool to formalize their mathematical work. They fed it half-finished theorems, proof sketches, and complex logical arguments—translating their ideas into Lean, a programming language for verifying mathematical proofs.

Buckmaster took what he believed were every reasonable precaution. He explicitly disabled the setting that allowed OpenAI to train on his data. He assumed his unpublished research, his private drafts, and his half-finished proofs were safe.