OpenAI's 88-Hour Math Proof: A Result Being Correct vs. Being Understood

Summary

On September 8, OpenAI said 10,000 of its agents, running for 88 hours, had produced a 166-page proof regarding the Navier-Stokes equations — which describe fluid movement and have remained an open question since 1934. It's one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize; only one has ever been awarded. OpenAI has said it won't be claiming the money, which is just as well, since outside estimates put the compute bill between $10 million and $40 million. Clay now says the problem has "apparently been settled," while the formal evaluation proceeds. The institute calls that process "deliberately unhurried." Before Clay will consider paying, a proof has to be published in a refereed journal of worldwide repute and then survive two years of mathematicians trying to break it. If you check Clay's website, it now labels Navier-Stokes "Active": neither unsolved nor solved. Those conditions were written in 2000, and you'll notice they don't ask whether the argument is formally correct; they ask whether mathematicians have read it, argued with it and failed to break it. It seems the machine has produced the proof much faster than the mathematical community can absorb it, and while the cost of producing the answer is visible, the cost of turning it into understanding is only starting to be calculated. Navier-Stokes is the sharpest case so far, but it isn't really a story about fluid dynamics. The interesting story is the gap between a result being correct and a result being understood. Earlier this week on September 11, 25 Fields Medalists signed a declaration saying the way AI labs chase mathematical problems is damaging mathematics. The next day Terence Tao, who signed it, gave his blog over to two philosophers of mathematics, Silvia De Toffoli and Eamon Duede, who explained the claim. They separated two concepts that had rarely needed separating before: a logical proof (deductive validity, which a machine can verify) and an intelligible proof (understanding why something is true in a form humans can explain and build upon). Historically, these came together because no human could construct the first without possessing the second. AI pulled them apart. Their verdict on the Navier-Stokes result: "What OpenAI has given us is an answer. But it is not clear that they have delivered a fruit…