Why mathematicians don't believe OpenAI has solved Navier-Stokes problem
What's the story
OpenAI has claimed that its reasoning AI has generated a proof for the Navier-Stokes equations, a major milestone in mathematics. However, the proof is not public, and mathematicians working on related problems have raised questions about how OpenAI arrived at this result. The Navier-Stokes problem is one of the seven Millennium Prize Problems identified by Clay Mathematics Institute, with a $1 million prize for a complete solution.
AI breakthrough
The proof is reportedly around 100 pages long
OpenAI's internal AI model has reportedly generated a proof of some 100 pages in just a few days.
The company is said to have devoted a large team and significant computing resources toward the problem after hearing about progress made by mathematicians on a closely related question.
However, there remains an important distinction between what has been independently established and what OpenAI is claiming.
Research progress
Related work by mathematicians
Mathematicians Tristan Buckmaster and Levent Alpoge spent about a year studying a related version of the Navier-Stokes equations with the help of AI.
Their work showed that a solution in the friction-free version of these equations can develop a singularity in finite time, often referred to as mathematical "blow-up."
While their result has been verified, OpenAI's alleged proof of the full Navier-Stokes problem remains undisclosed.
Ethical concerns
Allegations over private drafts
Buckmaster has questioned whether OpenAI's systems had been exposed to his private mathematical drafts, which he had been feeding into the company's tools during the year.
He also alleges that OpenAI initially portrayed its model as having been given the problem with little human assistance.
Further complicating matters, Buckmaster claims that when he was going public about this situation, he was told, "Why would you ruin your career?"
Proof verification
Proof not yet verified
The most consequential part of OpenAI's Navier-Stokes claim remains unverified.
If its model has indeed produced a valid proof of the full problem, it could mark an extraordinary moment for both mathematics and AI.
However, until the proof is made public for scrutiny, questions over its origins are likely to remain just as important as the claimed breakthrough itself.