AI’s dramatic acceleration of mathematics research continues apace, with the infamous Navier-Stokes puzzle being the latest and greatest solution yet produced by artificial minds. But not everyone is happy about the discovery. In short, a solution to the long-standing Navier-Stokes puzzle – one of the toughest and most enduring problems in mathematics.
Whoever solved it stood to win $1 million from the Clay Mathematics Institute, because it was one of its six Millennium Prize Problems. Major breakthrough made on famous Millennium maths problem The slightly longer version is that Navier-Stokes equations are used to model fluid flows, such as air over aircraft wings and blood in veins. There has been an outstanding problem in that we don’t know if these equations always work, or if there are situations where they stop making sense and start spouting nonsense, what mathematicians call “blow-ups”.
OpenAI has discovered they do, indeed, blow up. The work itself isn’t controversial. It hasn’t been peer-reviewed, but it has been formalised.
This is the process of theories and proofs being turned into computer code that allows machines to grapple with them, methodically working through the logic and exposing any flaws. That means we can be fairly sure the results are correct. The controversy arose because, shortly before OpenAI released its news, a pair of researchers, Tristan Buckmaster at New York University and Levent Alpöge at AI company Anthropic, rushed out their solution to a close cousin of Navier-Stokes, the Euler equations, which experts suggested could open the door to a full solution.
Those researchers heard rumours that OpenAI was due to make its announcement, and contacted the company for clarification – knowing its own solution was on the way. Buckmaster claims he was met with opaque responses, and put out a statement that stopped short of making any accusations but pointed out that his own work was being stored on OpenAI’s servers – as a customer, not a research partner. OpenAI has explicitly denied any wrongdoing, pointing out that no person or AI from the company had seen Buckmaster and Alpöge’s work, and that its solution was, in any case, different.
Although more will become clear when full papers of all the work emerge. All we know for sure is that AI is causing upheaval in the world of mathematics. In recent months, it has made rapid progress on mathematics problems, peaking with this week’s news.
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