Following on the post immediately below, "Turbulence: OpenAI Says It Has A Solution For The Navier–Stokes Millennium Prize Problem".
From Scientific American, September 8:
Prior to the announcement, rumors were circulating online among mathematicians over the proof’s origins—OpenAI has denied all allegations
For the second time ever, someone has solved one of the seven Millennium Prize Problems—math’s biggest targets, each worth a $1-million prize. But unlike the first time, that someone is an artificial intelligence start-up.
Today OpenAI announced that its internal model has proved that the Navier-Stokes equations, which mathematicians use to study how fluids move, are fatally flawed. The reveal comes after mathematician Tristan Buckmaster alleged that OpenAI had tackled the proof after the company became aware that Buckmaster and his colleague Levent Alpöge had been using a specific method to break a related problem. OpenAI has denied the allegations.
OpenAI’s proof shows that, on rare occasion, the Navier-Stokes equations “blow up,” meaning they dictate that a fluid’s speed becomes infinite at some points, something that is impossible in nature. The company says the proof has been certified using the programming language Lean, which all but guarantees its correctness.
“We’re a little bit in shock,” says Diego Córdoba. He and Luis Martínez-Zoroa originally developed the approach the AI used to solve the problem, which is called “forcing.” “If it’s done, that will be a big surprise for us,” Córdoba says.
The night before OpenAI announced the proof, Buckmaster posted on social media that he and Alpöge, who is a mathematician and an employee of Anthropic, had blown up the Euler equations, widely seen by the field as a step toward solving the Navier-Stokes problem. In a statement released on Monday, Buckmaster alleged that OpenAI had found out about the pair’s progress in the last week and had adopted the same method as Buckmaster and Alpöge had been using to solve the full problem.
In a press briefing on Tuesday, OpenAI mathematician Sébastien Bubeck denied the rumors about the proof’s origins. Bubeck said OpenAI’s internal model had independently solved the Euler problem by totally different means than those employed by Buckmaster and Alpöge. OpenAI’s solution to the full Navier-Stokes problem, however, did follow a similar method as that used by the two mathematicians. And the proof was developed over the weekend, according to Bubeck—that is, after the time that Buckmaster claims the news of his and Alpöge’s result had reached OpenAI. Bubeck emphatically denied that the two mathematicians’ work had influenced OpenAI. “We did not use their prompt or proofs to prompt our models,” he said....
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And at Reddit's r/codex, September 8:
Blown up: OpenAI allegedly stole mathematicians' private research from their Codex chats!
TLDR: Two mathematicians spent a year cracking one of the hardest problems in math and fed every draft of their works into Codex and Claude. Days before they could publish, OpenAI suddenly showed up with the same solutions. When asked if their model (Sol and Astra) was trained on the pair's private chats, OpenAI did not answer the question till this day.
For a full year, two mathematicians , Tristan Buckmaster (NYU mathematician) and Levent Alpoge, worked in silence on a problem that had stumped some of the best minds alive. The kind of problem where, if you solve it, your name goes in the history books.
And every single day, they testing their ideas, their drafts, their half-finished proofs into LLM such as Codex and Claude, which they paid for it out of their own pocket.
Then came the breakthrough. They finally cracked it. They were days away from telling the world.
That's when OpenAI suddenly said to them:
"Our model solved it too."....
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