OpenAI claims blockbuster math breakthrough amid swirl of controversy

For the second time ever, someone has solved one of the seven Millennium 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.

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