The Clay Mathematics Institute (CMI) has officially weighed in on the Navier-Stokes problem, one of seven Millennium Prize Problems proclaimed in Paris in 2000, each worth $1 million. The problem asks whether the equations governing fluid motion in three-dimensional space always have a smooth, complete solution.

The CMI says "the Navier-Stokes problem has apparently been settled" and hopes "to see waves of new human understanding unleashed as the innovations behind this work are analyzed and interrogated." The solution is now under review. "The process is deliberately unhurried, but we will provide updates," the institute writes. It also notes that the "increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation."

The potential solution comes with a bitter dispute. Mathematician Tristan Buckmaster accuses OpenAI of redirecting resources toward the problem after rumors about his research leaked, using his drafts in training data, and rejecting his co-author, Levent Alpöge, who works at Anthropic, from authorship.

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