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Controversy swirls as OpenAI claims its internal AI model solve Navier–Stokes existence and smoothness problem, provoking statement by NYU Prof. Tristan Buckmaster

OpenAI announced that its internal AI model solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems with a $1 million award, but NYU Math Professor Tristan Buckmeister posted a 3-page account questioning whether OpenAI's Codex was trained on his and Levent Alpoge's research, stating that when he asked OpenAI's Sebastien Bubeck about training, he did not get an answer.

by read1 min views3 publishedSep 9, 2026
Controversy swirls as OpenAI claims its internal AI model solve Navier–Stokes existence and smoothness problem, provoking statement by NYU Prof. Tristan Buckmaster
Image: Chatgptiseatingtheworld (auto-discovered)

The day after Labor Day was hardly a quiet return to work. After OpenAI announced its internal AI model solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems, with a $1 million award at stake, NYU Math Professor Tristan Buckmeister posted a 3-page single-spaced account stating that Levent Alpoge (coincidentally of Anthropic) and he had already been working on this problem. Buckmeister questioned whether OpenAI’s Codex was being trained on their research (via OpenAI’s Codex that Alpoge had reportedly used for this math project).

According to Buckmeister, in his inquiry with OpenAI’s Sebastien Bubeck: “I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.”

You can read Buckmeister’s account here. Bubeck of OpenAI then posted a lengthy post on X:

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