Inside the Dispute Between Two Mathematicians and OpenAI
How independent research on complex math equations led to a collision over timing, authorship, and data privacy.
By Aaron Rose · Tech Reader Magazine · September 8, 2026
Two Announcements
In the same week, two groups announced major advances on complex math problems. One was a pair of independent mathematicians; the other was OpenAI. They were working on different equations, but their releases landed so close together that outsiders — and even the teams themselves — briefly confused the two. Coordination efforts imploded, and now both sides are telling different stories about what went wrong.
The bullet points below lay out the situation before the article unpacks each twist.
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One team produced a result for the Euler math problem.
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Another team produced a result for the Navier–Stokes math problem.
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Both groups attempted to coordinate announcements.
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The coordination failed, leading to disputes over credit, communication, and data handling.
The Short Version
Independent of each other, OpenAI and mathematicians Tristan Buckmaster and Levent Alpöge announced advances on complex math problems in the same week. The results are related in theme but not in scope. The groups were not collaborating; they only began talking after both projects were nearly complete, when OpenAI mistakenly believed Buckmaster and Alpöge had solved the same problem. Attempts to synchronize announcements fell apart over authorship, credit, and questions about whether private research data had influenced model training.
The Clay Mathematics Institute continues to list the Navier–Stokes problem as unsolved.
What Each Group Did
Buckmaster and Alpöge spent about a year working privately with AI tools. In mid‑August, they obtained a result for the Euler problem and completed formal verification shortly afterward. Their papers were released in early September. They did not claim to have solved the Millennium Prize Problem.
Separately, OpenAI began training a new internal model in late August. After hearing rumors that major breakthroughs had occurred, researchers directed large numbers of AI agents to investigate complex math problems. The system first produced a result for the Euler problem, then shifted focus. After roughly 10,000 agents worked for several days, OpenAI announced a claimed solution to the Navier–Stokes problem, followed by formal verification. OpenAI spent millions of dollars on compute to generate this research.
The Difference in Problems
The two efforts addressed different mathematical problems:
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Buckmaster and Alpöge worked on the Euler problem.
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OpenAI worked on the Navier–Stokes problem.
These are distinct challenges with different criteria and different significance within the mathematical community.
The Failed Coordination
Communication began when Buckmaster learned rumors about his work had reached OpenAI. Believing both groups had solved the same problem, OpenAI’s Sébastien Bubeck contacted Buckmaster and Alpöge to coordinate announcements. Only later did OpenAI realize the outside team had solved the Euler problem, not Navier–Stokes.
From there, discussions about timing, authorship, and how to present the results quickly became contentious. Buckmaster says OpenAI proposed that he release his Euler result first, then later present OpenAI’s Navier–Stokes proof without Alpöge as an author because Alpöge works for Anthropic. OpenAI disputes this characterization. Each side now disagrees about what was proposed and why the coordination collapsed.
The Data Question
During their research, Buckmaster and Alpöge used AI tools and uploaded drafts into Codex. Buckmaster asked whether any of that material had influenced OpenAI’s model. OpenAI said its agents did not access user data during problem‑solving and that no specific private data was used. It also noted it could not fully rule out the possibility that de‑identified product data may have contributed to model training. Buckmaster said he was not accusing OpenAI of misuse but could not determine what had happened.
What Happens Next
Both sets of papers—Euler and Navier–Stokes—are now public. The mathematical community will evaluate OpenAI’s claimed Navier–Stokes result, determine whether it meets the Clay Institute’s criteria, and assess how the two research efforts relate.
Until peer review is complete, the Navier–Stokes result remains a claimed solution, not an accepted one.