Levent Alpöge
American mathematician (born 1992)
Levent Alpöge
Levent Hasan Ali Alpöge (born April 1, 1992) is an American mathematician. He is known for his work in number theory and arithmetic statistics. He was a junior fellow in the Harvard Society of Fellows and later joined the artificial-intelligence company Anthropic as a member of the technical staff. In 2025, he and collaborators gave a second proof that Hilbert's tenth problem has a negative answer over the ring of integers of every algebraic number field, a result originally established by Koymans and Pagano in 2024. On July 19, 2026, Alpöge presented an explicit counterexample to the Jacobian conjecture in three-dimensional space, stating that it was discovered using the Claude Fable 5 AI model. He announced a counterexample to the Carathéodory conjecture on August 19, 2026 using the model. Four days later, he announced a positive answer to Hopf's problem concerning the existence of a complex structure on a 6-dimensional sphere using AI tools. His AI-assisted work on Navier–Stokes existence...
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