AI-Assisted Proof Cracks 87-Year-Old Jacobian Conjecture in Higher Dimensions
Levent Alpöge, a mathematician at AI company Anthropic in San Francisco, reports finding a counterexample to the long-standing Jacobian conjecture in higher dimensions, using the firm’s large language model Claude Fable 5. The conjecture, posed 87 years ago, concerns polynomial functions whose Jacobian determinant is a non-zero constant and asks whether such functions must be invertible. Alpöge’s claimed counterexample, shared in a concise formula on X shortly after the FIFA World Cup Final, challenges decades of prevailing belief and is now subject to independent verification by experts.
Prepared by Jonathan Pierce and reviewed by editorial team.
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Levent Alpöge social media post published on July 19, 2026. https://x.com/alpoge/status/2079028340955197566
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AI-Assisted Proof Cracks 87-Year-Old Jacobian Conjecture in Higher Dimensions
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