AI cracks 87-year-old Jacobian conjecture, unsettling mathematicians
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An AI model resolved the Jacobian conjecture, a problem unsolved since 1939, with the result verified and announced by Anthropic employee Levant Alpöge. The breakthrough, which drew over 20 million views on X, has sparked a mix of awe and unease among mathematicians, who now grapple with AI's ability to solve problems without providing human-understandable explanations.
The Breakthrough
On Sunday, an AI model solved the Jacobian conjecture, a problem rooted in the work of German mathematician Ott-Heinrich Keller from 1939. The result, verified by Monday, was announced by Levant Alpöge, an Anthropic employee, and has garnered over 20 million views on X. Kevin Buzzard of Imperial College London called it "a big day" for mathematics.
Mathematicians' Reaction
The achievement is the latest in a series of AI-driven mathematical breakthroughs since mid-2025, including solving five of six International Mathematical Olympiad problems and disproving an 80-year-old Erdős conjecture. In June, 16 researchers from 15 universities issued the Leiden Declaration, urging guardrails on AI's role in mathematics. Mathematicians report a mix of dread and amazement as AI closes problems beyond human comprehension.
The Explanation Gap
While the result is correct, AI provides the "how" without the "why," said University of Chicago mathematician Akhil Mathew, who suggested the problem to Alpöge. The Jacobian determinant holds steady at −2 everywhere but sends three different starting points to the same destination, disproving the conjecture. Mathew noted that a human-readable story would be preferable.
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