AI Solves Another Century Old Math Problem
Artificial intelligence solved the Jacobian conjecture, a problem that has challenged mathematicians since 1939, while the world watched the 2026 World Cup final.
AI’s breakthrough and the immediate reaction
Anthropic employee Levant Alpöge posted the result on X, quickly amassing more than 20 million views. By the following morning, mathematician Kevin Buzzard of Imperial College London confirmed the solution had been verified. “It is a big day,” he told Fortune. “I think it’s a great time to be alive, personally.”
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The Jacobian conjecture, rooted in the work of German mathematicians Ott‑Heinrich Keller and Carl Gustav Jacob Jacobi, concerns whether certain polynomial maps are invertible. Alpöge’s model produced a map whose Jacobian determinant stays constant at –2 across space, yet three distinct inputs converge to the same output, violating the conjecture’s conditions.
Buzzard described the finding as “very exciting,” noting it shows language models edging toward the “supermathematician” described by Google Deep Learning scientist Christian Szegedy half a decade ago. Yet many in the field voiced unease. University of Chicago mathematician Akhil Mathew, who suggested the problem to Alpöge, said, “One can check out that it’s correct, but it would be nice to be able to tell a story.”
From Olympiads to century‑old problems
AI’s foray into pure mathematics accelerated after mid‑2025, when models solved five of six International Mathematical Olympiad problems. In May, OpenAI’s system disproved an 80‑year‑old Erdős conjecture on combinatorial geometry. By June, 16 researchers from 15 universities issued the Leiden Declaration, urging safeguards for transparency, attribution, and peer review as AI reshapes mathematical knowledge.
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Mathematicians now find themselves in a “shepherd” role, watching AI resolve questions faster than human reasoning can keep pace. The Jacobian result adds to a growing list of problems that have been “fallen” by machine intelligence.
Historically, mathematics has resisted automation. While calculators took over routine computation decades ago, advanced reasoning remained a human domain. Buzzard explained that a mathematician’s contribution lies in the “reason” behind results, not just the numbers themselves.
