AI Model Disproves 87-Year-Old Jacobian Conjecture as Lean Verifies Result Overnight
Updated
Updated · Fortune · Jul 20
AI Model Disproves 87-Year-Old Jacobian Conjecture as Lean Verifies Result Overnight
3 articles · Updated · Fortune · Jul 20
Summary
By Monday morning in London, Kevin Buzzard said the AI-generated disproof had already been machine-checked in Lean, turning Sunday’s result into a verified counterexample rather than a speculative claim.
Levant Alpöge credited Anthropic’s model with finding a construction whose Jacobian determinant stays at -2 everywhere yet maps three distinct inputs to the same output, falsifying Keller’s 1939 conjecture.
The breakthrough extends a fast run of AI math advances after models solved 5 of 6 International Mathematical Olympiad problems in 2025 and OpenAI disproved an 80-year-old Erdős conjecture in May.
Mathematicians said the result is both impressive and unsettling because current models can produce correct answers without a human-readable story, even as proof-checking tools like Lean remove one of humans’ remaining advantages.
That anxiety lands as the field is already under pressure: U.S. federal math funding is down about 72%, and PhD admissions at top research universities are down 15% for a second straight year.
Is the era of the lone mathematical genius over now AI solves decades-old problems?
An AI found the answer, but can it teach us the intuition humans missed for 87 years?
If AI co-authors a discovery, must its 'thought process' also be published for peer review?
The Disproof of the 87-Year-Old Jacobian Conjecture: How AI-Human Collaboration Reshaped Mathematics in 2026
Overview
On July 19-20, 2026, the long-standing Jacobian Conjecture, first posed in 1939 and unsolved for 87 years, was finally disproved. The breakthrough electrified the mathematical community, with news spreading quickly and experts calling the result remarkable. The disproof was achieved through a unique collaboration between mathematicians Levent Alpöge, Matthew, and the advanced AI Claude Fable 5, who together generated a specific counterexample. This explicit example provided clear evidence against the conjecture, marking a major milestone in algebraic geometry and showcasing the power of human-AI teamwork in solving deep mathematical problems.