Harvard's Levant AlpoGe Uses AI to Disprove 87-Year-Old Jacobian Conjecture

Harvard mathematician Levant AlpoGe announced on X that he has disproved the three‑variable version of the Jacobian Conjecture, a problem first posed in 1939 by German mathematician Otto Heinrich Keller. The counterexample was generated with the help of Anthropic’s large‑language model Claude Fable 5, demonstrating that artificial intelligence can tackle mathematical questions previously unresolved for decades.

The result shows AI’s growing capability in formal research; a similar breakthrough earlier this year saw OpenAI’s model produce a counterexample for the Erdős unit distance conjecture. AlpoGe cautioned that the finding currently applies only to the three‑variable case, and the simpler two‑variable version may still hold, but the work marks a significant milestone for AI‑augmented mathematics.

Experts highlighted the importance of human oversight, noting that while AI can locate counterexamples, developing new theories still relies on mathematicians. The discovery has sparked discussion across the mathematical community about the future role of AI in proof‑search and problem‑solving.