AI and Mathematicians Join Forces to Solve Longstanding Math Puzzle

WHO:

Phys.org - Levent Alpöge, a mathematician at Anthropic.

Fast Company - Levent Alpöge, a 33-year-old researcher at Harvard University.

Fast Company - Eduard Ott-Heinrich Keller, the German mathematician who proposed the Jacobian conjecture in 1939.

WHAT:

Phys.org - Alpöge announced on X that he found a counterexample to the Jacobian conjecture.

Fast Company - The Jacobian conjecture is a longstanding problem in algebraic geometry.

Fast Company - Alpöge's counterexample is 216 characters long.

Fast Company - Several mathematicians have confirmed the arithmetic of Alpöge's counterexample.

WHERE:

Fast Company - The announcement was made on X.

WHEN:

Fast Company - Alpöge announced the result on X on July 20, 2026.

WHY:

Fast Company - The challenge was to find a counterexample proving the Jacobian conjecture false.

HOW:

Phys.org - Alpöge used Anthropic's large language model Claude Fable 5 to find the counterexample.

Fast Company - Researchers used SymPy and Lean to conduct independent checks of the counterexample.

Fast Company - Additional AI systems, including OpenAI’s GPT models, were used for fact-checking.

(UPDATED July 22, 2026 12:24 UTC)

Levent Alpöge, a 33-year-old researcher at Harvard University, has announced that he found a counterexample to the Jacobian conjecture, a longstanding problem in algebraic geometry, using Anthropic's large language model, Claude Fable 5. His counterexample, which is 216 characters long, has been confirmed by several mathematicians through independent checks using tools like SymPy and Lean, along with additional fact-checking from AI systems including OpenAI's GPT models. The announcement was made on X on July 20, 2026, marking a significant development in the field of mathematics.