Home / Science / AI cracks century-old math puzzle: Jacobian conjecture falls!
AI cracks century-old math puzzle: Jacobian conjecture falls!
6 Aug
Summary
- AI found a counterexample to the Jacobian conjecture in three dimensions.
- The Jacobian conjecture has been a long-standing problem in algebraic geometry.
- The AI-generated counterexample was simple enough for quick verification.
A mathematician has found a counterexample to the Jacobian conjecture, a famous problem in algebraic geometry. Levent Alpöge, working at AI company Anthropic, announced his discovery on X, stating he used their large language model, Claude Fable 5. This development marks a significant moment in mathematics, showcasing AI's potential in solving complex problems.
The Jacobian conjecture, first proposed in two dimensions in 1884 and later generalized, posits that certain polynomial functions are always reversible if their Jacobian determinant is a non-zero constant. For decades, mathematicians attempted to prove or disprove it, with many claimed proofs ultimately invalidated.
Alpöge's counterexample, surprisingly simple, demonstrates that the conjecture is false for dimensions greater than two. The original two-dimensional conjecture remains open. The AI's ability to navigate vast possibilities to find this specific counterexample underscores a new frontier in mathematical research.
This AI-assisted breakthrough follows other recent notable discoveries, including the disproof of the unit distance conjecture. The ease of verifying Alpöge's counterexample suggests AI's power in identifying novel mathematical objects, potentially reshaping the future of mathematical exploration and discovery.
