Levent Alpöge
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Claude Fable 5 surfaces a three-variable counterexample that topples the 87-year-old Jacobian conjecture
Mathematician Levent Alpöge, using Anthropic's large language model Claude Fable 5, has found a three-variable counterexample to the 87-year-old Jacobian conjecture. This disproof, a compact formula with a Jacobian determinant of -2, invalidates the conjecture in dimensions above two, though the two-dimensional version remains open. The discovery highlights the potential of AI in finding unexpected mathematical objects.
An 87-year-old math conjecture just fell to Claude — but a Columbia professor is skeptical
A mathematician named Levent Alpöge claims to have used Anthropic's Claude Fable 5 AI to find a counterexample to the Jacobian Conjecture, a mathematical problem that has remained unsolved since 1939. While the AI's finding has gone viral and preliminary verification suggests it is valid, some experts like Columbia professor Andrew Blumberg remain skeptical about the AI's true understanding versus brute-force computation. This event highlights the growing role of AI in scientific research and the potential for collaboration between humans and machines in discovery.
