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Jacobian Conjecture

All articles tagged with #jacobian conjecture

AI tool Fable 5 allegedly disproves the Jacobian conjecture
technology11 hours ago

AI tool Fable 5 allegedly disproves the Jacobian conjecture

A mathematician, Levent Alpöge, used Anthropic’s Fable 5 to claim a counterexample to the Jacobian conjecture, a nearly 90-year open problem in algebraic geometry. Experts warn that a single counterexample, while notable, is not equivalent to a full proof and may offer limited insight, though the episode underscores AI’s potential in assisting mathematical research and discovery, with discussions also touching on OpenAI’s related progress.

AI-Engine Counterexample Cracks Century-Old Jacobian Conjecture
science19 hours ago

AI-Engine Counterexample Cracks Century-Old Jacobian Conjecture

Mathematician Levent Alpöge used Anthropic’s Claude Fable 5 to forge a concrete three-variable polynomial with Jacobian determinant -2 that is not invertible, producing a verifiable counterexample to the Jacobian conjecture (pending arXiv peer review); the episode underscores AI as a genuine research collaborator and highlights the rise of formal verification like Lean in AI-driven mathematics.