Woofun AI reports that Anthropic researcher Levent Alpöge utilized Claude Fable to identify a three-dimensional counterexample to the Jacobian Conjecture, a problem unresolved since 1939. The generated polynomial mapping possesses a Jacobian determinant of -2 yet maps three distinct inputs to identical outputs, proving non-invertibility. Subsequently, OpenAI researcher Aaron Lou confirmed that Codex independently derived a fundamentally similar counterexample in an offline setting.

While this capability allows for rapid scanning of previously exhaustive mathematical directions, it introduces significant risks. Models may generate incorrect proofs, shifting academic challenges from discovery to verification. More critically, if AI discovers efficient algorithms for factoring large integers or solving discrete logarithms, foundational cryptographic systems like RSA and elliptic curve cryptography could become vulnerable, necessitating an emergency update of global encryption standards.