Claude Fable produced a counterexample to the Jacobian Conjecture(xcancel.com)
700 points by loubbrad 1 day ago | 448 comments
tl;dr: A user (levent/@__alpoge__) claims that Claude "Fable" produced a counterexample to the Jacobian Conjecture, a longstanding open problem in algebraic geometry. The proposed map from ℂ³ to ℂ³ has constant Jacobian determinant -2 but is not injective, sending three distinct points to (-1/4, 0, 0). If verified, this would disprove the conjecture, which posits that polynomial maps with nonzero constant Jacobian determinant must be invertible.
HN Discussion:
  • Amazement that a small counterexample was found by AI when humans searched much harder for decades
  • Curiosity about the methodology Fable used to find the counterexample
  • Optimism that LLMs will unlock many overlooked results across science and math
  • ~Skepticism or caution about the validity of the result, noting verification challenges
  • ELI5 explanation and downstream implications (equivalent conjectures also falling)