Claude Fable Produces a Counterexample to the Jacobian Conjecture
Claude Fable produced a counterexample to the Jacobian Conjecture
I am thrilled to announce that the Jacobian Conjecture is false, thanks to my friend Akhil for the question and Claude Fable for working on it during the World Cup final. We discovered a specific polynomial map from C3 to C3 with a Jacobian determinant of -2 that maps distinct points to the same location, effectively disproving the long-standing mathematical hypothesis.
"This is the most hilarious / horrifying problem because it is like the canonical crank graveyard."
HN discussion
- Skepticism is warranted regarding the breakthrough, as a first-year undergraduate can verify the counterexample in ten minutes using high school math and Wolfram Alpha, suggesting the result is likely a trivial error rather than a novel discovery.
- The success of connectionist neural networks at symbolic manipulation supports the view that general intelligence is an emergent property of learning, with math serving as a playground where no firewall separates symbolic reasoning from real-world cognition.
- Critics argue that deep learning models possess no true emergent capabilities, but rather rely on search and feature vectors derived from massive datasets, characterizing the field's claims of AGI as a profitable deception driven by charlatans.
- Even if the AI required expert guidance, the result remains significant because the Jacobian Conjecture has resisted solutions from human experts for over a century, proving the tool's ability to augment human capability.
- An AI researcher expresses ethical hesitation about replacing human roles with machines, prioritizing human interaction and job security over efficiency, while also noting the massive environmental cost of training GPU clusters.