Overview
- Levent Alpöge, an Anthropic researcher, posted on X on Sunday that Claude Fable 5 produced a 216‑character polynomial map C^3→C^3 that has constant Jacobian determinant (reported −2) but is not injective because three different inputs give the same output.
- Multiple mathematicians checked the arithmetic by hand and with SymPy, and at least one group formalized the counterexample in the Lean proof assistant within about 24 hours, moving verification from doubt to confirmed status pending peer review.
- Experts say the result settles the conjecture in dimension three by counterexample but leaves open the deeper explanatory ‘why’ that mathematicians seek, so community unpacking and formal publication remain the next steps.
- The episode highlights a changing division of labor: models can search and produce concrete mathematical objects while human researchers focus on framing, rigorous proof-writing, and building conceptual understanding.
- The breakthrough is already reshaping investor narratives because repeated AI successes draw capital toward compute, chips, and model builders and affect crypto correlations as miners pivot to AI data‑center work.