A digestion of the Jacobian conjecture counterexample
Points and comments are a snapshot, not live.
A counterexample to the Jacobian conjecture discovered via AI Fable is retold in digestible algebraic geometry terms.
Terence Tao explains the newly found counterexample to the Jacobian conjecture (dimension ≥ 3) by restructuring it as a multiplication map on symmetric powers of C². The map (L,Q) → LQ is generically three-to-one because a cubic splits into three linear factors, yielding distinct (L,Q) pairs mapping to the same product. Tao shows how the explicit degree-7 polynomial with constant Jacobian −2 arises naturally from this geometric picture, removing the appearance of a miracle.
What commenters are saying
Commenters express awe at Tao's exposition but note the math quickly loses non-experts. Several point out the Jacobian conjecture was already widely suspected false for dim ≥ 3, so the result isn't surprising-the significance is that an LLM (Claude/Fable) found a simple counterexample. One commenter clarifies the motivation: it overturns a longstanding roadblock, not a pillar of mathematics. Another traces the example's roots to Vitushkin's 1999 rational construction, suggesting the AI built on prior work.