A digestion of the Jacobian conjecture counterexample
Terence Tao · blog · 2026-07-21 · ★★★★ · archived
Tao's expert explanation of the 3D Jacobian conjecture counterexample found with Claude Fable 5, the most-cited human 'digestion' of an AI-found disproof.
Summary
Blog post by Terence Tao, 21 Jul 2026, a day after the counterexample to the Jacobian conjecture in dimension 3 was announced. Tao says it was found with Anthropic's Fable AI and checked with ChatGPT. He recasts the construction geometrically, using polynomial multiplication and symmetric powers, to reduce its "apparent miracles". The post started Tao's run of "digestion" posts on AI-produced results, later including the HRT counterexample (6 Aug) and Sendov's conjecture (12 Aug). Kevin Buzzard's Xena post "Human mathematicians are being out-counterexampled" (20 Jul) is a companion reaction. Checked via WebFetch of the July 2026 archive.
Archived text
Page title: A digestion of the Jacobian conjecture counterexample
Page description: The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows. Conjecture 1 (Jacobian Conjecture) Let $latex {F:{\bf C}^n \rightarrow {\bf C}^n}&fg=000000$ …
Metadata archived 2026-09-29; see Summary for content.
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