Terry Tao publishes a geometric digestion of the Jacobian conjecture counterexample

Sources: Terry Tao blog, HN discussion
Summary: Terence Tao posted an explanation of the recent counterexample to the Jacobian conjecture in three dimensions, reformulating the degree-seven polynomial map through symmetric powers of homogeneous polynomials and a resultant normalization to show why its cancellations work. He presents the counterexample as established mathematics rather than expressing doubt, and discloses that he used an AI chatbot to discuss the problem and confirm several calculations, without attributing the underlying geometric insight to the AI. The counterexample itself was posted 2026-07-19 by Levent Alpoge and credited to Anthropic's Claude.
Why it matters: A leading mathematician independently reconstructing and confirming the map is the strongest validation yet of an AI-credited proof result, and separates a verifiable outcome from the unverified prose-proof claims earlier this month.
Follow-up: Watch for a formal paper, wider expert acceptance, and clarification of the model's role versus the human mathematicians.