Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
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Mathematician Terence Tao uses ChatGPT to rederive a known Jacobian Conjecture counterexample.
Tao shares a ChatGPT conversation where the LLM helps verify that a polynomial map from a5-dimensional hypersurface X is isomorphic to affine 3-space. The assistant confirms that composing this map with a further polynomial yields a map G: C^3 -> C^3 with constant Jacobian -1, which matches the known counterexample to the Jacobian Conjecture up to linear coordinate changes and output rescalings. The original counterexample has Jacobian -2.
The conversation shows the LLM performing symbolic verification, deriving explicit polynomial formulas, and connecting the construction to the published result.
What commenters are saying
Commenters are impressed by the LLM's role as a colleague-level assistant, not just a tool. Some question whether this is true intelligence or just fast symbolic computation. A top comment asks about real-world consequences, with several noting the Jacobian Conjecture attracted many false proofs over decades, making this a notable non-trivial example of AI-assisted mathematical discovery.
Others note that LLMs are increasingly capable of automating grindy intellectual work, but this specific result is primarily of mathematical interest rather than practical impact.