Terence Tao's ChatGPT Solves Jacobian Conjecture Counterexample

Fields Medalist Terence Tao has shared a remarkable ChatGPT conversation that produced a counterexample to the Jacobian Conjecture - a decades-old open problem in algebraic geometry. The exchange, published as a public ChatGPT share link, shows Tao guiding the model through complex mathematical reasoning, ultimately arriving at a result that challenges long-standing assumptions in the field.

The Jacobian Conjecture, first proposed in 1939, deals with polynomial maps and their inverses. Tao's conversation demonstrates how large language models can serve as collaborative reasoning partners - not just calculators, but genuine participants in mathematical discovery. The counterexample, while preliminary, has already generated significant discussion in both the AI and mathematics communities.

This highlights a broader trend: AI models are increasingly contributing to open research problems. Rather than replacing mathematicians, tools like ChatGPT are acting as proof assistants that can explore vast logical spaces and suggest novel approaches. Tao's willingness to share the raw conversation offers a transparent look at how this collaboration works in practice - including the model's mistakes and corrections.