Terry's session is his attempt to understand Fable's counterexample to the Jacobian Conjecture, not an attempt to solve any open problem.

Levent Alpöge's prompting that did solve this open problem does not appear to be public, but Aaron Lou at OpenAI succeeded in reproducing the result the next day using an internal version of Codex and (reportedly) without web search, and he shared his prompt at https://aaronlou.com/jacobian_counterexample_prompt.pdf. It is a mathematically-sophisticated statement of the problem and of general search strategies, but contains no concrete ideas for the solution whatsoever (even the idea to look for a counterexample instead of a proof).

Aaron reported that this 2-page prompt found a counterexample in one shot. (https://x.com/aaron_lou/status/2079222629794189515)