Claude Code and the Jacobian Conjecture Counterexample

Finding a counterexample to the Jacobian conjecture is a massive mathematical milestone, and it turns out Claude utilized a pipeline I spent two years building to get there. I released this implementation under CC0 about a month ago, and seeing an LLM apply it to a problem of this magnitude is a wild validation of the work.

For those interested in the technical trail, the entire development process—including logs and discussions with the original paper's authors—is documented in the repository. This wasn't a quick build; it was a deep dive into modeling specific mathematical boundaries.

The actual implementation used by Claude can be found here:

https://github.com/JGPTech/Fun/tree/main/Jacobian

If you want to see the specific commit where the package was released to the public:

https://github.com/JGPTech/Fun/commits/main/current_paper_locality_boundary_package

The logic was modeled after this specific research:

https://www.nature.com/articles/s41467-026-73900-9

It's a fascinating example of a real-world AI workflow where a human-developed tool provides the structural framework that allows an LLM agent to break through a long-standing mathematical wall. The fact that the mathematical community is now analyzing structures I developed as part of this counterexample is an incredible feeling.