Claude Code and the Jacobian Conjecture Counterexample

A developer's two-year pipeline, released under CC0, enabled Anthropic's Claude Code to produce a counterexample to the Jacobian Conjecture, a long-standing mathematical problem. The implementation, documented in a public GitHub repository, models specific mathematical boundaries based on research published in Nature Communications. The mathematical community is now analyzing the structures developed as part of this counterexample.

Claude Code and the Jacobian Conjecture Counterexample Claude /en/tags/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. Next Context Engineering: Why More Tokens ≠ Better Code → /en/threads/3078/