Jacobian Conjecture
AssessTechniques
A long-standing open problem in algebraic geometry about when polynomial maps with constant nonzero Jacobian are invertible.
Why it's here
Placed in Assess: 3 article(s) of evidence from 1 source(s), led by research-stage coverage, with 3 in the last 30 days. Confidence 36%.
Evidence (3)
- 4Hacker News·8/3/2026researchDomain expertise makes LLM prompting more effective
The post argues that the biggest skill in using LLMs is not generic prompt engineering, but deep domain knowledge. Using Terence Tao’s discussion with ChatGPT about the Jacobian Conjecture counterexample, it shows how expertise helps users ask better questions, spot issues, and steer the model toward useful answers. It also suggests that as models improve, human expertise remains important because the main bottleneck is often expressing the right problem to the model.
- 7Hacker News·7/21/2026researchTerence Tao Explains a Counterexample to the Jacobian Conjecture
Terence Tao published an expository post digging into a recently found counterexample to the Jacobian conjecture in three dimensions. The article reframes the construction in geometric terms and explains how local injectivity can fail to imply global invertibility in this setting. The conjecture remains open in two dimensions.
- 8Hacker News·7/20/2026breakthroughClaimed Counterexample to the Jacobian Conjecture
A Hacker News post claims that Claude Fable produced a polynomial map from C^3 to C^3 with Jacobian determinant -2, presented as a counterexample to the Jacobian Conjecture. The post also suggests related implications for the Dixmier Conjecture and Poisson Conjecture, though the claim appears to be presented informally on social media rather than in a peer-reviewed publication.