Jacobian
AssessTechniques
A mathematical tool used to identify the internal J-space patterns.
Why it's here
Placed in Assess: 4 article(s) of evidence from 1 source(s), led by research-stage coverage, with 0 in the last 30 days. Confidence 40%.
Evidence (4)
- 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.
- 7Hacker News·7/6/2026researchClaude Study Finds a Global Workspace-Like Internal Representation
Anthropic reports evidence that Claude has developed a small set of internal neural patterns, called the J-space, that appear to support conscious-access-like functions such as reporting, silent reasoning, and flexible task use. The paper argues this resembles the neuroscience theory of a global workspace, where a limited shared channel makes information available across systems. The finding is presented as an interpretability result about how language models represent and use internal concepts.