How to Get a Fable CoT for the Jacobian Conjecture Refutation
Details
- External ID
- 48986943
- Source
- HN
- Company
- —
- Product
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- Website domain
- —
- Launched
- July 21, 2026
- Cohort
- —
- Upvotes
- 7
- Upvotes percentile
- 0.3972520908004779
- Tags
- —
- Fetched at
- Sept. 7, 2026, 9:26 p.m.
- Updated at
- Sept. 7, 2026, 9:26 p.m.
Description
Since the publication of the Jacobian Conjecture refutation, many people have asked for a Chain of Thought to be published so they can better understand the mathematical intuition that leads to the counterexample.Since none was published, I tried to "clean room reverse engineer" it: give one Claude Fable the result and ask it to generate a writeup of how to arrive at it without any spoilers, then ask a second Fable to follow the write up, if it's too easy remove details, if it's too hard add hints. I could have simplified further, I stopped because it's time to sleep, and I'm sharing because it gave me some intuition for what's going on.This is what a successful run looks like (sadly Anthropic hide Chains of Thought):https://claude.ai/share/80526d56-1c23-407d-8f5c-59a704221454## IntuitionThis is my understanding of the interesting ideas (probably too summarized for Fable to consistently get it without a good harness; take with a grain of salt, I'm not a mathematician; later there is a full prompt that was tested and contains everything needed):* No Bass–Connell–Wright or Drużkowski normal forms (those are reparametrizations that feel natural in this search but they turn low-complexity examples into high-complexity by trading off degree vs dimension, and the counterexample is low complexity)* Look in C^3, not C^2, C^2 is probably not interesting enough* Look for a 3:1 cover, not 2:1, there's some result due to Euler (as always) that shows 2:1 will not work* Look for a composition of two functions (a ratio of polynomials and a shear) that have Jacobian determinants `x` and `c/x` everywhere, except at `x=0` (do the standard trick for not defining at a hole and shoving all the problems into that one hole, that's where the `1 + xy` comes from)## Prompt for reproducing CoTHere: https://gist.github.com/SonOfLilit/8882a145048ba260b160568ba...
Enrichment
- Theme
- scientific computing and deep tech tools
- Vertical
- Horizontal
- Function
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- Audience
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- AI stance
- —
- Project type
- Hobby / open-source project
- Normalized one-liner
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- Manually corrected
- False
Could you build this?
No This concerns theoretical mathematical research and formal reasoning around the Jacobian Conjecture, which requires deep algebraic geometry domain expertise.
What it would actually take: Constructing or refuting counterexamples to the Jacobian Conjecture requires deep specialization in polynomial automorphism groups, affine algebraic geometry, and differential algebra. Exploring this with LLMs demands rigorous verification tools (such as Lean, Coq, or computer algebra systems like Macaulay2) and mathematical reasoning far beyond standard prompt engineering or coding assistants.
Discussion
2 comments analyzed.
Concerns raised: Difficulty creating effective prompts without mathematical expertise, Prompts are too dense and complex to write
Feature requests: Better prompt generation assistance for non-experts, Simplified or guided prompt creation process
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Launched 263 days after the earliest competitor.
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