Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

TL;DR Highlight

Tao's ChatGPT conversation on a Jacobian Conjecture counterexample sparked HN debate

Who Should Read

Developers who want to use LLMs as research partners in specialized domains

Core Mechanics

The source is just a conversation link
- The article text is only the title 'ChatGPT - Jacobian Conjecture Counterexample'.
- The conversation contents and numbers are not in the source, so they are not summarized here.

Community Reactions

Short jargon-heavy questions worked
- One commenter said hard, short, jargon-heavy questions make models match the asker's level.
- Commenters noted Tao steers hard with field jargon and no softball questions.
One sentence in, three pages out
- One comment joked the session is one human sentence followed by three pages of LLM output.
- Another noted the counterexample polynomial was structured, not brute-forced.
The model pushed back and stayed on topic
- One commenter counted four caveats or corrections from the model.
- The model did Q&A, PDF ingestion, code and thinking over a long session while staying on topic, per that comment.
Keep going when the model says stop
- One commenter said ChatGPT claimed no more improvements were possible on a maze solver.
- They kept trying and got 3 breakthroughs, reaching 23 bytes solving 92.75% of unseen 2D mazes.

How to Apply

Ask short questions in domain jargon
- Write three short questions using your codebase's real terminology today.
- Compare answers against plain-language requests.
Try a new angle when the model says stop
- When the model says nothing is left, rephrase or decompose differently and ask again.
- Log the model's claim next to the actual result.

Try It

copy & run

# Paste into Claude or ChatGPT (simplified version based on usage patterns from comments; the source is only a shared link)

You are a co-researcher in {{field}}. If my assumption is wrong, push back first; if right, say 'yes, with this caveat'.

Problem: {{problem}}

1) Reframe the whole structure in another representation to find the core axis.
2) Split into small units and verify each independently.
3) Reassemble and check against the original problem.

Next: if you say there's nothing more to try, propose two different approaches.

Terminology

Jacobian ConjectureA conjecture that if a polynomial map has a nonzero constant Jacobian determinant, its inverse is also polynomial. This conversation concerns a counterexample.

counterexampleA concrete case showing a claim is false, like a failing test case.

JacobianA matrix of partial derivatives that linearly approximates a multivariable function at a point.