Exploring a Counterexample to the Jacobian Conjecture

Terence Tao's ChatGPT Conversation

Hacker News Discussion

2025

848

Hacker News Points

A viral discussion about AI and mathematical discovery

The Jacobian Conjecture

01

Long-standing Problem A famous unsolved problem in algebraic geometry since 1939
02

Deceptively Simple States that if a polynomial map has constant Jacobian determinant, it has an inverse
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Resistant to Proof Despite numerous attempts, no proof or counterexample has been accepted
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High Stakes Resolving it would advance our understanding of polynomial mappings

04

How Terence Tao engaged with ChatGPT on a proposed counterexample

ChatGPT can help mathematicians explore ideas,
but rigorous proof still requires human insight and verification.

Terence Tao

psychology

ChatGPT served as a sounding board for exploring the counterexample's logic

fact_check

The proposed counterexample required careful human scrutiny to validate

lightbulb

AI can suggest angles that prompt fresh mathematical thinking

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AI suggests potential approaches or counterexamples

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2

Mathematician tests and refines the ideas through dialogue

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3

Rigorous human analysis validates or rejects the claim

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4

Peer review ensures correctness before acceptance

AI tools are transforming how mathematicians work—but human insight remains essential

Source: chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed56