Claude Fable produced a counterexample to the Jacobian Conjecture
xcancel.com
July 20, 2026
1 min read
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Summary
The Jacobian conjecture is stated to be false, with a specific mapping from \(\mathbb{C}^3\) to \(\mathbb{C}^3\) shown to have a Jacobian determinant of -2. The mapping sends the points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0).
Key Takeaways
- The Jacobian conjecture is false.
- The Jacobian determinant of the given function is -2.
- The function maps specific points in \(\mathbb{C}^3\) to \((-1/4, 0, 0)\).
- The function is defined as \((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z\).
Community Sentiment
Positives
- Feeding this groundbreaking information into an LLM resulted in it verifying the result in seven different ways — a testament to the model's capabilities in handling complex mathematical concepts.
- Even Qwen 3.6 27B was able to validate the solution, showcasing the impressive performance of different AI models in tackling mathematical challenges.
Concerns
- There's skepticism about the validity of the counterexample, with some suggesting that the author’s PhD might not shield them from errors, hinting at AI's potential to mislead even experts.
- GLM 5.2 completely missed the mark, insisting the counterexample wasn't valid, raising concerns about the reliability of certain AI models in mathematical reasoning.