mathematics ai-research computational-theory wolfram-alpha

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 $(1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z$.

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Community Sentiment

Mixed

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.