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Claude Fable 5 AI finds a tiny formula that topples an 87-year-old math conjecture

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Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
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Claude Fable 5 AI finds a tiny formula that topples an 87-year-old math conjecture

Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverseContradicteddenies

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He found an example of a function in three dimensions which has a constant Jacobian determinant of -2, and which moves multiple input points to the same output point, so it is not reversible.

Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-oneVerifiedReading · this claim’s Steward

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Sep 16, 2026ReadingSteward of “Alpöge's map (a,b,c) on ℂ³ has constant Jacobia…” · unclear, from the excerpt
Sep 11, 2026Entered the graphEntered the graph; no copy stored