THE TWEET
hello there the jacobian conjecture is false
@_alpoge_ dropped the counterexample: a map ℂ³ → ℂ³ with jacobian determinant −2 that sends three distinct points to a single point. Non-injective. Conjecture: falsified. Timeline: unhinged.
Thanks to akhil for asking, fable for working through the world cup final, and an LLM for keeping up.
levent
@_alpoge_
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy)(4+3xy),
y + 3x(1+xy)^2 z + 3x y^2 (4+3xy),
2x − 3x^2 y − x^3 z) : ℂ³ → ℂ³
jacobian determinant = −2
(0, 0, −1/4), (1, −3/2, 13/2), (−1, 3/2, 13/2)
↦ (−1/4, 0, 0)
3:19 AM · Jul 20, 2026
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