A tweet says Claude Fable just broke an 87-year-old math conjecture

What Alpoge actually posted: a Jacobian determinant of -2, no arXiv paper in sight

The Jacobian Conjecture claims that any polynomial map with a constant, nonzero Jacobian determinant must be invertible everywhere it's defined. On July 20, mathematician Levent Alpoge posted a map, three polynomials in the complex variables x, y and z with Jacobian determinant exactly -2, that sends three separate points, among them (0, 0, -1/4) and (1, -3/2, 13/2), to the identical output. If the arithmetic checks out, the map isn't invertible, and the conjecture falls.

Alpoge credited two collaborators in the post: a friend named Akhil, "for asking about it," and Claude Fable, for doing the work "during the world cup final." He put the result on X, mirrored to xcancel.com, rather than arXiv or a journal. The conjecture also has proven equivalences: the Dixmier Conjecture for the third Weyl algebra and the Poisson Conjecture both fall with it, a link several commenters in the HN thread worked out independently within the first hour.

The correction that beat the celebration: "Fable" didn't do this alone

One of the most-read replies zeroed in on the announcement's wording, not its arithmetic.

"So where does it say that Fable 'produced' the counterexample? The tweet says it was a collaboration between two people, using Fable."

— a commenter who went back and checked the tweet's exact wording

The poster had already undercut his own moment, framing the search as "classic crank graveyard territory," mathematician slang for the pile of amateur disproofs that turn out to be wrong. A reply ran further with that admission:

"As @alpoge himself notes this is classic crank graveyard territory and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search. Wild!"

— a commenter quoting the poster's own admission

That kind of walk-back is an old pattern for this specific conjecture, not a new one: an engineer in the thread traced the claim back to Wikipedia's own footnote noting the conjecture is "notorious for the large number of published and unpublished proofs that turned out to contain subtle errors."

Independent checks did surface in the thread. One commenter fed the exact polynomials to GPT-5.6 Sol, which ran them through symbolic algebra and reported "no algebraic catch," adding that the result "deserves serious independent checking rather than casual dismissal." Nobody in the thread claimed a formal, peer-reviewed proof existed. Multiple independent systems, checked separately, kept returning the same arithmetic.

The mood among mathematicians: relief for some, dread for others

Not everyone in the thread was cheering.

"Speaking as a mathematician, it does seem like we're a bit fucked as a community. Anything that is at all accessible to currently existing methods and mathematical infrastructure is probably going to fall to the frontier models of today."

— a mathematician commenting under the thread

Nobody in the thread, including Alpoge himself, described how Fable actually found the map. Days into the thread, one reply reframed the whole choice of venue instead of the math:

"The most interesting point is that he chose to simply post it on X, instead of pretending it was his own result and posting it on arXiv. Respect for this spirit. Is this not also a sign that the old academic journal system is already outdated?"

— a developer based in China, replying days later