Levent Alpoge reportedly posts Jacobian counterexample, credits Claude Fable 5
Mathematician Levent Alpoge just shook up the math world by reportedly finding a counterexample to most versions of the Jacobian conjecture, a puzzle that's stumped experts since 1884 (the conjecture was first proposed in two dimensions in 1884; the all-dim version was posed in 1939).
His secret weapon? An AI model called Claude Fable 5.
Alpoge shared his "aha!" moment on X (formerly Twitter), simply posting, "Hello there the Jacobian conjecture is false," along with his counterexample.
Three-dimensional counterexample challenges Jacobian conjecture
The Jacobian conjecture basically said: if you have a certain kind of math function (with a constant nonzero Jacobian determinant), you should be able to reverse it.
But using Claude, Alpoge found a straightforward example in three dimensions where this rule breaks down: the function can't be reversed.
This suggests the Jacobian conjecture is false for dimensions higher than two, though the two-dimensional case is still unsolved.