Jacobian Conjecture

Anthropic's Claude Fable 5 built a degree-seven map with constant Jacobian -2 that still sends three different points to one output, breaking an 87-year-old conjecture's promise that such maps must be reversible.

Tao's post rebuilds that construction piece by piece rather than calling it a miracle, and admits he leaned on an AI chatbot to check his own math.

One longtime commenter said the write-up lost him at the algebra, and pointed everyone to Tao's own chat transcript instead as the clearer explanation.

The map: three polynomials in three complex variables, Jacobian determinant exactly -2, sending three separate points to one identical output, the exact collision the conjecture rules out.

One top reply wasn't about the math: it noted the announcement describes two people and a model working together, not a lone AI feat. Mathematicians split hard, from "sweeping up easy leftovers" to "we're a bit fucked."

PhD students are now expected to pay $200 a month for access to models like Sol and Fable — Harvard already comps the subscription for every student, postdoc and faculty member in its math department.

Not everyone in the thread is impressed: one commenter dug into the Jacobian conjecture's citation history and found mathematicians had already bounded the search space by 1983 — the AI didn't discover new territory, it just finally searched it.