University of Toronto mathematician Daniel Litt joins Bain Capital Ventures partner Slater Stich to break down a landmark moment in mathematics: an AI model's disproof of the Jacobian conjecture, and what it suggests about how much low-hanging fruit is still hiding in plain sight.

Daniel Litt works in arithmetic geometry at the University of Toronto, where he explores the interplay between algebraic geometry and number theory. In the second episode of Begin Proof, he talks with Slater Stich about a counterexample that upended a conjecture first posed in 1844, and what it means for a field that has historically measured progress in decades, not days.

The conversation starts with the proof itself. Litt walks through the construction behind the counterexample: a multiplication map between simple polynomial spaces, with a few carefully chosen deletions. Once explained, the argument takes mere minutes to verify.

The fact that this geometric insight sat untouched for nearly two centuries–in one of algebraic geometry's most-studied objects, no less–is an anthropological effect, according to Litt. Mathematicians believed the conjecture mostly on the strength of a long absence of counterexamples, rather than any real positive evidence in its favor. He points out that this is different from a case like the Riemann hypothesis, which fits into a dense web of other verified predictions. The Jacobian conjecture never had that kind of support. It was simply an old, isolated problem that people assumed was true because it had gone unchallenged.

Litt also thinks mathematicians rarely search a conjecture exhaustively for holes. Work tends to follow ideas opportunistically, drifting toward whatever direction feels promising rather than systematically stress testing a given claim. He compares it to a kind of Brownian motion through a very high dimensional space of possible arguments, a process bound to miss things. His expectation is that current models are running a similar undirected search, just with far more patience for trying dead ends.

The insight means that a number of well-known, long-standing conjectures may be resolvable with ideas mathematicians already have, if someone is willing to grind through the search space. Models are well suited to exactly that kind of work. They do not tire, and they will attempt hundreds of variations that a human mathematician might abandon after a handful of tries.

He is careful to draw a line between that kind of progress and genuine conceptual breakthroughs. Problems like the Riemann hypothesis or the Hodge conjecture are not attention bottlenecked. They require new mathematical ideas that current models have not shown any sign of producing. What is changing, in Litt's view, is the space in between: the isolated, technical corners of math where a wrong belief has gone unchallenged simply because too few people were looking.

For Litt, the more interesting question is less about whether models can prove theorems and more about what their aesthetic and research instincts reveal about how mathematics itself gets done, and how much of that process still depends on human judgment that is hard to measure.