The contrarian take comes from Timothy Gowers, the British mathematician who won the Fields Medal in 1998.

Lately Gowers laid out the most striking AI math results of the past few months and noticed something remarkably consistent. Jacobian conjecture? Find a counterexample. The Erdős unit distance conjecture? Find a counterexample. The non-sofic group problem? Construct a case nobody had found before. Multicolor Ramsey numbers? Again, the core move was constructing a new object that satisfies the requirements.

Human mathematicians ask: why does this result hold? The AI, in effect, asks first: does it actually hold?

So why do AI systems keep diving into the counterexample pile when they tackle open conjectures?

First, a distinction worth making: the "counterexamples" Gowers refers to are not the proof-by-contradiction technique taught in school. Reductio is a proof strategy — assume the claim is false, derive a contradiction, and thereby prove it true. What Gowers describes is blunter. If someone claims every object with property A has property B, the AI only needs to pull one object out of the pile that has A but clearly lacks B. Done. The conjecture dies on the spot.

It is no surprise Gowers noticed the pattern, because several of the most celebrated AI math breakthroughs lately were produced exactly this way.

Take the Erdős unit distance problem, which an internal OpenAI model worked on last month. For nearly eighty years, the field had converged on a growth estimate that most research simply assumed — a lot of work aimed at proving it. The AI did not push further along that decades-old human path. Instead it spent a large share of its reasoning budget on a different question: could the estimate simply be wrong, and is there a counterexample?

There was. The model imported a toolkit from algebraic number theory into discrete geometry, built a whole family of point sets over more intricate number fields, and produced unit-distance counts that grow faster than anyone had expected. A decades-old belief, punctured by one concrete construction.

What amused mathematicians most was tracing its reasoning afterward: a large share of the time really did go into trying constructions and hunting for counterexamples.