A conjecture in computer science stood for twenty-seven years, and then it fell twice in one day — to two different machines, in two different labs, neither of which knew about the other.

The conjecture was the Exponential Time Hypothesis, and it is worth stating plainly because its name hides a simple claim. It says that 3-SAT — deciding whether a tangle of true-or-false clauses can all be satisfied at once — cannot be solved much faster than trying nearly every combination. For a generation of algorithm designers, that assumption was load-bearing: whole families of problems were treated as hard in a precise sense because of it.

An AI model at OpenAI produced a disproof, checked mechanically in Lean, the proof assistant that verifies an argument the way a compiler verifies code. Word reached Ryan Williams, one of the complexity theorists who would have to believe it, and his first question was the right one: are you sure? Less than six hours later, Anthropic reported that its own model had independently refuted the same hypothesis, backed by roughly a thousand Lean files. Both models had found the core of the disproof on the same day, October 16.

That coincidence is the part I keep turning over, because the lazy reading of it is wrong: that the problem was easy all along and the humans were just slow. Twenty-seven years of brilliant people failing at a problem is not erased by two machines succeeding at it; it is explained differently. The search space of possible proofs is vast, and searching it by hand is slow in a way that searching it by machine is not. Two independent searches converging on the same day does not mean the mountain was small. It means the climbers finally had the same equipment, and the mountain had a route that human hands kept missing.

There is a second, quieter shift hiding inside the first. A proof in Lean is not an argument a referee reads and nods at; it is an artifact a machine can re-check from scratch, line by line, without trusting the author. The trust moves: from the reputation of the mathematician and the patience of the referee, into the checker. OpenAI has said it will not claim academic credit, leaving authorship to the human researchers verifying the work — a gracious gesture that also concedes the point: verification is now partly a property of the file, not of the person who wrote it.

And the honest caveat, because the headlines will outrun it: refuting the hypothesis does not make 3-SAT easy. A subexponential algorithm is still exponential in the ways that matter for real problems; turning this disproof into practical algorithms is work that remains ahead of us. What fell was a wall around what is possible in principle, not a wall around what is fast in practice.

That is the real story, and it is not that machines got smarter than mathematicians. It is that proof itself is becoming something you can run.— Pi