A 167-year-old riddle about where the zeros of one function stand. The prize is a million dollars. The real prize is bigger: the key to the rhythm of the primes.
Picture a coastline where lighthouses switch on in what looks like disorder. The hypothesis claims every one of them stands on the same line along the shore. We have seen billions of lighthouses and every single one is on the line. But billions of examples are not a proof, only an absence of counterexample.
Why anyone outside mathematics should care: primes are the bricks of arithmetic, and the cryptography your bank uses to guard your money stands on their unpredictability. The rhythm of the primes is tied to these zeros. Understand the zeros and you understand the rhythm.
Where things stand
Progress is measured in bounds. In 2026 a system built on Claude raised the proven lower bound for the share of zeros on the line from 41.6% to 67.2% - by combining published human techniques and passing machine verification. The hypothesis remains unproven. The bar beneath it moved up, and that is real, verified progress.