Puzzles
One unproven guess about prime numbers has stood for over 160 years
In 1859, Bernhard Riemann proposed a precise pattern governing where prime numbers should cluster among all the other numbers, tied to the zeros of a function called the Riemann zeta function. Mathematicians have verified the hypothesis for trillions of cases and built entire fields of number theory assuming it's true.
Reveal the answer
It's still unproven. The Riemann Hypothesis is one of the seven Millennium Prize Problems, worth $1 million to whoever proves or disproves it, and many other theorems are stated as 'true, if the Riemann Hypothesis is true' — a large share of modern number theory quietly rests on a guess nobody has confirmed.
— Bernhard Riemann, Über die Anzahl der Primzahlen unter einer gegebenen Grösse — 1859