There is a certain class of mathematical problem whose importance grows rather than diminishes with the passage of time. The Riemann Hypothesis belongs firmly in this class. Proposed in a single eight-page memoir by Bernhard Riemann in 1859 — a paper titled Über die Anzahl der Primzahlen unter einer gegebenen Größe ("On the number of primes less than a given quantity") — it has resisted the sustained assault of brilliant mathematical minds across four generations. It stands today as one of the seven Millennium Prize Problems, carrying a one-million-dollar reward from the Clay Mathematics Institute, and it is the only one of those seven with the added distinction of appearing on Hilbert's famous 1900 list of problems for the twentieth century.

...