The Millennium Prize Problems – An Overview

In 2000, the Clay Mathematics Institute announced seven unsolved problems, each with a $1 million prize. Solved: Poincaré conjecture (Perelman, 2003, but he declined). Unsolved: Riemann Hypothesis, P vs NP, Birch and Swinnerton‑Dyer conjecture, Hodge conjecture, Yang–Mills existence and mass gap, Navier‑Stokes existence and smoothness. These span number theory, algebraic geometry, topology, physics, and PDEs. One of them – the Navier‑Stokes equations – describes weather, ocean currents, and blood flow. Their solution would change mathematics.