The Clay Mathematics Institute announced the Millennium Prize Problems to mark the 100th anniversary of David Hilbert's lecture at the second ICM. The Problems were set forth by two of the greatest mathematicians of the 20th century: John Tate and Michael Atiyah. Tate describes in his lecture three Millennium Prize Problems: the Riemann Hypothesis, the Conjecture of Birch and Swinnerton-Dyer, and the "P=NP?" problem. These questions described are among the most important unsolved problems in analysis, number theory, and theoretical computer science. His lecture gives a lucid description of the essential nature and history of these great problems. The lecture itself is a significant event in the history of mathematics, which will be sure to captivate the imagination of anyone interested in the frontiers of mathematics. The set of two lectures by Tate and Atiyah together comprise a complete description of the Millennium Prize Problems, in a style that is entertaining and easy to understand.