The Millennium Problems

In May 2000, the Clay Mathematics Institute in Paris announced that $1m prizes were being offered for solutions to each of seven unresolved problems of mathematics.

This book doesn't explain the problems in detail but rather aims to give the background that a lay reader can understand and more important why the problems themselves are considered important.

The Riemann Hypothesis - about the pattern of primes
Yang-Mills Theory - quantum physics behaviour of particles
P vs NP problem - proof that certain equations are unsolvable by computation
Navier-Stokes equations - familiar to engineers of fluid dynamics but there is no formal solution to them
The Poincare conjecture - how do you tell the difference between an apple and a doughnut?
The Birch and Swinnerton-Dyer Conjecture that builds on Fermat's Last Theorem and points to possible solutions
The Hodge Conjecture - about an obscure issue deep within abstract topology.