It's very difficult to write a book about a maths problem so difficult that it has resisted the efforts of Mathematiaians for nearly 150 years, but still make it interesting and intelligble to the layman. But Professor du Sautoy manages this very well. He does it by focussing on the individuals involved - larger than life characters such as Bombieri, Erdos, Hardy and the like - and making us sympathise with their goals. Riemann himself only lived to 39 so does not come alive to the same extent.
At the same time he gives sufficient description of the problem itself, and more importantly why in the "real world" it matters, so that the reader feels she / he understands it.
The understanding may fade over a few days, but the fascination and the hope that one of the "heros" wins the $1m prize for finally finding the solution, lives on.