Peter Ash has a nice blog about mathematics and education, and he has given a nice review of what appears to be an interesting book in a blog post about "Poincare's Prize". Here is the intro of his post, to tickle your interest:
I recently read Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles by George C. Szpiro. I recommend it highly. Some time back I recommended another book on the same topic, The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O'Shea. If you can only read one book on the topic, I recommend the Szpiro book.