Multiple answers have mentioned books by Dieudonne. I can recommend one more: [_Mathematics- The Musics of Reason_][1] (Springer, 1992) or the French original [_Pour l'honneur de l'esprit humain: les mathématiques aujourd'huis_][2] (Hachette, 1987). Its stated purpose is to give a generally accessible account of major mathematical developments after 1800, of which it does a remarkably good job.


  [1]: http://books.google.se/books?id=lQosnIw05dYC
  [2]: http://www.amazon.fr/dp/2010119509