Multiple answers have mentioned books by Dieudonne. I can recommend one more: Mathematics- The Musics of Reason (Springer, 1992) or the French original Pour l'honneur de l'esprit humain: les mathématiques aujourd'huis (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.
Igor Khavkine
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