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I read:

H. Poincare. Value of science

F. Klein. Development of Mathematics in the 19th Century

J.E. Littlewood. A Mathematicians Miscellany

G.H. Hardy. A Mathematician’s Apology

R. Courant, H.Robbins. What Is Mathematics?

V.I. Arnold. Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians.

What else? The author must be an influent mathematician and the book must not be "just another popular math book".

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    $\begingroup$ André Weil's "Souvenirs d'apprentissage" (English translation: The Apprenticeship of a Mathematician) is a book I like. $\endgroup$
    – user9072
    Commented Jan 29, 2015 at 0:03

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Geometry and the Imagination by David Hilbert and Stefan Cohn-Vossen.

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Not sure if it counts, because not a math book, but

  • Alice's Adventures in Wonderland by Lewis Carroll (Charles Lutwidge Dodgson)
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