Perhaps one of the following will be suitable:
Davis, Martin. Engines of Logic: Mathematicians and the Origin of the Computer. New York: Norton, 2000.
Gowers, Timothy. Mathematics: A Very Short Introduction. New York: Oxford University Press, 2002.12002.
Kaplan, Robert, and Ellen Kaplan. Out of the Labyrinth: Setting Mathematics Free. New York: Oxford University Press, 2007.22007.
Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery. New York: Cambridge University Press, 1976.31976.
Poincaré, Henri. Science and Hypothesis. 1905. New York: Dover, 1952.41952.
Whitehead, Alfred North. An Introduction to Mathematics. 1911. New York: Oxford University Press, 1958.51958.

