Is God a Mathematician?
by Mario Livio
Simon & Schuster, 2009
"How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?" A. Einstein.
The is an excellent book that discusses two philosophical points about mathematics: Was mathematics invented or discovered? and why is mathematics so unreasonably effective?
Starting with the ancients, Pythagoras, Plato and Archimedes and continuing through Descartes, Newton, Leibniz up to the present time, Dr. Livio interweaves the work and thoughts of mathematicians and philosophers about where mathematics comes from and why it works so well. The many examples of mathematics discovered (or invented) long before there was any practical use for it add a facinating depth to the discussion (e.g. hyperbolic geometry there ready when Einstein needed it for General Relativity).
Many of the "popular" books on math and science available today are really just so much fluff; this one is not. It is a very good and intelligent discussion understandable to anyone. It will help your students (and you too) to get a much broader view of mathematics in all its bredth and depth.
Dr. Livio is an astrophysicist. He has written several other books that I have read and recommend: The Equation That Couldn't Be Solved (Galois, symmetry and groups) and The Golden Ratio. He also wrote The Accelerating Universe that I plan to read soon.
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