Professor Stewart's Cabinet of Mathematical Curiosities

This book, written by Professor Ian Stewart, is possibly one of the best books I have ever read. Despite this, it has a format quite unlike an ordinary book; it has no coherent theme, and is full of tricky, and sometimes unsolved, math problems. When I first picked it up, I read the first few problems, and was about to set it down when I decided to flip just a few more pages ahead, and fell upon an essay about Fermat's last theorem.

What had at first had seemed like a book full of trivially simple math and logic problems had another side. I bought the book, and I'm very glad I did. Stewart does an amazing job of mixing those first few trivial problems in with harder ones, and ones so hard that it makes your head hurt just thinking about it. Interspersed thought this are short essays about various unsolved (or previously unsolved) math problems, colorful biographies of Gauss and Euler, and simple but thought provoking explanations of topology or just mathematics in general. About halfway through the book, I realized how much I was learning: random math factoids, the importance of unspoken assumptions in proofs, the Poincare' conjecture: each new paragraph contained some new, fascinating jewel. Though all of this I could not help but be reminded of the closing paragraph of Innumeracy, by John Allen Paulos.
The discrepancies between our pretenses and reality are usually quite extensive, and since number and chance are among our ultimate reality principals, those who possess a keen grasp of these notions may...more easily become subject to feelings of absurdity. I think there's something of the divine in these feelings of our absurdity, and they should be cherished, not avoided

I think that this kind of book is exactly what Paulos had mind when he wrote of the widespread innumeracy in modern culture; Stewart's book is an ambassador of the “warmly rational” sense of wonder that can come from taking a closer look at even the most mundane and boring of situations.

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