John D. Barrow — One Hundred Essential Things You Didn’t Know you Didn’t Know: Maths Explains Your World — Norton, 2008, 284 pp. ISBN 978-0-393-07007-1
This isn’t really a math book; there’s hardly any real math, it’s rather a book about math, or maybe more a book about math in our daily lives, more precisely about things that are indeed solved by maths in our daily lives. The reader needn’t a very high level of knowledge about mathematics to enjoy the read. If it contains several little gems1, it also contains a number of chapters (as each of the 100 things you didn’t know you didn’t know is presented in a standalone chapter) that aren’t all that interesting. Still very much worth the read, though.
1 One I like particularly is the trick proposed by von Neumann to transform a biased coin into a fair coin. Let’s say we have a coin that lands on head with probability and on tail with probability (both quite far from ). Von Neumann observes that if you throw the coin twice, it will land twice on heads with probability , twice on tails with probability . But head followed by tail and tail followed by head have the same probability of . The quantity isn’t , but if each time we throw two consecutive heads or tails we “forget” them, keeping only the draws with one head and one tail (HT or TH), we get an unbiased, or fair, coin. Suffice to map HT to heads and TH to tails (or vice-versa) and we’re done.