Review of "You are a Mathematician" by David Wells

Nick Todd, Wellington College

Twenty-five years ago the only mathematics books which one could easily buy were either text-books or the Pelican Books by Martin Gardner¹ and by W. W. Sawyer². Nowadays, following the success of "The Brief History of Time", there is a plethora of popular science books including quite a few which popularise Mathematics. Many are excellent and enjoyable, notably those written by Ian Stewart³, but none can compare with "You are a Mathematician" by David Wells.

 While the others usually provide a tour of the curious, interesting and recent areas of mathematical knowledge, this book tries to involve the reader by making him or her actually do mathematics. Wellsís premise is that Mathematics is not a spectator sport and that the age old question, "What is Mathematics?", can only be answered by making the reader think like a mathematician. This is an ambitious objective, but for those readers who are prepared to work this book certainly achieves it.

 The reader definitely has to think and that perhaps is a difficulty. This book is not an easy book and many of the concepts and ideas are beyond the general reader who is interested in mathematics. Every chapter has up to a dozen problems which the reader is asked to think through -- these are not trivial, although Wells does provide clear and concise answers at the end of each chapter. For example, the first problem in chapter 4 is, "If x and y are any two different positive numbers, which is larger, x² + y² or 2xy ?"

 The last chapter is a mathematical adventure consisting of 48 frames each of which either contains a problem or solution and ends with the direction to another frame in the adventure. The reader is invited to start and work through the problems in a manner similar to some American self-learning texts. This is not easy and considerable persistence is required -- Iíve still not finished my adventure but would love the time to complete it.

 There is old saying "you only get out what you put in" and any teacher or very good student who is prepared to work at this book will gain a lot from it. Within the field of Mathematics books I believe this will become a classic. It may not be anything like "Mathematical Recreations and Essays" by Rouse Ball, "Mathematics and the Imagination" by Kasner and Newman, "What is Mathematics?" by Courant and Robbins or "Mathematics for the Million" by Hogben, but in fifty years I suspect there will be still be a small core of people who will discover it and be intrigued by it.

¹ Mathematical Puzzles and Diversions, More Mathematical Puzzles and Diversions, etc.

² Mathematicianís Delight and Prelude to Mathematics.

³ Game, Set and Math, Does God play Dice? , From Here to Infinity

Review of "The Penguin Book of Curious and Interesting Mathematics" by David Wells

Brian Greer, Queen's University, Belfast

This book contains an extraordinarily diverse collection of anecdotes about mathematicians, and quotations about mathematics, arranged according to no detectable system. (There is also a sprinkling of corny jokes, and whoever at Penguin decided the cover should depict the most blatant stereotype of an eccentric mathematician should be locked away with only a copy of Principia Mathematica to read, but these are minor blemishes).

For each extract, one or more references is provided. Here are three examples:

 When Flaubert was a very young man, he wrote a letter to his sister, Carolyn, in which he said: "Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May -- How old is the captain? "

 "By keenly confronting the enigmas that surround us, and by considering and analysing the observations I had made, I ended up in the realm of mathematics. Although I am absolutely innocent of training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists" (Escher)

 Charles Babbage, inventor of the Difference Engine, a forerunner of modern computers, was interested in mechanisms as a small child. As he records, "My invariable question on receiving a new toy, was 'Mamma, what is inside it?' Until this information was obtained those around me had no repose, and the toy itself, I have been told, was generally broken open if the answer did not satisfy my own little ideas of 'the fitness of things'."

 I would recommend this book for anyone as an antidote to the all-too-common perception of mathematics and mathematicians as devoid of cultural, aesthetic, humorous, emotional, spiritual -- in a word, human -- qualities.