Math Geek: From Klein Bottles to Chaos Theory, a Guide to the Nerdiest Math Facts, Theorems, and Equations
A math geek is a person with a particular interest in mathematics. If `particular interest' means that the geek sees mathematics in everything, or finds every occasion fit to tell a math-related story, then this is definitely a math geek book. However, one should not mistake it in a nerdy or guru sense. Rosen succeeds to write a math geek book but almost without proper mathematics in it. Formulas are hardly present. The reference to mathematics is a description of a concept, triggered by some fact of our daily lives, but only in rather general terms. Sometimes the `mathematics' is just restricted to a remark in the style of `in mathematics this is called...' or `mathematicians have studied this and found...', but the mathematics itself is left out. If the subtitle mentions `a guide to the nerdiest math facts' it has to be understood as math facts for the non-mathematician. The proper mathematics are carefully shooed away. Just like Steven Hawking and other cosmologists can write or lecture about the astonishing and marvelous things happening in our universe without ever showing you how they solve the complicated mathematical equations, Rosen writes about mathematics essentially avoiding all the `difficult stuff' of proper mathematics.
Rosen, a science writer, not a mathematician himself, has collected here 100 short `facts' described on one to three pages and ending with some afternote. The title of each item attracts the attention. A subtitle tells you to what mathematics it is related. Each item is a brief snack, a bite to be taken in a short moment of idleness. Somewhat like a block calendar with lightly digestible almanac data printed on its leafs. There exist coffee-table books about mathematics. Usually large size, thick, on glossy paper and with many colorful illustrations. This book is exactly the opposite. Small, light, handy format, no colors, few but effective illustrations. It is a toilet-book in the most positive sense of the word.
Many of the items will be known to people who are already familiar with popular math books. Some examples: fractals and self-similarity in nature, should one walk or run in the rain to catch the least rain, origami, slicing pizzas, golden ratio, juggling, public key encryption, pi, Monty Hall problem, etc. They are organized in four parts: shapes, behavior, patterns, and special numbers. Let me take a less obvious but representative example from each of these four parts.
`There's math behind your tangled cords' (about knots). Ear phone cords, Christmas lights, etc. have the tendency to knot because there are many more configurations resulting in knots than there are to remain untangled. This has been investigated in knot-theory: what kind of knots appear most frequently, how this depends on the length. The afternote just mentions that industry has invented several methods to avoid tangling of the cords of telephones in the pre-mobile era.
Most efficient checkout line in a supermarket (queuing theory). Erlang, a Danish engineer studied the optimal number of telephone lines to avoid long queues in the ear of manually operated switching boards. The erlang is till used as a unit in telecommunication or in traffic. Mathematicians have found that one line of serpentine queuing for multiple counters is better than individual lines for each counter. The afternote suggests that if you have the choice between left or right in a queuing situation, it might be better to choose left because most people are right-handed.
`Mathematical patterns in Van Gogh's paintings' (about turbulence). Some of his paintings like Starry Night show swirling patterns, similar to turbulence patters which are studied by mathematicians in fluid dynamics. In fact the paintings have been analysed and the swirls satisfy equations formulated by Kolmogorov. The afternote is a short biographical note about Kolmogorov.
`Do cicadas use math to protect their species?' (prime numbers). These animals spend most of their lives under the ground, but emerge every 13 or 17 years to mate. These prime cycles are intended to outsmart their predators. Because this reduces drastically the probability that those will have the same cycle. The afternote is about Japanese bamboo that flowers every 120 years. The idea is that with such a long period in between, the rodents that feed on them will have died out in between flowerings. Ti is thus also a system to control the rodent population.
These samples should illustrate that this is all `light-weight' mathematics, all complications are kept at a `safe distance'. By reading the book, you might get the impression that mathematics is mostly frivolous `spielerei', which of course it isn't. However it certainly illustrates that it is not difficult to see mathematics is omnipresent in the sense that patterns, shapes, regularities and laws appear everywhere. Of course cicadas don't `do' mathematics, and Van Gogh never studied turbulence, but it is the task of mathematicians to catch these mathematical laws in models which can be used to analyse the phenomena involved. But that is where real mathematics and real mathematicians are needed. If this book can contribute in getting youngsters interested in a mathematical career, it should get the widest possible circulation. Every household should have one on the toilet shelf.