Secondary title: "How mathematical genius discovered the language of symmetry"
This is a typical "popular math" book, following a single unifying concept and on the way telling interesting stories from the history of mathematics.
The unifying concept of this book is symmetry and group theory. The author tries to show how many aspects of life are connected through the concept of symmetry - music, art, mathematics, the appearance of animals and humans, physics and so on. While the book is generally well written and easy to read, I find the author's attempt to unify everything under symmetry unsatisfying.
While symmetric transformations in mathematics are easily modeled and explored using group theory, it doesn't work the other way around. Not everything that can be computed with group theory has something to do with symmetry. So each time the author shows how some concepts are explained by group theory (for example some properties of quarks in particle physics) and mentions that it is another proof of "symmetry underlying everything", I flinch. Perhaps I have misunderstood something, but then it shows a problem with the book which was written for laymen (and I'm more math-savvy than the average reader).
Moreover, this book lacks in depth in several crucial places, and this also reduces the fun. For example, after a long discussion of the race to solve the cubic equation, the author just mentions in passing that the solution was found, without showing anything from it !
Nevertheless, this book is still quite fun to read. Here are some interesting facts I learned from it, in no particular order:
- All human chromosomes come in pairs, which helps them fight damaging mutations by swapping genes. The male sex chromosome Y, however, lacks a partner. So it "uses" a fascinating trick to combat mutations - a large share of its genes come in palindromic sequences ! This is a very simple, yet effective, way of error detection.
- All moving animals have a concept of "front" (the direction where they move) and "back" (the direction from where they move). The Earth's gravity creates a clear distinction between bottom and top. However, there is nothing major to distinguish between left and right. This explains why most animals have right-left symmetry, but not front-back or top-bottom. Interestingly, anchored life forms like starfish don't have the front-back distinction, so they are symmetric in that dimension as well.
- There's a very entertaining description of mathematical competitions in the 16th century. People would compete by solving various equations. This really reminds of today's math and computer programming olympiads.
- A cool quote by the historian Morris Kline: Premature abstraction falls on deaf ears
- A brief and interesting explanation of why the speed of light is constant: The constancy of the speed of light to all observers eliminates such paradoxes in which effects precede their causes
All in all, this is an average book. While it contains some interesting tidbits of information, one's reading time can be spent better.
Eli Bendersky's website