A Book Review

After reading the book, Why Beauty is Truth: A History of Symmetry by Ian Stewart, I have learned much of the history of mathematics. Looking at the title, I assumed that the book would focus on symmetry as we know it to be (reflections being the same, symmetries of shapes, etc), but this book focuses on symmetry found in mathematics.

The story starts off at the beginning of mathematics with the Babylonians. Stewart states that it is the Babylonian's work with mathematics that set humanity on the path to symmetry. From the Babylonians we travel through each mathematician that had some role in discovering something new, or was on the verge of discovering something that was later corrected and adjusted to make the discovery, or a new one altogether. We learn about books or papers that were published to give credit to the individuals, or if they chose to be secretive about it, we also learn about that. One such book is Elements, published by Euclid, which is divided into two categories. One being theorems, which tell you that something is true and the other being constructions, which tell you how to do something. We learn about all of the number systems that we use today as well as ones that did not work out. We also learn about quadratic equations, cubic equations and quintic equations. Nearly every large scale mathematics breakthrough is seen in this book.

This book is more than just the history of mathematics itself, however. Instead of just listing who did what and what it meant, Stewart shares the lives of each person. He shares their studies at school, their family lifestyles, the love interests that arose. All of these details adds tremendously to what would be a straight forward text about the history of a field. With these additional details about who each person was, it adds to the story. It gives some insight to the time in which each lived and had to go through, as well as giving a way to compare mathematicians upbringing (if we so choose to do so).

From this book I have learned much about the mathematics that I have studied and the potential that it brings. A quote from this book shares something interesting about the field of mathematics. "The history of mathematics shows repeatedly that it is dangerous to dismiss some clever or beautiful idea merely because it has no obvious utility" (267) This quote stood out to me because some of the "breakthroughs" in mathematics weren't even considered useful at the time they were found.

It is not a terribly hard read, but it does require some background knowledge on mathematics. Although Stewart explains things well, it does help to have that prior knowledge. One detail I both enjoy and dislike is the lack of equations. Stewart refrains from using much, if any equations, but rather explains them through words. This makes most ideas more understandable, but it is also nice to see the equation that we may already know something about. "The true strength of mathematics lies precisely in this remarkable fusion of the human sense pattern ('beauty') with the physical world which acts both as a reality check ('truth')  and as an inexhaustible source of inspiration." (279) I feel that the book accomplished what it set out to do, share the history of symmetry, through the history of mathematics itself. Showing us that the patterns we see as beauty, are mathematical concepts, and being able to prove these patterns gives us the truth that we seek.