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.

Why Mathematics?

When deciding what I wanted to be when I graduate, I ended up choosing Elementary Education. With this, there was a secondary choice to make, what teachable major I prefer. These choices include: Science; Social Studies; English; Mathematics. Social Studies was out of the question to begin with as it is not one of my favorite subjects. Science didn't sound too appealing to me either. The choice was between writing papers or solving equations. In the end, I chose mathematics.

Mathematics hasn't been the hardest subject in school for me, but not always the easiest. It is one subject that completely builds upon itself in different directions. We start young learning the basic building blocks of mathematics, and as we progress through the different courses we study, we build on those fundamentals in different ways. For example, staying in the elementary level, we start by learning to count and then learning addition. From this we end up learning how to multiply, by way of repeated addition. This trend continues as we learn more and more about mathematics. The interesting part is when two completely different topics in mathematics end up relating to one another in some way.

I think that mathematics is a great subject to choose for a teachable major. Knowing how to solve problems involving mathematics can and essentially is used in every day life. When going out to eat we leave a tip based on a percentage. When getting gas, we can estimate how much we are going to spend based on the price per gallon. Every day tasks can involve mathematics, and as a teachable major for an elementary school teacher, it is good to know the in's and out's to better teach the future generations.

A Preliminary Report

     I have been reading the book Why Beauty is Truth by Ian Stewart. As the subtitle tells us, it is "A History of Symmetry". This is a key thing to remember in reading this book. Having not completed the book yet, I do not yet know what is yet to come, but thus far the story is not only about the history of symmetry, but rather the history of all mathematics.

     As most stories about the history of something start, this one starts at the beginning. In this case, we start with the Babylonian time. Stewart describes the different eras that follow, describing both the major players and the important findings they had made. These are not just stories about solely the mathematics that they found, Stewart tends to delve into their personal lives as well giving a background to who they were. Another great part about this book is that when describing the mathematical findings, there is also a description of the why. Knowing why the breakthrough was important or why the proof failed but still had a big impact are just as important as what these things were because it allows us as the readers to understand more of the time period and what was important to them and how it has effected each time period following.

     One drawback to this book is the daunting task that it has taken on. To be able to share the history of Mathematics and that of symmetry, it is tough work to do in the 280 pages that the book has. While mostly everything needed to understand the mathematics found within the pages, it is introduced only briefly. Also, Stewart mentions that he will stray away from listing equations, which results in lengthy narratives that describe the equation. This isn't all bad though, as reading about the equation allows you to see more of the "why" and "how" opposed to just knowing you can plug in numbers and have it worked. This shows more of the process involved rather than the end product.

     I hope as I continue to read this book that it talks more about symmetry in general. Whether it be how the ideas came about or the process of using it. As the book is about the history of symmetry, one would hope for a little more focus on the topic. Although learning about the history of mathematics does entail this concept of symmetry, so I can't be too disappointed by this.

Teachings of Old & New

While reading through a discussion board post from a Liberal Studies course that I am taking, I came across the quote "Are textbooks printed in order to teach children, or are the contents of these textbooks to be controlled by the Southern oligarchy and the commercial health of publishing houses?" from Report From Occupied Territory, page 733. This excerpt is found in a book of Collected Essays by James Baldwin. This brought me to thinking about how students were taught previously and how they are being taught today. As per most of my homework experience from elementary school, my parents could help me if it was something they learned. That is, if it followed an algorithm that they learned from their schooling, they could show me how to do it. Now, however, students are not encouraged to memorize a formula or algorithm, but rather understand how the formula works and where it comes from. Students are still (normally) taught the algorithm in the end, but work through it to understand. Mathematics seems to have transitioned from just doing a problem to get an answer to understanding how to solve a problem. More than likely those who only learned the algorithm at one time knew the underlying mechanics, but that part doesn't stick with you very easily. Now students are even more encouraged to understand those mechanics so that they can apply that knowledge to a problem that may look slightly different.

To Win or Not To Win

Playing games in Math classes can be fun and enjoyable, but also can be a way of learning. In class the other day we played a game much like master mind in the sense that you have to try to match your sequence to your opponents. This game differs from master mind by the way you play. Player 1 is given a 6x6 array in which to start the game, Player 1 chooses a sequence of 1's and 0's to fill in the first row of the 6x6 array. After this is done, Player 2, in their 1x6 array, fills in a single 1 or 0. This process continues until Player 1 fills in the 6th row of their array and Player 2 fills in their last square. The goal, much like master mind, is for Player 1 to end with the same sequence that Player 2 creates, allowing Player 1 to win. For Player 2 to win, they must ensure that Player 1 does not match their sequence.

The Book of Choice