What is this book about?
This book is written as a sandwich with four layers. The first is about concrete mathematics; the second is about the history of mathematics; the third is about mathematicians, their life and discoveries; the fourth is about societies in which those mathematicians lived and worked.
You will learn why it is easy to divide a given angle in half and why it is impossible to divide the angle into three parts. You will read about people who tried to do this impossible trisection. You will learn why the Fundamental Theorem of Arithmetics is fundamental, why the Fundamental Theorem of Algebra is fundamental, and what is the connection between those two. You will learn many important mathematical facts that you didn’t know and you will understand why they are important.
Besides mathematical things, you will read about life in ancient Greece, including the fashions of Greek women and men, elections, Olympics, dances, food, clothing, education, Spartan’s girls and boys, weddings, colonization and democracy. You will read that Pythagoras didn’t eat beans because he thought that the human soul lives inside the bean.
You will learn that the unity of Mathematics comes from many things (nature, logic, the language and symbols of math), but the main reason for its unity is its axiomatic method, which takes some obviously true assumptions, and deduces all consequences, all theorems. What can be simpler?
The history of Greece, Germany, and Russia is presented in an unusually short manner. The history of Mathematics is explained from various sources such as personal, social, economic, but most of all - from Mathematics’ own sources.
I am trying to describe neither all of mathematics, nor the main part of mathematics, nor all mathematicians in all countries, because my main purpose is to show what makes Mathematics simple and unified science. Joseph M. Kats