If you have been following me on Instagram or Goodreads, you probably know that I have been reading “Taming the Infinite” by Ian Stewart. This was the book chosen in the LThMath Book Club on Goodreads for the August-September reading challenge.

## Overview

This book review is split into different parts for your convenience.

- General description
- Chapters
- For non-mathematicians
- For mathematicians
- The author
- Goodreads review
- Final words – video

## 1. General Description

In his famous straightforward style, Ian Stewart explains each major development—from the first number systems to chaos theory—and considers how each affected society and changed everyday life forever. Maintaining a personal touch, he introduces all of the outstanding mathematicians of history, from the key Babylonians, Greeks, and Egyptians, via Newton and Descartes, to Fermat, Babbage, and Godel, and demystifies math’s key concepts without recourse to complicated formulae. Written to provide a captivating historic narrative for the non-mathematician, this book is packed with fascinating nuggets and quirky asides, and contains plenty of illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made the world what it is today.

## 2. Chapters

This book has 20 Chapters:

- Tokens, Tallies and Tables
- The Logic of Shape
- Notations and Numbers
- Lure of the Unknown
- Eternal Triangles
- Curves and Coordinates
- Patterns in Numbers (this chapter is about Number Theory)
- The System of the World (this chapter is about Calculus)
- Patterns in Nature (this is about Differential Equations)
- Impossible Quantities (this is about Complex Numbers and Complex Analysis)
- Firm Foundations (this is about Analysis, especially Riemann Hypothesis)
- Impossible Triangles (this is on Non-Euclidean Geometry)
- The Rise of Symmetry (this is on Group Theory – my favorite)
- Algebra Comes of Age
- Rubber Sheet Geometry
- The Fourth Dimension
- The Shape of Logic
- How Likely is That?
- Number Crunching
- Chaos and Complexity

## 3. For Non-Mathematicians

If you have studied mathematics at school and you are still a math-lover at heart, you will find this book interesting and challenging at the same time. The author mentions a couple of complex theorems using easy to understand language, but still you will need to stop from time to time and reconsider what you thought mathematics is. Moreover, the book has a lot of interesting applications of mathematics in different aspects of our society. Therefore, if you ever struggled to understand where exactly all this “mathematics” is ever used, the book offers a lot of examples to satisfy your curiosity.

## 4. For Mathematicians

If you are a mathematician or you are studying mathematics at the moment, this book will read a beautiful journey into the history of your favorite topics. The author doesn’t forget to mention some of the most important theorems or mathematicians in each topic described. Do not expect to find out something major about the topics mentioned in terms of research or explanations. On the other hand, you will totally understand how the theory evolved during years and years of study.

## 5. The Author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.

Here are other incredible books by Ian Stewart: Letters to a Young Mathematician, Professor Stewart’s Cabinet of Mathematical Curiosities, How to Cut a Cake, In Pursuit of the Unknown: 17 Equations That Changed the World, and many more.

6. Goodreads Review

Taming the Infinite: The Story of Mathematics from the First Numbers to Chaos Theory by Ian Stewart

My rating: 5 of 5 stars

This is one of the best books on history of mathematics I have read in a very long time. The author has a wonderful way of starting with something basic and getting to complicated aspects in just a couple of pages. I loved it.

The chapters are very interestingly divided into small sub-chapters; everything seems to be organised so that each chapter starts with a basic idea and by the end you get the full on complicated aspects. From this point of view, I don’t think the book is for everyone. I will say you need to have a basic idea of some concepts such as differentiation, solving equations, polynomials, probabilities, geometry. It will be even more interesting if you had an idea of about differential equations, abstract algebra or topology – this is not a must, but it will give you a better understanding of the history behind these topics.

Moreover, the author has a great way of explaining applications of those topics in our society. Every chapter ends with a bit on “how [insert topic] do for us”, which gives an example from another science or domain that uses that part of mathematics.

Also, the book has small biographies on different mathematicians per topic. I think it is great that after you read about the discovery of a proof or theorem by a great mathematician, you also get a couple of paragraphs about his life. He doesn’t spend much time or space on this, just basic information that offers more context. For me it felt like transforming a name related to a theorem into the actual person that worked and struggled to discover that.

## 7. Final Words – Video

Here is a short video composed of a collection of short clips filmed during the “reading process”. Hope you enjoy it:

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*Lots of love and don’t forget that maths is everywhere! Enjoy!*