FOR MORE THAN 2,500 years, mathematicians have been obsessed with solving for x. The story of their struggle to find the roots —the solutions—of increasingly complicated equations is one of the great epics in the history of human thought.
Category: Non-fiction, General Knowledge
Steven Strogatz is a Professor of Applied Mathematics at the Cornell University, USA. He works in the areas of nonlinear dynamics and complex systems. Now isn’t that intimidating! Wait, there’s more. His Curriculum Vitae runs into 25 pages. Yes you read that right.
You would expect a mathematics book from a mathematician to be heavy and dry. I had those thoughts too when I ordered this book in 2020 – but those fears were very short lived. The joy of reading the first paragraph of the first chapter lasted throughout the 280+ pages. “Fish, fish, fish, fish, fish, fish”. Now I wouldn’t want to reveal what THAT is – for that you will have to read this book. And if mathematics wasn’t your cup of tea in high school or college, believe me this book will transform that fear of math (Is there such a book, “Fear of Math” ?), into a life-long love and respect, if not passion, for this subject. Someone once said, “Mathematics is the language of the Universe”, and so it is but natural that we should all understand this universal language to know what the Universe is whispering to us about its secrets.
Before I go any further, let me state this – it is not a book based on any syllabus, for any course, not even a 101 course. But it could form part of the reading list of all high school students and graduates who are not from quantitative sciences.
The book is arranged into six main parts and each part touches upon the concepts of mathematics that we use at various stages of our academic career. Part 1 starts with, well, “Fish, fish, fish, fish, fish, fish”. Now that makes you curious? Count the number of times you read “fish” in the last sentence, there’s the secret. I won’t disclose more on this.
Part 2 discusses relationships between numbers, Part 3 about geometry and trigonometry, Part 4 is about what we study in undergraduate classes – “rate of change of displacement with respect to time” – yes, calculus. You will be amazed at the refreshing approach to calculus here – none of those dry differentiation and integration formulae. And yes, it goes on to explain the role of ‘infinity’ in math. As Prof Strogatz says, “The domestication of infinity was the breakthrough that made calculus work. By harnessing the awesome power of the infinite, calculus could finally solve many long-standing problems that had defied the ancients….”.
Any book on mathematics will be incomplete without the mandatory discussion on statistics, probability, networks, and data mining. In Part 5 of this book we find a very readable and interesting introduction to these topics. Part 6 of this book touches on the Frontiers of Mathematics, the boundary between the known and the unknown.
Spread thoughout the book are such gems as:
“The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive but none in which a double positive makes a negative—to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.”
Chapter 8 of this book discusses complex numbers (the square root of -1, etc) in an interesting way. In college, we thought complex meant ‘complicated’, this chapter explains why something like (a + ib) isn’t really complicated.. Strogatz calls complex number as the “pinnacle of number systems”. Graphically, he explains why i2 = -1.
If and when you do take your eyes off the picture in chapter 11, you will begin to understand about functions, curves, and logarithms. Yet another chapter (chapter 14) explores parabolas, ellipses etc. Chapter 15 will tell you where you can find sinusoidal waves in nature. I would not like to reveal all that is in the book – for that would not be fair, but chapter 24 discusses about the web (the Internet) and how linear algebra makes Page Rank algorithm and hence Google possible. So even if you feared linear algebra, you are using it everyday in Internet search. Read chapter 26 to understand what is the “Group Theory in the Bedroom” – you will be surprised where it is used! A number of weblinks for each chapter make this an interesting reading.
So for whom is this book recommended? If you are already a student of physics, math, statistics, econometrics, and other numerical sciences, you will be more than familiar with all topics in this book. But reading this book gave me new insights and I understood more interesting ways of looking at many concepts. Since I teach physics, mathematics and computer science, I have discovered newer ways of explaining many math-related topics from this book. Teachers of various levels will find it useful for classroom teaching to liven up what can be sometimes be dull and dreary math lectures. This is certainly the book for everyone who abandoned mathematics in high school but finds it is necessary to know the subject in this age of algorithms and data. Even if you are appearing for competitive exams, this book will make the most basic concepts very clear and applications of math to everyday problems becomes easy – like how to distribute an entire estate of 10 dirhams between two sons and a daughter so that each son receives twice as much as the daughter! Remember, this is not a book of math tricks, or tips, nor does it contain recipes to solve such problems. It does an excellent job of explaining mathematics. And mathematics is to be understood, not feared. Go for this book – its a must have in your collection. And if you do lend it, be prepared to buy a new copy.
Prof Strogatz has excellent lectures on nonlinear dynamics, chaos and other topics on YouTube – a must watch if you are in the field.