Yukai Du

13 Classic Mathematics Books for Lifelong Learners

When I was a college student, I saw a list of essential math books on a blog. I promised to myself to read all those books in 10 years because there were 50 books on that list. I am still trying to finish the list. And now it is time to share some of them with you.

Mathematics is beautiful and astounding. There is a lot of joy in understanding mathematics, for instance, how the proof of Fermat’s Last Theorem or the secrets of pi, e, epsilon…

Anyway, if you passed a lot of math courses but failed to make any sense out of them during your education, those books were written for you.

Zero: The Biography of a Dangerous Idea. | Charles Seife

This is a great book that could make almost anyone love math. I found it to be quite interesting, despite my already knowing quite a bit about the topics being covered. I absolutely love Seife’s writing style. He had me laughing out loud more than a few times.

It’s hard to imagine that anyone could spend 220 pages talking about one number. While you are reading, you do not need to work through the actual with a pencil and paper. Instead the author walks you through the logic.

The history parts of this book were interesting enough to make it worth it. It covers a lot of world history. It begins with humans use of numbers and counting. I learned about Archimedes, Laplace, Newton, Euler, their contributions to math and their lives.

You can buy the book from here.

Measurement | Paul Lockhart

This book is a must read for math teachers. It is about how mathematics should be taught. When you start reading, you will realize that, the book is a powerful criticism on the prevalent curriculum of Mathematics in elementary, middle and high schools.

Paul Lockhart thinks that, mathematics is an art, and it is much more than memorization of notations and formulas. For him,

mathematics is a life-long love.

He believes that, we have to stop teaching mathematics in the traditional way and we need to start using our natural curiosity to teach and learn mathematics.

It is a serious read involving actual mathematics and should be treated as a reference book and should be referenced from time to time, specially if you are in high school or college.

The author makes sure that you stay at the edge of your seat during the book, perhaps even after you’ve read the whole thing.

You can buy the book from here.

Prelude to Mathematics | W.W. Sawyer

This book is literally a classic and it is a very enjoyable read. It is about how a mathematician thinks and how to grow a mathematician.

“Prelude to mathematics” would be very meaningful for a reader who was not already familiar with such topics.

Mr. Sawyer attempts to provide an understanding of Mathematics for pretty much anyone.

You can buy the book from here.

Proofs from The Book | Aigner and Ziegler

“But to tell the truth, what they really want to prove, once in their lifetime,…”

This book contains only the “best” proofs from many different fields of mathematics. And this book is not a textbook. Ziegler and Aigner take us briefly to another world.

If you are going to read this book, you should have the knowledge of calculus and linear algebra. Otherwise, you can struggle in order to follow the proofs.

What makes it fun is that the author walks you through the most famous proofs in all of mathematics simplifying them to simple equations that you can solve in your head.

I’d heard much praise for this book and it is certainly worth it. I wish I had a book like this assigned along with the textbook during my high school math classes.

You can buy the book from here.

The Joy of x | Steven Strogatz

“The joy of x” should be beginner's book, because this book introduces us to the wonders of mathematics very simply. It is really a brilliant introduction to mathematics.

For this book, the content is coming from a long-running blog. Each chapter is very short and about a particular feature of mathematics. Mr. Strogatz’s writing style is very engaging.

However, if you have a strong knowledge of mathematics, this book will be a easy read for you. Thus, you don’t need a PHD to enjoy this book.

You can buy the book from here.

Things to Make and Do in the Fourth Dimension | Matt Parker

This book is a nice and recommended read. It’s about “fun parts of mathematics.” The author’s writing style is so light and clear and these makes all the content understandable without a heavy background of mathematics.

The book consists of several chapters, and each chapter covers one topic in mathematics. Mr. Parker uses everyday life examples for each chapter to explain the basics of mathematics.

In this book, you can find beautiful activities that you and your family can enjoy together. You can show everyone mathematics is a magic.

You can buy the book from here.

What is Mathematics? | Courant and Robbins

For one of my best friend, this book is at the top. For me, this book is challenged. For some parts of the book, you don’t need any knowledge of mathematics because it is about logic.

You can buy the book from here.

A History of π | Petr Beckmann

I really enjoyed this book. Especially, when I realized that so many smart people just spent their entire lives only for a number, π, I could not understand the reason at the beginning. It was too hard for me to picture that a bunch of people working together and just trying to calculate a number.

When you read the book, you will see that, some mathematicians just ignored π, some of them were perplexed, and most of them boldly went where no one had gone before.

The maths in the book is followable to anyone with A-level standard.

You can buy the book from here.

An Imaginary Tale | Paul Nahin

x² + 1 = 0.

Isn’t this equation so beautiful. Absolutely brilliant. Among my favorite equation. Anyway, I think every calculus students should read this book more than once. This book is perfectly written and Calculus students would love it.

In this book, you can learn how various mathematicians dealt with the complex number i. And you can learn a lot of things about Euler, the great mathematician in our world.

This is an interesting mix of history and calculus, that leading the reader to appreciate the development of the understanding of i, the square root of minus one.

You can buy the book from here.

e: The Story of a Number | Eli Maor

This is one of those books that I read again after I finished it. It is also an essential reading.

At the beginning, it looks like this book is only about the special number e, but actually it is not. That is one half of the book. When you read, you will see the discovery of first numbers, rational and irrational numbers. Some chapters are like history lessons focusing on people and events at the times and places.

You can buy the book from here.

Imagining Numbers | Barry Mazur

As someone fascinated with imaginary numbers, I read a lot of articles on the matter.

Mr. Mazur starts with the basics. Then gets deeper into the square root of negative numbers and shows how beautiful our imaginary numbers.

You can buy the book from here.

Journey Through Genius | William Dunham

If you want to learn mathematics history, this is a beautiful book with short and interesting stories from the mathematics history. Actually this book is a must read for everybody.

I think, if you remember high school mathematics, then the “Journey through Genius” would be very understandable book for you. It is not too advance for an average math person. It will definitely help you spark the excitement for mathematics. For instance, I couldn’t stop shaking my head and dropping my jaw in fascination and awe at the wonderful world of mathematics. The author beautifully introduces all the great names of Math throughout history to the us. He also beautifully builds the connection between their lives and their works.

This book is definitely not boring and it can be a great introduction to many students who are interested in mathematics. I am pretty sure that they can really enjoy it. I mean, really fun read.

You can buy the book from here.

Prime Obsession | John Derbyshire

One of the most fascinating books I’ve read. After reading the first two chapters, I’ve found that learning the reasons why people wanted answers to mathematics questions has made the mathematics much more interesting.

This book is about Riemann Hypothesis and it is perfectly written for beginners. It is very understandable and enjoyable.

Rereading this book really helped me better understand both zeta function and complex numbers.

You can buy the book from here.