The best books to find out why math isn’t what you think

Who am I?

As a kid I read every popular math book I could lay my hands on. When I became a mathematician I wanted to do more than teaching and research. I wanted to tell everyone what a wonderful and vital subject math is. I started writing popular math books, and soon was up to my neck in radio, TV, news media, magazines... For 12 years I wrote the mathematical Recreations Column for Scientific American. I was only the second mathematician in 170 years to deliver the Royal Institution Christmas Lectures, on TV with a live tiger. The University changed my job description: half research, half ‘outreach’. I had my dream job.

I wrote...

Flatterland: Like Flatland Only More So

By Ian Stewart,

Book cover of Flatterland: Like Flatland Only More So

What is my book about?

Edwin Abbott Abbott’s 1884 Flatland, a classic of popularization, tells of a world of two dimensions inhabited by geometric figures. Really, it’s about the Fourth Dimension, much in vogue at the time. That’s mild compared to the inventions of today’s mathematicians and physicists.

Flatterland explores these mindboggling new ideas using Abbott’s scenario of imaginary worlds. Victoria Line, a thoroughly modern young woman in Flatland’s disintegrating male-dominated culture, explores these novel universes, guided by the Space Hopper. She encounters the doughmouse at the topologists’ tea party, puzzles over the five-sided squares of Platterland, argues with Superpaws the quantum cat, and grapples with relativity in the domain of the Hawk King. Like Flatland, the book is partly about imaginative and important math, and partly about social inequality.

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The books I picked & why

Book cover of Gödel, Escher, Bach: An Eternal Golden Braid

Why did I love this book?

This Pulitzer Prize winner is one of my favorite books. It explores logical paradoxes, the difference between information and meaning, and other almost philosophical issues in the fundamentals of computer science. It links limits to the foundations of mathematics (Gödel) to music (Bach) and the visual arts (Escher). The style is unique, with characters like Achilles and the Tortoise giving an Alice-in-Wonderland feel that illuminates difficult concepts. I first read about it in Martin Gardner’s celebrated column in Scientific American, and it opened my eyes to the relation between math and deep issues in science.

By Douglas R. Hofstadter,

Why should I read it?

11 authors picked Gödel, Escher, Bach as one of their favorite books, and they share why you should read it.

What is this book about?

Douglas Hofstadter's book is concerned directly with the nature of maps" or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Goedel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

Book cover of Descartes' Dream: The World According to Mathematics (Dover Books on Mathematics)

Why did I love this book?

Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are. 

By Philip J. Davis, Reuben Hersh,

Why should I read it?

1 author picked Descartes' Dream as one of their favorite books, and they share why you should read it.

What is this book about?

"A passionate plea against the use of formal mathematical reasoning as a method for solving mankind's problems. . . . An antidote to the Cartesian view that mathematical and scientific knowledge will suffice to solve the central problems of human existence." — The New York Times
"These cogitations can and should be read by every literate person." — Science Books and Films
"A warning against being seduced or intimidated by mathematics into accepting bad science, bad policies, and bad personal decisions." — Philadelphia Inquirer
Rationalist philosopher and mathematician René Descartes visualized a world unified by mathematics, in which all intellectual…

Book cover of Riddles in Mathematics: A Book of Paradoxes

Why did I love this book?

I was given this book when I was about 15, and devoured it. It is an eclectic collection of mathematical paradoxes, fallacies, and curiosities so strange that they seem impossible. Mathematical magic tricks, a proof that all numbers are equal, a proof that all triangles are isosceles, a curve whose length is infinite but whose area is finite, a curve that crosses itself at every point, a curve that fills the interior of a square. Infinities that are bigger than other infinities. The Saint Petersburg Paradox in probability, a calculation that you should pay the bank an infinite amount of money to play one fair coin-tossing game. The smallest number that cannot be named in fewer than thirteen words (which I’ve just named in twelve words).

By Eugene P. Northrop,

Why should I read it?

1 author picked Riddles in Mathematics as one of their favorite books, and they share why you should read it.

What is this book about?

Two fathers and two sons leave town. This reduces the population of the town by three. True? Yes, if the trio consists of a father, son, and grandson. This entertaining collection consists of more than 200 such riddles, drawn from every branch of mathematics. Math enthusiasts of all ages will enjoy sharpening their wits with riddles rooted in areas from arithmetic to calculus, covering a wide range of subjects that includes geometry, trigonometry, algebra, concepts of the infinite, probability, and logic. But only an elementary knowledge of mathematics is needed to find amusement in this imaginative collection, which features complete…

Book cover of Four Colors Suffice: How the Map Problem Was Solved

Why did I love this book?

The Four Color Problem was one of the most baffling questions in mathematics for over 120 years. First posed in 1852, it asks whether every map can be colored with four colors, or fewer, so that regions adjacent along a boundary have different colors. The answer (yes) was finally obtained in 1976, with massive computer assistance. This method was initially controversial, but the result is now firmly established. This highly readable account, with full-color illustrations, opens up the history and the personalities who tackled this topological enigma, as well as making the mathematics comprehensible. The path to the final solution is littered with blunders and mistakes, but also illustrates how mathematicians can join forces across the generations to chip away at a problem until it cracks wide open. 

By Robin J. Wilson,

Why should I read it?

1 author picked Four Colors Suffice as one of their favorite books, and they share why you should read it.

What is this book about?

On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little…

Book cover of Wonders Beyond Numbers: A Brief History of All Things Mathematical

Why did I love this book?

One of the friendliest routes into mathematics, for many people, is its history. In math, unlike many sciences, ideas last indefinitely. Pythagoras’s Theorem is about 4,000 years old, understood in ancient Babylon a thousand years before Pythagoras was born. It was true then, and it is still true today. The history of math tells of the construction of a towering edifice, with each new level built on top of the previous ones. There are many histories of mathematics, but none quite like this one. The author is a much-loved English TV personality, famous for his enthusiasm for math and his ability to make it entertaining for children of all ages. His book is a rollicking yarn, a wild ride that nonetheless remains true to its subject.

By Johnny Ball,

Why should I read it?

1 author picked Wonders Beyond Numbers as one of their favorite books, and they share why you should read it.

What is this book about?

In this book, Johnny Ball tells one of the most important stories in world history - the story of mathematics.

By introducing us to the major characters and leading us through many historical twists and turns, Johnny slowly unravels the tale of how humanity built up a knowledge and understanding of shapes, numbers and patterns from ancient times, a story that leads directly to the technological wonderland we live in today. As Galileo said, 'Everything in the universe is written in the language of mathematics', and Wonders Beyond Numbers is your guide to this language.

Mathematics is only one part…

5 book lists we think you will like!

Interested in math, recreational mathematics, and artificial intelligence?

9,000+ authors have recommended their favorite books and what they love about them. Browse their picks for the best books about math, recreational mathematics, and artificial intelligence.

Math Explore 219 books about math
Recreational Mathematics Explore 10 books about recreational mathematics
Artificial Intelligence Explore 220 books about artificial intelligence

And, 3 books we think you will enjoy!

We think you will like Cosmos, Men of Mathematics, and How Not to Be Wrong if you like this list.