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.

The books I picked & why

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Gödel, Escher, Bach: An Eternal Golden Braid

By Douglas R. Hofstadter,

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

Why 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.

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

By Philip J. Davis, Reuben Hersh,

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

Why 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. 

Riddles in Mathematics: A Book of Paradoxes

By Eugene P. Northrop,

Book cover of Riddles in Mathematics: A Book of Paradoxes

Why 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).

Four Colors Suffice: How the Map Problem Was Solved

By Robin J. Wilson,

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

Why 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. 

Wonders Beyond Numbers: A Brief History of All Things Mathematical

By Johnny Ball,

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

Why 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.

5 book lists we think you will like!

Interested in math, recreational mathematics, and artificial intelligence?

5,887 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 103 books about math
Recreational Mathematics Explore 8 books about recreational mathematics
Artificial Intelligence Explore 112 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.