Books like Riddles in Mathematics — picked by fans

Every "computer person" should read GEB at least once. Preferably in high school, when you still have the free time to dive deep into all the recreational math exercises. If you're already working 40-hour weeks and wonder who has time for Hofstadter's 750-page "metaphorical fugue on minds and machines," all I can say is: Better late than never!

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. 

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. 

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.

I stumbled on this in a used bookstore. What a find! The old-school, kid-friendly illustrations lead swiftly from simple beginnings (“What happens when you stretch a painting?”) to the depths of undergraduate topology. I haven’t used this in the classroom yet, but honestly, I could imagine busting it out with anyone from first-graders to first-year PhD candidates.

Peter Winkler is famous for his collections of counterintuitive puzzles. Thousands of people, including me, have spent many sleepless nights trying to understand the mysteries in these puzzles, for which, I am forever grateful.

Haunting puzzles in the book include hats and infinity, all right or all wrong, comparing numbers version 1/2, wild guess, laser gun, precarious picture, names in boxes, sleeping beauty, and dot-town exodus.

Most puzzle books exclude counterintuitive puzzles for unknown reasons. So, many people incorrectly assume that counterintuitive puzzles are majorly found in paradoxes. Peter Winkler in this book shows that counterintuition can come from either puzzles or solutions or both, and they need not come from paradoxes alone.

Finally, reading Winkler's statements is an absolute delight due to its enjoyable and entertaining nature.

They say that Plato was not a mathematician but was a maker of mathematicians. The same could be said of Martin Gardner, a prolific author who wrote, among many other things, the “Mathematical Games” column for Scientific American for a quarter of a century. Although all his books are excellent, The Colossal Book of Mathematics is a great entry point to Gardner’s oeuvre. It consists of what Gardner viewed as his 50 best Scientific American columns along with addenda containing updated material on each topic. With topics like topology, geometry, recreational mathematics, the infinite, and probability, each article is an informative, playful, well-written gem. 

I have always liked the classical geometry of triangles and circles, but Matt Parker's book helped me go way beyond that and broaden my whole outlook. And the attractively hand-drawn diagrams and zany humour just added to the whole experience. After all, how many maths authors do you know who decide to build a computer out of 10,000 dominoes, just to calculate 6 + 4? 

Anany Levitin introduced me to algorithmics – my second love (my first love is mathematics), through his legendary algorithmics textbook. He was one of my superheroes in my young adult life and he got me addicted to algorithms. His book is my favorite because it is beautifully organized based on design techniques, well-written, and uses nice puzzles to teach algorithms.

Levitin went much deeper and wrote this book on algorithmic puzzles. This book is the first mainstream book in the puzzle literature that taught beautiful algorithmic puzzles via various algorithm technique techniques. Levitin claimed several mathematical puzzles as algorithmic focusing on aspects of the solutions that are automatable.

Elegant puzzles (with extensive references) in this book that I have enjoyed include missionaries and cannibals, bridge crossing, circle of lights, MU puzzle, turning on a light bulb, chameleons, poisoned wine, game of life, twelve coins, fifteen puzzle, hats with numbers, and… show more.

Over many years, Martin Gardner authored a column on popular mathematics for Scientific American and a series of popular books. His writings also helped change my life, showing me how exciting and marvelous mathematics can be. 

He illuminated how mathematics underlies nature—from the patterns and shapes of petals and leaves to the weather—and much of our daily lives. He illustrated how geodesic and other domes stand up without support structures in the middle, how past and secret military codes work, and how simple paper cutouts can have seemingly magical properties and reveal paradoxes.