Fans pick 100 books like Origami, Eleusis, and the Soma Cube

David Hilbert was the most important mathematician at the dawn of the 20th century. In 1900, he gave the mathematical community its homework for the next 100 years setting out the list of open problems that had to be solved by 2000. While to the rest of the mathematicians, he may have appeared as their professor, he was also the class clown. As colorful and funny as he was brilliant, you cannot but come away loving this great mathematical genius.

This book is out of print, but I include it in the hope that some public-spirited publisher may be persuaded to reissue this large-format picture book. It was the first book on mathematics that I read at about the age of ten and it contained precisely what I needed to show me that this was a subject with a history and a use. (Nor am I the only mathematician to have this experience.)

As an adult, I found the same author’s Mathematics for the Million a bit crass and utilitarian but I pardon him everything for a wonderful first experience.

This classic rumination on the nature of mathematics is perhaps the most famous book ever written by a mathematician.

I’ve read it several times, and each time, it brings up another facet of the subject in some new light. Portions of what Hardy says ring eerily true, and seem to be part of the identity, the very DNA, that all mathematicians must surely share. Other parts seem so alien to be almost repugnant – such as his contention that most mathematics we classify as useful is ugly and inelegant.

I’d love to argue face-to-face with Hardy about this highly opinionated work of his. In the end, I suspect we’d find lots of common ground, since intrinsically, we both love mathematics so much.

More mathematicians than you might expect have had eventful lives (and most of the others are grateful that they did not). Fourier, one of my mathematical heroes was twice in danger of the guillotine, played a substantial role in Napoleon’s Egyptian campaign, is known as one of the Fathers of Egyptology, and was the first person to write about the ‘green-house effect’. To mathematicians and physicists this is all secondary to his work on heat conduction and, of course, the Fourier series. Herevel is an excellent guide to a remarkable life. (Herevel also had a non-standard career — the ‘Herevel tip’ was instrumental in early successes against Enigma.)

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? 

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 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).

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.

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.