100 Books Like Algorithms to Live By

This is a book that is at once a biography, a testament to human genius in the face of imminent danger, and a story of human injustice. Alan Turing had an idea about a ‘universal machine’. A machine, when built at Bletchley Park, allowed the Allies in World War II to crack the German Enigma ciphers. This universal machine laid the foundations for modern computing and all the amazing advances we enjoy today. But at a price for Turing, he fought inner demons about his homosexuality and eventually paid the ultimate price.

I marveled at his genius, cheered his cryptographic successes with each cipher cracked, shouted against the tragedy of his arrest, cried at his untimely death. A death at his own hand at the age of 41. The world lost a genius due to a society’s labelling of homosexuality as a crime.

We still live in this world of… show more.

This book is not about computing, but it is relevant in an indirect way. I love this book, since it is written in such an engaging style and illustrates with many examples that math is not a dry subject to be practiced only by mathematicians but helps everyone to solve real-world problems. The book shows how important it is to be precise in describing problems and that applying a little mathematical rigor goes a long way in solving them. Ellenberg describes mathematics as the “extension of common sense by other means.” In a similar way, I view computer science as the extension of problem-solving methods (aka “algorithms”) by other means. 

A primary reason to love math is because of its usefulness. This book shows two sides of math’s applicability, since it is so ubiquitously used in various algorithms.

On the one hand, such usage can be good, because statistical inferences can make our life easier and enrich it. On the other, when these are not properly designed or monitored, it can lead to catastrophic consequences. Mathematics is a powerful force, as powerful as wind or fire, and needs to be harnessed just as carefully.

Cathy O’Neil’s message in this book spoke deeply to me, reminding me that I need to be always vigilant about the subject I love not being deployed carelessly.  

A graphic novel about Ada Lovelace, Charles Babbage, and their quixotic Victorian escapades designing computers and algorithms nearly a century before their time? As fascinating as that may already sound, it’s only the beginning. This is the only graphic novel I’ve read that has footnotes to the footnotes—immensely amusing footnotes. While reading this book, I feel constantly in the presence of insane genius. (But please read this book on physical paper. It is a work of art.)

This book starts in a similar historical location as Bod’s book but quickly moves through the nineteenth and twentieth centuries—settling into the “information theory” era established by Claude Shannon, Norbert Wiener, and others in the 1940s-1960s.

I love this book because it situates the intellectual climate leading to our current dystopia of information overload. Gleick’s teasing of chaos theory inevitably pushes the reader to explore his book on the subject from the 1980s: Chaos: Making a New Science (1987).

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.

The most important unanswered question in computer science has a huge public relations problem. Back in the 1970s, this question became known as “P=NP?”—and who could write an exciting book about that? Luckily for us, Lance Fortnow can. As one of the world’s foremost experts on P-vs-NP, he takes us on a wild and truly accessible ride through the most important question about computing. I’ve seen many attempts at making “P=NP?” accessible/understandable/intriguing for non-experts. But Fortnow nails it like nobody else, reformulating P-vs-NP as a search for one of the golden tickets in Charlie and the Chocolate Factory. (Which is another one of my favorite books, even though it’s not going to make it onto this list about algorithms.)

In a world full of buzzwords about the latest AI algorithms, Leslie Valiant is one of the few authors who can shrug off the hype and deliver something truly profound. Valiant is a Turing Award winner whose work has changed the face of computational learning theory. His ideas show how algorithms can arise naturally, as part of evolution. (He calls them ecorithms.) These ideas are stunningly original. I admire Valiant’s no-nonsense prose style immensely—it’s such a pleasure to read something where the ideas and explanations are simultaneously so clear and so deep that they provide their own star power.

Knuth’s unique mix of playfulness and rigor came to define computer science as an intellectual discipline: computer science didn’t really have anything to do with computers, but everything to do with a particular way of seeing the world.  Just browse and wonder at the beauty and precision achieved in these books.   

Volume 3 (Sorting and Searching) is my personal favorite, and I encourage you to start there. During the pandemic, I finally got around to reading Volume 4A (Combinatorial Algorithms), which was published thirty plus years after Volume 3. It was the same feeling I had watching the movie The Phantom Menace years after growing up with the original Star Wars trilogy. I had forgotten just how unique and distinctive Knuth’s Art of Computer Programming is.

Ulam was a Polish mathematical prodigy, publishing significant mathematics by the time he was 20. He was part of the rich Polish math community centered around Stefan Banach. Unlike most, he was heading to the United States in 1939 (with his younger brother) when Germany invaded Poland. All the rest of his family were murdered by the Nazis. He on the other hand ended up in Los Alamos, providing critical help on the Manhattan Project. Later in life, he wrote this book, his autobiography. Based on his history, one could well think that it would be a book full of tragic grief. Instead, it is a pean to the joys of doing mathematics and of living a life full of mathematics, without downplaying the horrors of the mid-twentieth century.