10 books like The Art of Logic in an Illogical World

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. 

Logicomix is a revelation. It tells the colorful life stories of some incredibly important philosophers and mathematicians of recent times, how they met and how their lives reflect their thoughts about some of the most difficult questions ever posed. The stories are beautifully illustrated with a detail that conveys more than mere words. It feels wondrous how the most abstract ideas can be made comprehensible and captivating when we had only the vaguest notions about what these ideas even meant.

Love and Math is a mathematical autobiography, seamlessly interweaving an inspiring personal journey with profound mathematical ideas. Born in the Soviet Union, Frenkel aspired to become a professional mathematician, only to see his hopes crushed by entrenched antisemitism at Moscow State University – home to the premier mathematics program in the country. While sitting for the entrance exam, he was confronted by two advanced graduate students who were sent to question him personally and make sure he failed. Rejected but undeterred, Frenkel turned instead to an informal network of top-flight but marginalized Soviet mathematicians, who like him were denied employment in the field they loved. With the end of the Cold War he was invited to Harvard on a fellowship that later turned into a permanent job. In one of the book’s emotional highs, he confronts his old tormentor from Moscow State, who unsuspecting American academics had invited to give… show more.

That Steven Strogatz, Cornell Professor and longtime New York Times columnist, is unsurpassed as an expositor of mathematics, goes without saying. No one can make the abstract and technical appear simple and intuitive like Strogatz. In Infinite Powers he takes on the Calculus -- the central pillar of modern mathematics that is also the bane of many a high-school student. It is an immensely powerful field, and at its core is a concept that is both counter-intuitive and paradoxical: the infinite.

The roots of the calculus, we learn, go back to the ancient Greeks, whose notions of the infinite were put to powerful mathematical use by Archimedes. Strogatz continues with Galielo’s dynamics and Kepler’s laws of planetary motion, before reaching the turning point: The discovery of the Calculus by Newton and Leibniz. This leads straight to a discussion of differential equations, which are responsible for so much of what makes… show more.

This remarkable book is authored by Francis Su, the past president of the Mathematical Association of America. The author describes human flourishing as follows: “a wholeness of being and doing, of realizing one’s potential and helping others do the same, of acting with honour and treating others with dignity.” He explains how human beings, of all ages and ability levels, can experience flourishing through the doing of mathematics.

In each of the final twelve chapters, the author explores a trait of mathematics, how it relates to our journey as humans, and how the development of each trait enables us to flourish: Exploration, Meaning, Play, Beauty, Permanence, Truth, Struggle, Power, Justice, Freedom, Community, Love. As a mathematical researcher and educator, I have experienced these traits first-hand, and recommend this book to anyone and everyone.

For decades, the most famous opening chord in rock and roll was an unsolved problem, since no one could reproduce it. But in 2004, Jason Brown, a professor at Dalhousie University, used mathematics to recreate the opening chord of the Beatles hit song, “A Hard Day’s Night”. I remember when newspapers around the world reported on Jason’s findings, as I was at Dalhousie at the time, as one of Jason’s Ph.D. students.

Jason’s Beatles story serves as the final chapter in this wonderful book, a collection of short vignettes about how mathematics relates to every aspect of our lives, including garbage pickup routes, grocery shopping, political polling, and social networks. The book’s thesis is that as we understand mathematics better, our lives become more meaningful. I couldn’t agree more.    

The full title of this wonderful book is The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy. Bayes’ Theorem is a one-line mathematical formula, named after a Scottish church minister, that calculates the updated probability of an event occurring given new information that we receive.  Applications of Bayes’ Theorem are diverse and profound, from recommendation systems to automated translation algorithms to weather prediction.

This well-researched book does a deep dive into the most important characters of mathematical statistics over the past three centuries, and explains how Bayes’ Theorem was used to solve problems that were deemed unsolvable, including cracking the German Enigma Machine during World War II. I teach Bayes’ Theorem in several of my courses, and have found much inspiration in McGrayne’s book.

John Urschel is an African-American mathematician specializing in graph theory, who recently completed his Ph.D. in mathematics at MIT. But he is better known for his football career, as a starting offensive lineman for the Baltimore Ravens. Six of Urschel’s papers were completed while he was still in the National Football League.

Mind and Matter is John Urschel’s memoir, co-authored with his wife Louisa Thomas. Each chapter alternates between football and mathematics, and how his success on the field translated to success in the classroom, and vice-versa. I loved how accessible the book is, for readers of all ages, and I fully agree with the author’s perspective that mathematics gives us a way of making sense of the world, and helping us see past the confusion of everyday life.

If there is one book I wish I’d written myself, it is How to Become a Really Good Pain in the Ass. One of the things I admired most about the people who shaped my education and career path most was their ability to listen carefully and ask critical questions that uncovered even more than what was first expressed. Christopher DiCarlo’s book is a manual to practicing these traits. The book provides all of the tools needed to question beliefs and assumptions held by those who claim to know what they’re talking about, while at the same time providing practical solutions for today’s world of misinformation. The book also convinced me that faulty reasoning can be spotted by asking the right sorts of questions—what better gift to give someone? 

Booth was a professor of English at the University of Chicago and a president of the Modern Language Association. Surprisingly, he wrote this elegant book showing that Cartesian doubt as the basis of science (or of anything else) is silly, not a dogma that anyone can actually live by. Like the other books here, he shows even science to have—or course—a “rhetoric,” that is, “the art of discovering good reasons, finding what really warrants assent because any reasonable person ought to be persuaded by what has been said.”