10 books like How Not to Be Wrong

Entropy. The Uncertainty Principle. Schrodinger’s Cat. Such examples of the aligning of mathematical and verbal paradoxes rise to a wholly new level under the wings of Doug Hofstadter.

In this great classic, the incomplete math of Gödel twirls across the contradictions of Zen philosophy and the nucleotides of DNA, falling into the mesmerizing art of Escher and Magritte and then landing on the thematic acrobatics of Bach (one of whose melodies spells “BACH”). If you have any geek inside, you will be obsessed.

In the mood for a graphic novel starring Bertrand Russell and a supporting cast of famous thinkers like Whitehead, Frege, Gödel, and Wittgenstein? Logicomix is for you!

Flip to Chapter Six, “Incompleteness,” for a peek of Vienna in the 1930s. The logic and philosophy illustrated throughout provide a great context for the work of Vienna’s famous philosophical circle led by Moritz Schlick, whose 1936 murder provides a chilling contrast to the intellectual pursuits of that time.

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.

The author explains the importance of abstraction in logic, demonstrating its three main components: paths made of long chains of logic, packages made of a collection of concepts structured into a new compound unit, and pivots to build bridges to previously disconnected places.

Eugenia Cheng does an excellent job of abstracting principles of logic to better understand challenging real-world societal issues such as affirmative action and cancer screening. I found it quite compelling to understand how and why she came to her positions on various issues, through her axiom that "avoiding false negatives is more important than avoiding false positives." I appreciated the expertise by which she weaved numerous hard topics, in both mathematics and social justice, into a coherent and compelling narrative.

The previous book is about the most prevalent forms of AI, many of which focus on prediction or classification.

For example, a bank may use an AI system that utilizes data about those applying for a loan to predict whether they're likely to default. The judicial system might use an AI model which takes into account a convicted person's attributes in order to predict whether that person is likely to re-offend. A hospital might observe attributes of cells in order to classify them as cancerous or not.

Judea Pearl, a computer scientist at UCLA, has been in a long-running effort to get those working in AI to focus more on designing systems which could engage in causal reasoning. And in doing so, he's had a major influence on a number of disciplines, including computer science, philosophy, statistics, epidemiology, and the social sciences.

In The Book of Why, Pearl teams up… show more.

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.

We have to learn how to properly use the Internet to prevent it from using us. We must comprehend the limits of artificial intelligence to take advantage of what it has to offer. Christian and Griffiths explore how algorithms can help us solve common – decisions and find strategies to humans.

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.