100 books like How Not to Be Wrong

This book picks up where Evening in the Palace of Reason leaves off, with Bach composing the Musical Offering on a horrible theme from King Frederick.

It explains canons and fugues, and thus helps you understand Bach’s work better, but it then goes on a safari through the intellectual landscape of ideas related to fugues–strange loops, self-similarity, recursion, and of course the guys in the title. It’s not for everyone, but if you like any two of logic, philosophy, or music, give this a try.

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.

Frenkel came from the Soviet Union, where discrimination against Jews made it impossible for him to get into Moscow State University. During the oral exam they sent two graduate students to question him, pick holes in his responses, and ensure he failed. He turned to an informal network of Soviet mathematicians for help.

Like him, they were denied serious employment in the field, but after the 'cold war' against the Soviet Union, Harvard invited him to take a fellowship that later turned into a permanent job. Years later, when his old tormentor from Moscow State arrives to give a talk, he confronts the man in a lecture room with first-hand evidence of allegations against the system. Faced with a victim, the Russian mathematician's denials rang hollow. 

This book reaches beyond mathematics to anyone of independent thought in an environment where it is not permitted to step out of line or,… 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.

In the ongoing debates over artificial general intelligence (AGI), Judea Pearl is taking a firm stand: He argues that an intelligent robot should be able to reason about causality and that the currently fashionable approaches to AI miss this aspect.

A celebrated AI researcher and a Turing Prize laureate, Pearl has developed an amazingly original approach to this problem. This book is a high-end popular exposition of his approach.

But it’s so much more than that. It’s a history of statistics and its conflicted attitude to causality. It’s a story of heroes (or villains?) in this history. And it’s a scientific autobiography that describes Pearl’s journey. Pearl likes picking fights with the AI community, statisticians, or economists. He’s boastful, provocative, extremely intelligent, and knows how to tell a story.

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.

I always find myself applying algorithmic thinking in my everyday life—it affects the way I put away dishes, navigate to the store, and organize my to-do lists. And I think others could benefit from that mindset.

So, when I read this book, my reaction was "Yes! That's what I want people to know. I just wish I could have said it that well!" The authors (who I know, but didn't know they wrote a book together), did a fantastic job of selecting algorithms with deep human connections. Really! And they explain them just right, without getting too mathematical but while still hitting the key ideas with clarity and accuracy. Fantastic!

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.