100 books like Mind and Matter

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.

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.    

Can you love a book that you disagree with? I do! I love this extravagant account of how Bayesian Statistics was enmired in controversy and, after 200 years, saved everything from Western Civilization to Captain Dreyfus.

I don’t think that Bayesian statistics is the foundation of all rational thought, but I am happy to celebrate all its wonderful achievements. Every page of this book is lively and personal, engrossing, entertaining, masterful…all of that.

It is fair to say that many people—even those who loved mathematics as students—view mathematics as having always existed. The idea that definitions and theorems that fill our school textbooks were created or discovered by human beings is something that has never crossed their mind. In fact, mathematics has a long, fascinating, and rich history, and William Dunham’s Journey Through Genius is a perfect introduction to the topic. Dunham expertly writes about the history of topics like geometry, number theory, set theory, and calculus in a way that is entertaining, understandable, and rigorous. After finishing Journey Through Genius, readers will not think about mathematics in the same way, and they will be eager to learn about the history of other mathematical topics, people, and cultures.

First published in 1937, this lovely book is a true classic. In two volumes Bell brings to life 30 or so mathematicians, from Archimedes to Cantor. When first reading the book many years ago I had remembered some of the names from school and college, but only as labels to theorems or equations, and I felt taken into a delightful new realm of knowledge – I could now think of Fermat, Lagrange, Gauss, and Riemann as people. And I began to want to know more about the scientists whose names I had heard in school and college. Bell’s book had sparked a lifelong interest.

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.

One way of enlivening any presentation of mathematics is by including some history of the subject, but this only really works if there is some serious scholarship behind it. I especially like Hollingdale's book, partly because of the concise writing style, and partly because of the unusually good balance between history and mathematics itself. The calculus, in all its various forms, with some aspects going right back to the Ancient Greeks, is treated especially well.

For me, this book got the closest to the nitty-gritty of why mathematicians like me, whose job is to prove theorems, find this activity so compelling.

It’s always been the long hunt, with all the frustration as well as the occasional success, that I’ve found so addictive. Doxiadis brought out the nuances of such pursuits brilliantly – the wily Uncle Petros tells the narrator to prove a mathematical statement despite knowing it is almost surely false.

Ah, these little tricks that we mathematicians enjoy playing on unsuspecting souls (I’ve been known to do this to my students a couple of times).

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.