100 books like The Theory That Would Not Die

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.    

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.

I am laughing out loud, even now that I am rereading this book for the umpteenth time. Fraudsters are so clever, and so is advertising. And then there is sloppy journalism with its “wow” statistics.

I like his book enormously, not least because of its witty illustrations. It is subversive, comic, and provocative, and it makes me wise to seductive, misleading practices–and it does so with a light touch.

One day, in conversation with Ian Hacking, he announced a new passion: Archaeology of ideas. The concept we now have of probability was new, he said; it was born in the 17th century and was different from anything before!

I love this book because it is, first of all, a philosopher’s take on history. Hacking confronts the conceptual puzzles that defeated some of the best mathematical minds, raises controversial questions about what it all meant, and gives us a new vision of the history of concepts.

What could be more exciting?

I found a copy of this book in the sixties. That copy, much loved, was lost in moves and mayhem. Now, I only have a Dover reprint (water-logged during yet another move), but I have never been without and would search high and low if I were.

This is also a history of probability but with a very different focus. Ms. David was a statistician able to explain the calculations intuitively (good to assign to my students). But she was also thoroughly interested in the personalities involved. What was Galileo like? What happened to Pascal at Port-Royal?

I felt personally drawn into the historical narrative that often reads like a novel. 

I love this book because it builds practical advice on a philosophical critique.

Can philosophy generate truly practical advice for planning and public policy? Randomized Controlled Trials are the gold standard for evidence in industrial planning and public policy. But if the results are taken naively, they mislead.

I’m a long-time fan of author Nancy Cartwright, a McArthur Genius Award winner. I love her provocative approach when abstract thought has to confront real practice.  

Gregor Mendel was a lone genius who, pottering with pea plants, unlocked the secrets of modern genetics; Charles Darwin boldly took on the power of the Church with his theory of evolution; chance favoured the prepared mind of Louis Pasteur…right? Well, no, not according to historian John Waller who takes a sledgehammer to the heavily mythologised historical accounts of scientific discovery that are so often found in textbooks before kindly picking up the pieces to rearrange them into a much more honest and authentic account of how science works. Physicist-turned-philosopher Thomas Kuhn once warned that trying to learn the history of science from the pages of a science textbook was no better than assuming an intimate knowledge of a foreign country and its customs after having briefly thumbed through a glossy travel brochure. If the past is indeed a foreign country, then Waller is a reliable local guide who speaks… show more.

Edward Grant’s book begins, as mine does, with the medieval rediscovery of Aristotle’s works, but he focuses more intensively than I do on the impact of the new learning on scientific education and discovery. Writing clearly and gracefully, Grant demonstrates that a real scientific revolution began three hundred years before the “Scientific Revolution” of the sixteenth century. Along the way, he has some fascinating things to say about the curriculum of medieval universities and life among the first generation of European scientists. A valuable and enjoyable read.