100 books like The Joy of X

A primary reason to love math is because of its usefulness. This book shows two sides of math’s applicability, since it is so ubiquitously used in various algorithms.

On the one hand, such usage can be good, because statistical inferences can make our life easier and enrich it. On the other, when these are not properly designed or monitored, it can lead to catastrophic consequences. Mathematics is a powerful force, as powerful as wind or fire, and needs to be harnessed just as carefully.

Cathy O’Neil’s message in this book spoke deeply to me, reminding me that I need to be always vigilant about the subject I love not being deployed carelessly.  

Have you ever been to a mathematics lecture where the speaker wore a tuxedo and baffled the audience with his mystifying knowledge of numbers? Well, I have and the speaker was Arthur Benjamin, who combined mathematics and magic. He even displayed this knowledge with Stephen Colbert on his earlier show The Colbert Report. It is our good fortune that he describes much of this mathematical wizardry in this fascinating book. 

Told by one of the most famous orators and expositors of mathematics, Paul Halmos tells us what it’s like being a mathematician – at least what it was like for him being a mathematician. While I was fortunate to have had a conversation with such a unique person (about writing mathematics), it is even more fortunate that he has done many of us a favor by writing this book.

I well remember when Erdos came to MIT to visit my wonderful friend Gian-Carlo Rota. He traveled without money and without a place to stay. He depended entirely on friends. What he offered in return was something of much greater value: his ideas. A mathematician searches everywhere for the right problems to work on – not easy, not random, but opening a door from what we know to what we don't know. Erdos gave that ideal gift to his friends. If you wrote a paper with him, your Erdos number is 1.  

This classic rumination on the nature of mathematics is perhaps the most famous book ever written by a mathematician.

I’ve read it several times, and each time, it brings up another facet of the subject in some new light. Portions of what Hardy says ring eerily true, and seem to be part of the identity, the very DNA, that all mathematicians must surely share. Other parts seem so alien to be almost repugnant – such as his contention that most mathematics we classify as useful is ugly and inelegant.

I’d love to argue face-to-face with Hardy about this highly opinionated work of his. In the end, I suspect we’d find lots of common ground, since intrinsically, we both love mathematics so much.

Robin Wilson, the famous mathematical historian and storyteller with a great sense of humor, along with his co-authors, tell the story of how one particular area of mathematics (graph theory, my favorite area) got its start in the 18th and 19th centuries in Europe, found its way across the Atlantic to America, and what effect Americans had on this area of mathematics. It also tells the fascinating story of how and where more advanced mathematics became part of America. 

This book will be available Fall 2022.

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).

I’ve read a whole bunch of books on the history of mathematics, but this is by far my favorite.

Singh uses the most famous problem in mathematics, called “Fermat’s Last Theorem” to give us a kaleidoscopic account of the subject, starting with the Greek greats like Pythagoras and Plato, and taking us all the way to Andrew Wiles, the contemporary mathematician who finally solved Fermat’s theorem after a few centuries’ worth of attempts.

The book truly gets to the heart of what drives mathematicians. It also is so full of delicious anecdotes and thoroughly engaging math puzzles that I simply couldn’t put it down. I especially love the fact that Singh shows how so much of mathematics came from non-European civilizations, a fact we often forget.

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 is another book about the new research into how babies think. I am excited about this research because of its implications for how people learn mathematics and how researchers create math. This book taught me something important about how we all think. Gopnik distinguishes between what she calls flashlight consciousness and lantern consciousness. Flashlight is the way adults think. You focus on one thing at a time and give it your full attention. But babies, she claims, use their minds differently. Their lantern consciousness is unfocused and is aware of the big picture all at once.  

So what happens to lantern consciousness when you grow up? The answer is that creative individuals use it and alternate between lantern and flashlight consciousness. When we are creating or learning something new, we have to drop back to lantern consciousness. Logic comes from flashlight consciousness and, by itself, will never produce anything… show more.