100 books like Shape

Blew my world apart. 

Without one single formula, Feynman takes you to the heart of quantum theory. The foundations of everything you thought you knew about light get ripped out and replaced by new foundations that cover every success of the 19th-century theory yet offer new vistas. I will probably read this tiny book every year for the rest of my life; each time I get new insights into physics (and the presentation of physics).

After reading it, you will understand the stationary-phase principle better than most Physics PhD students without one formula.

Math is so much more than algebra.

Steve Strogatz is our generation’s poet laureate of math. I could not put this book down because, although I use math daily, I was amazed at how Strogatz connects everything to everyday experience. Just one example: Hardly anyone gets told about “group theory” in high school because it’s “too advanced”—but here we find it beautifully illustrated with the problem of flipping your mattress twice a year.

This book will help you have your own ideas by opening your eyes to a world of things that just make better sense through the lens of careful analysis, the interplay of the visual and the symbolic, and (just enough) abstraction.

Elegant, deep—I learned many things here. 

This book will help you develop your own good ideas because the author respects you too much to give a jumble of just-so stories wrapped in glib human interest. Instead, he explains, often with brilliant metaphors from everyday experience. I especially liked the chapters on embryos, organs, the microbiome, and scaling, which are particularly fresh, insightful, and beautifully clear.

Also, unlike so many popularizations, this one is full of graceful but precise illustrations that pull you in and actually clarify key points—not just eye candy. This book will help you have your own ideas by interconnecting physics and biology ideas that are hardly ever mentioned in the same breath.

A thread that ties together so many things.

Throughout science, math, finance, and your personal life… underlying almost everything is the concept of a random walk. I love how Mlodinow builds our intuition for this simple yet subtle idea. Yes, the expectation may be zero, but the variance grows without limit—it took me years of study to truly feel that statement and others in my bones, but Mlodinow shows this and much more through vivid, often hilarious examples. It is no exaggeration to say that after Chapter 6, you will understand conditional probability—where so many of us stumble when we think about real situations—better than you would after a whole course on statistics.

And although this is a science book, I challenge anyone to read the last five pages and end up dry-eyed. Years later, as I reread them, the impact is undiminished.

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.

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. 

I was given this book when I was about 15, and devoured it. It is an eclectic collection of mathematical paradoxes, fallacies, and curiosities so strange that they seem impossible. Mathematical magic tricks, a proof that all numbers are equal, a proof that all triangles are isosceles, a curve whose length is infinite but whose area is finite, a curve that crosses itself at every point, a curve that fills the interior of a square. Infinities that are bigger than other infinities. The Saint Petersburg Paradox in probability, a calculation that you should pay the bank an infinite amount of money to play one fair coin-tossing game. The smallest number that cannot be named in fewer than thirteen words (which I’ve just named in twelve words).

I stumbled on this in a used bookstore. What a find! The old-school, kid-friendly illustrations lead swiftly from simple beginnings (“What happens when you stretch a painting?”) to the depths of undergraduate topology. I haven’t used this in the classroom yet, but honestly, I could imagine busting it out with anyone from first-graders to first-year PhD candidates.

Picking up this short picture book, I expected a dose of Phantom Toolbooth-esque wordplay. Not at all. This five-minute love story, about a line yearning for a dot, somehow enlarges into a meditation on geometric structure itself. From such a brief book, I didn’t expect new insights about how simple geometry underlies our most intricate thinking—but then again, that’s what delightful visuals will do for you.

Robin Evans was a versatile architectural historian and theorist who died too young. This highly original and unusual book, published after his death, is about the relationship of geometry to architecture, and how methods of drawing, including perspective and orthographic projection, can influence what is conceived and built. I admire the way in which Evans, unlike many architectural historians, is able to combine deep scholarship with a working practical understanding of how buildings are made, and how they are used in practice. There has been no other recent writer on architecture with so subtle a mind.