Books like Great Circles — picked by fans

This book is a brilliant interweaving of politics, history, and intrigue, with characters living ordinary lives, described in the spirit of a Russian novel. With one story threading into another, the book moves us forwards. We fly over the tall mountains, misty valleys, and green fields of current abstract maths and fundamental physics to witness the true beauties of truth. And in the end, Stewart confesses: “No one could have predicted that a pedantic question about equations could reveal the deep structure of the physical world, but that is exactly what's happened.”

As with many of Stewart’s books, Why Beauty is Truth is a joy to read. It brings us through current material with ease of understanding and out oversimplifying. I love the way Stewart uses tangible examples to describe the fundamental forces of nature as he escorts us with clarity through so many eloquent connections between mathematics and physics.… show more.

For me, this book was an adventure. I felt as if I was on an expedition to Virginia with Harriot teaching me astronomy and navigation. There I was, infatuated with rainbows and imagining myself scrutinizing scientific wonders of elliptical planetary motion, atomic theory of matter, and how cannonballs could be stacked to fill space. I found myself with Harriot back in 1591 searching for a sphere-packing formula, an old problem questioning the most stable way to stack cannonballs on ships. Thomas Harriot is a fast-moving biography packed with the world- and mind-changing curiosities.

Ekeland’s book is an entwinement of philosophical views of scientists with metaphysics dealing with nature’s directives. It’s an embroidery of lively anecdotes involving illustrious individuals and great historical moments of human decisions. We go through the Peloponnesian Wars, Venetian concessions to the Hapsburg emperor Maximilian, Darwin’s voyage to the Galapagos, and other enriching accounts. His explanations are clear, elegant, fluid, exhilarating, and suspenseful, reminding me of the effortless style of Richard Feynman. While reading, I felt compelled by a force of nature and purpose to learn about the best of all possible worlds.   

More than any other, this book influenced me most about wanting to study mathematics. Of course, I was young at the time and strongly partial to Einstein’s remark, “This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands.” Many years later, when I exhaustively tried to find the book in any bookstore I passed, it was out of print. So I suggested it to my publisher, who immediately acquired the rights and republished it under my editing guidelines. It is the quintessential lure into mathematics for readers of any age.   

From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.

But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.

She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).

A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.

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.

In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.

My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.

The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.

I highly recommend this book as a second book on linear algebra.

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. 

Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are. 

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.