A Few More Math Books For The Nonmathematician

Mathematics: A Very Short Introduction, Timothy Gowers (2002)
Amazon: The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school.
The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and
imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics.

Fermat’s Enigma, The Epic Quest to Solve the World’s Greatest Mathematical Problem, Simon Singh (2017)
Amazon: “I have discovered a truly marvelous proof, which this margin is too narrow to contain”. With these tantalizing words the seventeenth-century French mathematician Pierre de
Fermat threw down the gauntlet to future generations. What came to be known as Fermat’s Last Theorem looked simple, yet the finest mathematical minds would be baffled for more than three and a half centuries. Fermat’s Last Theorem became the Holy Grail of mathematics. … Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

Chaos, Making a New Science, James Gleick (2011)
Amazon: Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. In Chaos, James Gleick, a former science writer for
the New York Times, shows that he resides in this exclusive category. Here he takes on the job of depicting the first years of the study of chaos–the seemingly random patterns that characterize many natural phenomena. This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. …

Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, John Derbyshire (2003)
Amazon: In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime
Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hypothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime
Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Infinite Powers, How Calculus Reveals the Secrets of the Universe, Steven Strogatz (2019)
Amazon: Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

How to Prove It, A Structured Approach, Daniel J. Velleman (2019)
Amazon: Geared to preparing students to make the transition from solving problems to proving
theorems, this text teaches them the techniques needed to read and write proofs. The book begins
with the basic concepts of logic and set theory, to familiarize students with the language of
mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step
breakdown of the most important techniques used in constructing proofs. …

The Number Devil, A Mathematical Adventure, Hans Magnus Enzensberger, Rotraut Susanne Berner & Michael Henry Heim (2000)
Amazon: The international best-seller that makes mathematics a thrilling exploration. In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the
amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone – from those who fumble over fractions to those who solve complex equations in their heads – winds up marveling at what numbers can do.

A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.
Paul Lockhart, Keith Devlin (2009)
Amazon: A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever. “One of the best critiques of current mathematics education I have ever seen.”—Keith Devlin, math columnist on NPR’s Morning Edition

Love and Math, The Heart of Hidden Reality, Edward Frenkel (2013)
Amazon: What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.
In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Proofs from THE BOOK, Martin Aigner, Günter M. Ziegler & Karl H. Hofmann (2018)
Amazon: This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 “Steele Prize for Mathematical Exposition,” “… It is almost impossible to write a mathematics book that can be read and enjoyed by people
of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-
mathematicians what it is that mathematicians mean when they speak about beauty.”

Calculus Made Easy, Silvanus P. Thompson, Martin Gardner (2018)
Amazon: Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers
of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made
Easy has been thoroughly updated for the modern reader.

God Created the Integers: The Mathematical Breakthroughs That Changed History, Stephen Hawking (2007)
Amazon: Bestselling author and physicist Stephen Hawking explores the “masterpieces” of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from
the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter
begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

Mathematics and the Imagination by Edward Kasner & James Newman (2001)
Amazon: You don’t have to love math to enjoy a hand of cards, a night at the casino, or a puzzle. But your pleasure and prowess at games, gambling, and other numerically related pursuits can be
heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics. A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet
bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of
chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how
calculus, among its other uses, helps trace the path of falling bombs. Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-
Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting.” — Saturday Review of

Mathematics for Human Flourishing, Francis Su & Christopher Jackson (2021)
Amazon: In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all.

99 Variations on a Proof, Philip Ording (2021)
Amazon: This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.

Logicomix: An epic search for truth, Apostolos Doxiadis & Christos Papadimitriou (2009)
Amazon: This exceptional graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, Russell crosses paths with legendary thinkers
like Gottlob Frege, David Hilbert, and Kurt Gödel, and finds a passionate student in the great Ludwig Wittgenstein. But his most ambitious goal-to establish unshakable logical foundations of mathematics-continues to loom before him. Through love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness,