Is Math Real?: How Simple Questions Lead Us to Mathematics' Deepest Truths

by Eugenia Cheng

Overview

Winner of the Los Angeles Times Book Prize 
A New Scientist Best Book of 2023

One of the world’s most creative mathematicians offers a new way to look at math—focusing on questions, not answers 

Where do we learn math: From rules in a textbook? From logic and deduction? Not really, according to mathematician Eugenia Cheng: we learn it from human curiosity—most importantly, from asking questions. This may come as a surprise to those who think that math is about finding the one right answer, or those who were told that the “dumb” question they asked just proved they were bad at math. But Cheng shows why people who ask questions like “Why does 1 + 1 = 2?” are at the very heart of the search for mathematical truth.  

Is Math Real? is a much-needed repudiation of the rigid ways we’re taught to do math, and a celebration of the true, curious spirit of the discipline. Written with intelligence and passion, Is Math Real? brings us math as we’ve never seen it before, revealing how profound insights can emerge from seemingly unlikely sources.   

Product Details

ISBN-13:	9781541601826
Publisher:	Basic Books
Publication date:	08/15/2023
Pages:	336
Sales rank:	43,485
Product dimensions:	6.30(w) x 9.40(h) x 1.20(d)
Age Range:	12 - 18 Years

About the Author

Eugenia Cheng is Scientist in Residence at the School of the Art Institute of Chicago and honorary visiting fellow at City, University of London. She has authored numerous titles, including How to Bake Pi, Beyond Infinity, The Art of Logic, and x + y. Cheng lives in Chicago, Illinois.

Editorial Reviews

★ 08/07/2023

“Math might seem like it’s about getting the right answers, but really it’s about the process of discovering,” according to this invigorating philosophical take on the field. Mathematician Cheng (The Joy of Abstraction) explores how such questions as “how many sides does a circle have?” and “why does –(–1)=1?” reveal surprising profundities about math. She suggests that situations in which one plus one does not equal two (one pile of sand placed on another makes for one pile) shows how numbers are ways of abstracting and simplifying the world that require individuals to decide what to count (piles of sand) and what to ignore (the individual grains in each pile). Classrooms, she laments, typically shun such modes of inquiry in favor of instilling “rigidly imposed rules,” contrary to the “point of math,” which, she argues, is “learning how to decide what counts as a good answer when there is no answer key.” Cheng has a talent for making mathematical discussions accessible, and her wide-ranging analysis leads to some surprisingly weighty conclusions, as when she argues that expecting students to accept mathematical rules without question sends the message that truth comes from authority, making it nigh impossible to reason with students “because their beliefs aren’t based on reason; they’re based on authority.” It adds up to a stellar meditation on the nature of knowledge and math. (Aug.)

Publishers Weekly

2023-04-24
An abstract if oddly entertaining foray into the more philosophical realms of mathematics.

A noted popularizer of mathematics, Cheng, the author of Beyond Infinity and How To Bake Pi, works at the frontiers of the discipline in an arcane area “called category theory,” which “doesn’t involve numbers and equations at all.” If the thought of math without numbers makes your head hurt, the author’s latest book will be a constant challenge. Math is real, she tells us, in much the same way that Santa Claus is real: as an idea. Thus, as she puts it, it’s entirely possible that another idea can come into play, namely that 1 + 1 does not equal 2; the question then becomes not “What is 1” or “What is 2,” but instead, “What is a world in which 1 + 1 = 2?” Given that math, in concert with physics, admits the possibility of an infinite number of worlds, or dimensions, a world where 1 + 1 = 1 isn’t out of the question. Our world gives the answer of 2 because that’s the abstraction we agree on, just as we agree (for the most part) on the laws of logic—and that’s a key idea, for, as Cheng says brightly, “Mathematics is the logical study of how logical things work.” The strict rules of logic can, of course, make a person’s head hurt, too; one has only to think of Zeno’s paradox, wherein neither the tortoise nor the hare actually wins a race because “the sum doesn’t converge.” Some of the author’s examples take the form of equations, and while it helps to be numerate, the numerophobic shouldn’t shy away from digging in. Despite her provocative title, others are fun examples from the very real world, such as using a recipe for mayonnaise to discuss the process of commutativity.

For the budding mathematician in the house, to say nothing of lovers of puzzles and enigmas.

Kirkus Reviews

Winner of the 2023 Los Angeles Times Book Prize in Science & Technology

A New Scientist Best Book of 2023

“[Cheng] also succeeds in making the reader feel that not understanding something in mathematics isn’t the same as being bad at it: rather, it is a clue that you are onto something deeper, the pursuit of which could reap rewards.  The book is infused with personal ruminations that lighten the load and keep the tone conversational…Cheng wears her heart and politics on her sleeve, segueing seamlessly…from mathematics to social concerns…Nicely parried, while providing fodder for those who want to chew on this some more.”—New Scientist

“The maths content of Eugenia Cheng’s book is brilliant …The mathematical journey that Cheng takes us through is mesmerizing….do read it if you want to know more about the nature of pure mathematics and about being a mathematician.”—Popular Science

“[Is Math Real?] demonstrates the ways that seemingly naïve questions can unlock fascinating journeys to understanding math for math’s sake.”—Science News

“An invigorating philosophical take on the field…Cheng has a talent for making mathematical discussions accessible, and her wide-ranging analysis leads to some surprisingly weighty conclusions…It adds up to a stellar meditation on the nature of knowledge and math.”—Publishers Weekly (Starred)

“A fantastic, thought-provoking read. Cheng is the kind of mathematician and writer who performs some sort of creative magic that enables you to understand what you thought you couldn’t, and makes math fascinating.”—BookRiot

“[An] entertaining foray into the more philosophical realms of mathematics… For the budding mathematician in the house, to say nothing of lovers of puzzles and enigmas.”—Kirkus

“Is Math Real? is a generous tour of mathematics for anyone whose instincts tend less towards ‘Just tell me the answer’ and more towards ‘Wait, but why?’”—Jordan Ellenberg, author of Shape

“This book is a brilliant rebuttal to those who see math as only about right answers, rather than about creative discovery. In her singularly inviting style, Cheng digs deep to engage fundamental questions that others might dismiss. She masterfully uncovers what’s simply profound in the profoundly simple and demonstrates how math can help us express the nuance and the richness of our world.”—Francis Su, author of Mathematics for Human Flourishing

“In a delightfully accessible style, Eugenia Cheng invites us to move beyond the prototypical love-hate relationship with mathematics and embrace a unique appreciation of mathematics as tool for human flourishing. Escaping negative, socially engrained perspectives, Is Math Real? invites us on a journey of discovery and illuminates a path to joyfully embracing the mathematician in all of us.”—Talithia Williams, author of Power in Numbers

“Cheng narrates in a gently instructive first-person voice, inviting readers back into the world of mathematics…Cheng’s affable style carries her central message through to the end.”—Scientific American

From the Publisher