How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

by Eugenia Cheng

Overview

One of the world's most creative mathematicians finds the meaning of mathematics in the kitchen in this "whimsical...rigorous and insightful" (New York Times) book

What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the bechamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works.

Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.

Product Details

ISBN-13:	9780465097678
Publisher:	Basic Books
Publication date:	05/10/2016
Edition description:	First Trade Paper Edition
Pages:	304
Sales rank:	369,866
Product dimensions:	5.40(w) x 8.20(h) x 1.20(d)

About the Author

Eugenia Cheng is Scientist in Residence at the School of the Art Institute of Chicago and an 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.

Table of Contents

Part I: Math
1. What Is Math?
2. Abstraction
3. Principles
4. Process
5. Generalization
6. Internal vs. External
7. Axiomatization
8. What Mathematics Is

Part II: Category Theory
9. What Is Category Theory?
10. Context
11. Relationships
12. Structure
13. Sameness
14. Universal Properties
15. What Category Theory Is

Editorial Reviews

"Cheng never quite overeggs her metaphor of the mathematician as chef...and her tone is clear, clever and friendly. Even at her most whimsical she is rigorous and insightful. Potentially confusing ideas are expressed with a matter-of-fact simplicity.... How to Bake Pi is a welcome addition to the popular-math shelf, unusual not only because of its quirky premise but also because Cheng is a woman, a lucid and nimble expositor, and unashamedly proud of her domestic obsessions.... It would be wonderful if this book attracted a new audience to the field. And there's no better ambassador (or dinner-party host, I'd wager) than Eugenia Cheng."—Alex Bellos, New York Times Book Review

"[A] slyly illuminating dispatch on the deep meaning of mathematics.... Cheng manages to do for us what the mathematician Keith Devlin has said mathematicians do for themselves: she compels us to see numbers and symbols as vivid characters in an ongoing drama, a narrative in which we are alternately observers and participants."—Natalie Angier, The American Scholar

"[O]ften entertaining...frequently illuminating.... [How to Bake Pi] offers enough nourishment for the brain to chew on for a long time."—Columbus Dispatch

"In her new book, How to Bake Pi, mathematician/baker Eugenia Cheng offers a novel, mathematical approach to cooking.... How to Bake Pi is more than a mathematically-minded cookbook. It is just as much a book about mathematical theory and how we learn it. The premise at the heart of the book is that the problem that stops a cookbook from teaching us how to cook is the same problem that makes math classes so bad at actually teaching us to do math."—Ria Misra, io9

"Invoking plenty of examples from cooking and baking, as well as other everyday-life situations such as calculating a taxi fare, searching for love through online dating services and training for a marathon, [Cheng] explains abstract mathematical ideas—including topology and logic—in understandable ways.... Her lively, accessible book demonstrates how important and intriguing such a pursuit can be."—Scientific American

"[Cheng's] book, a very gentle introduction to the main ideas of mathematics in general and category theory in particular, exudes enthusiasm for mathematics, teaching, and creative recipes. Category theory is dangerously abstract, but Cheng's writing is down-to-earth and friendly. She's the kind of person you'd want to talk to at a party, whether about math, food, music, or just the weather.... Cheng's cheerful, accessible writing and colorful examples make How to Bake Pi an entertaining introduction to the fundamentals of abstract mathematical thinking."—Evelyn Lamb, Scientific American's Roots of Unity blog

"Combined with infectious enthusiasm for cooking and a zest for life, Cheng's perspective on math becomes this singular book: a funny, lively, and clear journey no popular book on math has explored before. How to Bake Pi...will dazzle, amuse, and enlighten."—Gambit Weekly

"This is the best book imaginable to introduce someone who doesn't think they are interested in mathematics at all to some of the deep ideas of category theory, especially if they like to bake."—MAA Reviews

"Beginning each chapter with a recipe, Cheng converts the making of lasagna, pudding, cookies, and other comestibles into analogies illuminating the mathematical enterprise. Though these culinary analogies teach readers about particular mathematical principles and processes, they ultimately point toward the fundamental character of mathematics as a system of logic, a system presenting daunting difficulties yet offering rare power to make life easier. Despite her zeal for mathematical logic, Cheng recognizes that such logic begins in faith—irrational faith—and ultimately requires poetry and art to complement its findings. A singular humanization of the mathematical project."—Booklist, starred review

"Cheng is exceptional at translating the abstract concepts of mathematics into ordinary language, a strength aided by a writing style that showcases the workings of her curious, sometimes whimsical mind. This combination allows her to demystify how mathematicians think and work, and makes her love for mathematics contagious."—Publishers Weekly, starred review

"What a charming and original book! The central analogy—math is like cooking—turns out to be surprisingly apt and often funny. Light and tasty, yet so, so good for you, How to Bake Pi is a real treat."—Steven Strogatz, Professor of Mathematics, Cornell University and author of Infinite Powers and The Joy of x

"Eugenia Cheng's charming new book embeds math in a casing of wry, homespun metaphors: math is like vegan brownies, math is like a subway map, math is like a messy desk. Cheng is at home with math the way you're at home with brownies, maps, and desks, and by the end of How to Bake Pi, you might be, too."—Jordan Ellenberg, Professor of Mathematics, University of Wisconsin-Madison, and author of Shape and How Not to Be Wrong

"With this delightfully surprising book, Eugenia Cheng reveals the hidden beauty of mathematics with passion and simplicity. After reading How to Bake Pi, you won't look at math (nor porridge!) in the same way ever again."—Roberto Trotta, author of Starborn and The Edge of the Sky

"Math is a lot like cooking. We start with the ingredients we have at hand, try to cook up something tasty, and are sometimes surprised by the results. Does this seem odd? Maybe in school all you got was stale leftovers! Try something better: Eugenia Cheng is not only an excellent mathematician and pastry chef, but a great writer, too."—John Baez, Professor of Math at the University of California, Riverside

"From clotted cream to category theory, neither cookery nor math are what you thought they were. But deep down they're remarkably similar. A brilliant gourmet feast of what math is really about."—Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick, and author of Visions of Infinity and What's the Use?

"An original book using recipes to explain sophisticated math concepts to students and even the math-phobic.... [Cheng] is a gifted teacher... A sharp, witty book to press on students and even the teachers of math teachers,"—Kirkus Reviews

"[A] well-written, easy-to-read book."—Library Journal

"A curious cookbook for the mathematical omnivore."—The Irish Times

From the Publisher

…[Cheng's] tone is clear, clever and friendly. Even at her most whimsical she is rigorous and insightful. Potentially confusing ideas are expressed with a matter-of-fact simplicity…How to Bake Pi is a welcome addition to the popular-math shelf, unusual not only because of its quirky premise but also because Cheng is a woman, a lucid and nimble expositor, and unashamedly proud of her domestic obsessions. The vast majority of university math professors are men, as are the vast majority of popular math authors. It would be wonderful if this book attracted a new audience to the field. And there's no better ambassador (or dinner-party host, I'd wager) than Eugenia Cheng.

The New York Times Book Review - Alex Bellos

★ 03/02/2015
Cheng, a lecturer in mathematics at both the University of Sheffield and the University of Chicago, sets an ambitious agenda for herself: to explain to non-mathematicians how mathematicians think and to educate readers about the tools mathematicians employ when seeking solutions to complex problems. She begins each chapter with recipes (mostly desserts) that she then employs to illustrate the thought processes that underlie mathematical reasoning—a surprisingly stimulating and successful conceit. Having grabbed the reader’s attention, Cheng playfully walks through numerous math problems of varying difficulty, taking care to provide understandable and illuminating solutions. She often departs from mathematical theory to highlight the pragmatic values of logic and rationality as employed by mathematicians in everyday life, and she possesses a lighter side that recognizes mathematical reasoning is not life’s holy grail, underlining her point with an entertaining, and wise, six-point indictment of pure logic as a tool with which to approach “all that life throws at us.” Cheng is exceptional at translating the abstract concepts of mathematics into ordinary language, a strength aided by a writing style that showcases the workings of her curious, sometimes whimsical mind. This combination allows her to demystify how mathematicians think and work, and makes her love for mathematics contagious. Agent: George Lucas, Inkwell Management. (May)

Publishers Weekly

03/01/2015
In this humorously titled work, Cheng (mathematics, Univ. of Sheffield, UK; Univ. of Chicago) combines her love of mathematics and cooking in an attempt to explain category theory to the layperson. There is hope that this theory, which provides a way to express ideas common to different areas of mathematics, may bring about advances in science. However, most of the areas of study in which category theory reveals insight through structural commonalities are fields such as group theory, topology, and mathematical logic; subjects that are themselves well beyond the mathematical background of most readers. Thus, the examples that the author has to offer are of the most elementary nature and really shed little light on the topic. In this personal memoir, Cheng tells us of her musical talent and training, her marathon running, and her general outlook on life. There is no doubt that she is a multitalented person and an outstanding expositor, but readers come away from the book knowing a great deal about the author and not much about the subject. VERDICT This is a well-written, easy-to-read book, but one that has a limited audience.—Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

Library Journal

Tavia Gilbert narrates with a liveliness and lightness that one might not expect in a book about the world of mathematics. Various recipes are used to highlight points about math, revealing that math, like cooking recipes, is made up of ingredients and method. Gilbert persuasively presents this edible exploration into mathematical concepts, making them seem as familiar and unintimidating as cooking. Gilbert’s fluid voice conveys the themes of beauty and power in both the concrete and abstract aspects of math. While it’s uncertain whether or not everyone will come away with a complete understanding of the concepts, Gilbert’s lyrical narration, together with her deliberate speed as she delivers the formulas, brings clarity and a down-to-earth approach to this often intimidating subject matter. M.F. Winner of AudioFile Earphones Award © AudioFile 2015, Portland, Maine

JUNE 2015 - AudioFile

2015-03-03
An original book using recipes to explain sophisticated math concepts to students and even the math-phobic. In a chapter on generalization, Cheng (Mathematics/Univ. of Sheffield and Univ. of Chicago) begins with a recipe she adapted to produce a cake that was vegan as well as gluten-, sugar-, and dairy-free, thus extending the recipe's usefulness to serve more people. A chapter on axiomatization describes the difference between basic ingredients and things you can make with basic ingredients (e.g., marmalade). Math uses basic ingredients—axioms—that are assumed to be true and proofs that use hard logic to derive new truths. That's what math is all about, writes the author; it is different from science, which gathers evidence to draw conclusions. By this time, Cheng has introduced readers to number systems, groups and sets, algebra, and topology. She also discusses internal vs. external motivation. In cooking, this is the difference between looking at what is on the shelves and figuring out how to use it in a recipe you invent (internal motivation) versus having a recipe in mind and gathering all the ingredients you need to make it (external). The author laments the way math is often taught, with the teacher providing a problem to solve and students finding the correct answer. She is strongly internally motivated in the pursuit of her specialty, category theory. She calls it the mathematics of mathematics, a field that seeks the most abstract generalizable concepts in relation to the worlds of mathematical objects. Cheng explains how category theory works by emphasizing contexts, relationships, structure, and universal properties, giving examples. The reading is tougher going here, probably because readers are in a state she describes as believing what she is teaching but not fully understanding it. However, Cheng is such a gifted teacher, readers will want to dive in again. A sharp, witty book to press on students and even the teachers of math teachers.

Kirkus Reviews