Review by Choice Review
In this book, food recipes and cooking, both as a process and science, motivate a wide range of mathematical discussions. Overflowing with analogies and metaphors, the text forces a rethinking of understandings, knowledge, and beliefs within mathematics. The multiple views and reviews of simple mathematics demonstrate the need for caution in how one regards the doing and content of mathematics. Cheng (Univ. of Sheffield, UK) delves into a wide and diverse menu of mathematics, intentionally setting the stage for her argument that one can use category theory to "make difficult mathematics easy." The text does raise interesting questions and perspectives regarding mathematicians' use of abstraction, generalization, principles to support process, internal and external motivations, axiomatization, logic, proof, structure, and universal properties. At times, however, the author flits too fast from one idea to another or leaves a difficult mathematical idea unresolved, creating an aftereffect of half-baked notions that don't satisfy the appetite. The text's final chapters on category theory seem incomplete or oversimplified. Nonetheless, readers uninterested in the significant mathematical questions being raised can perhaps focus on the interesting recipes--provided in a mathematics book, no less! The UK paperback edition has the title Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths (Profile Books). Summing Up: Recommended. All readership levels. --Jerry Johnson, emeritus, Western Washington University
Copyright American Library Association, used with permission.
Review by New York Times Review
TO MAKE MATHEMATICS palatable for the lay reader, the author must sweeten the pill. There are many ways to do this, but Eugenia Cheng is surely the first to have approached the task literally, writing a math book in which almost every chapter begins with a recipe for dessert. Math and cooking are similar, she writes. Both involve ingredients and methods. Just as a baker needs to master the principles of his ingredients, a mathematician must learn the principles of numbers. Puff pastry is an example of how basic ingredients can make something sophisticated and delicious. Likewise math can get very complicated and fascinating with only a few simple concepts. And when you adapt a cake to be gluten-free, dairyfree, sugar-free or Paleo-compatible, you are modifying the notion of what it is to be a cake, in the same way mathematicians generalize from, say, a particular triangle to a family of triangles. Cheng never quite overeggs her metaphor of the mathematician as chef, however, 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 matterof-fact simplicity: "As long as your new idea doesn't cause a contradiction," she writes, "you are free to invent it." The math is presented in bite-size chunks and made relevant through personal stories from Cheng's school years in Britain and life in America, where she is scientist in residence at the School of the Art Institute of Chicago. Math and cooking, however, have some important differences. Mathematicians value the process more than the ingredients, and Cheng's aim is to explain how mathematicians think, rather than focus on the mathematical objects they think about. Her own recipe for the book is to prep the reader with explanations of concepts like abstraction, generalization and axiomatization, before serving up her signature dish: category theory, her own research area, which she calls "the mathematics of mathematics." If math is a system, or organizing principle, that enables us to make precise statements about concepts and to make clear arguments about them, then category theory is a meta-system that allows us to study the structures of mathematics itself. These structures, called categories, consist of objects and the relationships among them. The objects can be anything (numbers, distances, shapes) and the relationships can also be anything (adding, squaring, rotating). Category theorists get excited when the same structures emerge in very different mathematical areas. As may be inevitable in a book about structure and process, Cheng is conscientious about telling you at every stage what she's doing and why. The reader won't get lost, as is often the case in math. But while she successfully conveys a love of her subject, I felt shortchanged; Cheng never explains exactly how category theory has shaped math, never shares its major results and its great unsolved questions. Perhaps she thought the answers would be too arcane or complicated for a book aimed at general readers. Still, "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. Eugenia Cheng's signature dish is category theory, 'the mathematics of mathematics.'
Copyright (c) The New York Times Company [July 22, 2015]
Review by Booklist Review
*Starred Review* When James Bond and Vesper Lynd first meet in Casino Royale, they do not talk about mathematics. Yet in their meeting Cheng finds an engaging illustration of the category theory that she and other mathematicians use when assessing how context determines the meaning of numbers. But then Bond cinema is only one of the surprising venues Cheng visits in helping readers understand mathematics. To explicate various mathematical concepts, Cheng takes readers to see a Cambridge soccer tournament, a group of children playing with Legos, and even a murder trial. But it is the gourmet kitchen that Cheng visits again and again to clarify just what it means to do mathematics. 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.--Christensen, Bryce Copyright 2010 Booklist
From Booklist, Copyright (c) American Library Association. Used with permission.
Review by Publisher's Weekly Review
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) © Copyright PWxyz, LLC. All rights reserved.
(c) Copyright PWxyz, LLC. All rights reserved
Review by Library Journal Review
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 (c) Copyright 2015. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
(c) Copyright Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
Review by Kirkus Book Review
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 ingredientsaxiomsthat 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. Copyright Kirkus Reviews, used with permission.
Copyright (c) Kirkus Reviews, used with permission.
