Starred review from March 2, 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.
March 15, 2015
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.
March 1, 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
Copyright 2015 Library Journal, LLC Used with permission.
Starred review from May 15, 2015
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 faithirrational faithand ultimately requires poetry and art to complement its findings. A singular humanization of the mathematical project.(Reprinted with permission of Booklist, copyright 2015, American Library Association.)