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How to Bake Pi: Easy recipes for understanding complex maths [Paperback] [Jun 02, 2016] Eugenia Cheng
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, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.
At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.
304 pages, Paperback
First published June 4, 2015
453 people are currently reading
5254 people want to read
About the author
Eugenia Cheng
18 books331 followersEugenia Cheng is a mathematician, pianist, and lecturer. She is passionate about ridding the world of math-phobia. Eugenia’s first book, How to Bake Pi, has been an international success. Molly’s Mathematical Adventure is her first children's book.
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June 11, 2015
Popular maths books are the most difficult to make interesting to those beyond the hard core readers who are happy to spend their time on mathematical puzzles and diversions, and the reason this book gets four stars despite a couple of problems is that is one of the most original and insightful books on the nature of mathematics for the general reader that I've ever seen.
Rather than simply throw mathematical puzzles and diversions at us, or weird and wonderful numbers, Eugenia Cheng takes us on something close to a journey through the mathematical mind, introducing us first to abstraction, then through the processes of mathematics, the way it generalises and the essential foundations of axioms. This is all as an introduction to the second half the the book on Cheng's speciality, category theory, which will I suspect be as unfamiliar to most non-mathematicians as it was to me.
So in terms of what it sets out to do and what, to some degree, it achieves it is absolutely brilliant. Cheng writes in a light, engaging fashion and really pushes the envelope on the way that you can explore mathematics. The basics are there - the inevitable doughnut/coffee cup topology comparison (though she prefers bagels, as doughnuts are not always toroidal), for instance, but this quickly then evolves into the much more challenging concept of 'taking the complement' of something by removing it from three dimensional space with an imaginary three dimensional eraser and examining what remains through topological eyes.
I can't totally ignore the issues. The lesser one is that as a gimmick, each section begins with a recipe which is then used to illustrate a mathematical point (though also to talk about food) - I found this a touch condescending and very irritating, though some readers will probably like it. The bigger problem is that the author isn't great at structuring a book. The first chapter particularly is all over the place, and she has a tendency to use concepts before they are explained. This is particularly true of category theory, which never really gets a clear, approachable definition, but rather is feinted at to begin with, and then introduced as example after example, which without a structure explaining just what it does is quite difficult to put together as a total picture of a discipline.
So, flawed it certainly is, but that doesn't get in the way of it being an unusually interesting attempt at doing something far more significant than most popular mathematics books do. I've always felt that pure maths was uncomfortably abstract and arbitrary, coming up with rules that have no obvious justification. This is the first book of read where it's possible to get a sense of, 'Hey, that kind of makes sense' - which surely is an impressive achievement. If you can look past the gimmicky aspect and the occasionally confusing structure you are in for a treat.
Rather than simply throw mathematical puzzles and diversions at us, or weird and wonderful numbers, Eugenia Cheng takes us on something close to a journey through the mathematical mind, introducing us first to abstraction, then through the processes of mathematics, the way it generalises and the essential foundations of axioms. This is all as an introduction to the second half the the book on Cheng's speciality, category theory, which will I suspect be as unfamiliar to most non-mathematicians as it was to me.
So in terms of what it sets out to do and what, to some degree, it achieves it is absolutely brilliant. Cheng writes in a light, engaging fashion and really pushes the envelope on the way that you can explore mathematics. The basics are there - the inevitable doughnut/coffee cup topology comparison (though she prefers bagels, as doughnuts are not always toroidal), for instance, but this quickly then evolves into the much more challenging concept of 'taking the complement' of something by removing it from three dimensional space with an imaginary three dimensional eraser and examining what remains through topological eyes.
I can't totally ignore the issues. The lesser one is that as a gimmick, each section begins with a recipe which is then used to illustrate a mathematical point (though also to talk about food) - I found this a touch condescending and very irritating, though some readers will probably like it. The bigger problem is that the author isn't great at structuring a book. The first chapter particularly is all over the place, and she has a tendency to use concepts before they are explained. This is particularly true of category theory, which never really gets a clear, approachable definition, but rather is feinted at to begin with, and then introduced as example after example, which without a structure explaining just what it does is quite difficult to put together as a total picture of a discipline.
So, flawed it certainly is, but that doesn't get in the way of it being an unusually interesting attempt at doing something far more significant than most popular mathematics books do. I've always felt that pure maths was uncomfortably abstract and arbitrary, coming up with rules that have no obvious justification. This is the first book of read where it's possible to get a sense of, 'Hey, that kind of makes sense' - which surely is an impressive achievement. If you can look past the gimmicky aspect and the occasionally confusing structure you are in for a treat.
May 30, 2015
A very good introduction to what Category Theory *is* and to what mathematics *is*. Lots of helpful examples of concepts, mostly through food and baking. It is important to note that this is *not* a cookery book. It is a book about mathematics that uses recipes for illumination.
The book has one major failing: it lacks a further reading section. It would be great if such a knowledgeable author could have provided a sign post on where to go next to learn more Category Theory. If it had an annotated further reading section it would have been perfect.
The book has one major failing: it lacks a further reading section. It would be great if such a knowledgeable author could have provided a sign post on where to go next to learn more Category Theory. If it had an annotated further reading section it would have been perfect.
July 18, 2024
A jargon-free book about category theory? Wow! As a maths teacher with a passion for categories, I really had to read this book. The premise - comparing maths to cooking - and the diagrams inside the text seemed to certify that the essay was both fun and rigorous, so I had pretty high expectations when I started the reading.
What a disappointment I had! Though the author really seems to be bright, and surely does her best to expose herself and her personal life in order to provide real-life examples, metaphors and "feeling" to the mathematical ideas in the text, almost nothing in the book is actually worth your or my time.
As a graduate in mathematics, I was really sad to find that both rigour and "illumination" - the kind of intuition which often fuels mathematical reasoning - were totally missing in the mathematical flow of the book. Even worse, the text keeps on mentioning them! Just referencing, and never using. It skips almost every detail, oversimplifies all reasonings, omits proofs, stretches concepts and metaphors too much... And does this just while explicitly talking about the importance of details, strict reasoning, careful proofs, and caution while generalising!
But - you might well think - this book really wasn't for me in the first place. I'm a maths teacher, I studied category theory as an undergraduate, so I can't complain this "category theory for dummies" doesn't meet my needs. Ok, suppose you're NOT trained in higher mathematics, but you want to understand the gist of it. Would you appreciate being told that it's all about rigour, clear reasoning, simplification that brings abstraction... and being sistematically deprived of them? Would you be happy to read "this is very straightforward to proof" (about Arrow's theorem: a result whose proof can be easily understood by a secondary school student) and seeing that the book features no proof for it?
I don't know if the fault of all these drawbacks is the author's or her editor's. I suspect the latter: they're the kind of omissions publishing houses seem to impose ("readers wouldn't understand that... skip that detail... cut down this proof"). But the end result is unsatisfying in a way I never met in a "maths for everybody" book (and I've ready a lot of them): there's not a single good idea that I found in the entire book. It shows good intentions but doesn't fulfill them. Just read something else.
What a disappointment I had! Though the author really seems to be bright, and surely does her best to expose herself and her personal life in order to provide real-life examples, metaphors and "feeling" to the mathematical ideas in the text, almost nothing in the book is actually worth your or my time.
As a graduate in mathematics, I was really sad to find that both rigour and "illumination" - the kind of intuition which often fuels mathematical reasoning - were totally missing in the mathematical flow of the book. Even worse, the text keeps on mentioning them! Just referencing, and never using. It skips almost every detail, oversimplifies all reasonings, omits proofs, stretches concepts and metaphors too much... And does this just while explicitly talking about the importance of details, strict reasoning, careful proofs, and caution while generalising!
But - you might well think - this book really wasn't for me in the first place. I'm a maths teacher, I studied category theory as an undergraduate, so I can't complain this "category theory for dummies" doesn't meet my needs. Ok, suppose you're NOT trained in higher mathematics, but you want to understand the gist of it. Would you appreciate being told that it's all about rigour, clear reasoning, simplification that brings abstraction... and being sistematically deprived of them? Would you be happy to read "this is very straightforward to proof" (about Arrow's theorem: a result whose proof can be easily understood by a secondary school student) and seeing that the book features no proof for it?
I don't know if the fault of all these drawbacks is the author's or her editor's. I suspect the latter: they're the kind of omissions publishing houses seem to impose ("readers wouldn't understand that... skip that detail... cut down this proof"). But the end result is unsatisfying in a way I never met in a "maths for everybody" book (and I've ready a lot of them): there's not a single good idea that I found in the entire book. It shows good intentions but doesn't fulfill them. Just read something else.
May 12, 2015
Math, bleh. I struggled to get through this. I read it in small increments and almost got excited about math from her level of enthusiasm. I suffer from math trauma and hoped this book could be a possible redo for my math spirit. I was lost in the system at school finishing only what was required (forced) on me to graduate. I bake an thought the connection would bring out the light bulbs in my head. The author did a good job of tying in the recipes with a mathematical concept. I could see some of what she was saying but I didn’t always see the connection. I think it was from my lessons in the past being so “find the correct answer” not “why/how to work it.” She expected more out me as a reader. I didn’t enjoy the book but I did end it felling like I gained a stronger connection between my cooking and math in a way I never considered before. Basically I had flashing glimpse of brilliance, several times.LOL.
I would have done well with a teacher who brought some of these ideas to life in a classroom. It felt like she was leaning towards a teaching method that would take students to a new level of understanding. I hope so. Everyone should feel that math is not that hard. I think basic HS algebra and up is the level for this. There is a little test to see where your level of abstraction comfort is. I don’t want to talk about what level I tested on.
The recipes ? Not the greatest but hey it’s not a cookbook. There are a couple that made my tongue want to run away.
So did I like the book or not ? I don’t know, I cringe and smile when thinking back on my experience. I did gain some knowledge of myself and mathematical category theory. When I was perusing cookbooks for recipes to try I caught myself using some of her lessons. Dang it, I learned something. I have plans to re-read this slower next time.
I would have done well with a teacher who brought some of these ideas to life in a classroom. It felt like she was leaning towards a teaching method that would take students to a new level of understanding. I hope so. Everyone should feel that math is not that hard. I think basic HS algebra and up is the level for this. There is a little test to see where your level of abstraction comfort is. I don’t want to talk about what level I tested on.
The recipes ? Not the greatest but hey it’s not a cookbook. There are a couple that made my tongue want to run away.
So did I like the book or not ? I don’t know, I cringe and smile when thinking back on my experience. I did gain some knowledge of myself and mathematical category theory. When I was perusing cookbooks for recipes to try I caught myself using some of her lessons. Dang it, I learned something. I have plans to re-read this slower next time.
February 8, 2017
I hoped this book would teach me category theory. The book talked a lot ABOUT category theory but did not give any theorem, nor illustrate with a problem. It is as if it talked ABOUT addition but did not show you how to add 2 numbers, nor give you a summation problem and tell you if you did it correctly. The book repeats much basic information. It bored me and failed to illuminate its subject matter.
March 2, 2015
How to Bake Pi by Eugenia Cheng is a fascinating look at mathematics from an atypical perspective. In this work Eugenia shows how math is far larger, varied, and more encompassing than merely solving equations. She introduces each of her chapters with a "recipe" involving real food as an analogy to illustrate the points she makes.
In the early part of the book Eugenia describes how many people find math difficult and drop away at different stages. For some, arithmetic is hard. For other algebra or geometry is where they drop away. For some it might be trigonometry. For others calculus. And so on.
In my own personal experience, I found that I could not get past the plateau of calculus. This book finally gave me insight into why: up to calculus, math was still primarily about solving problems/equations and finding the "right" answer. Starting with calculus and going further into advance mathematics, problem-solving and finding the "right" answer is no longer the goal. My belief was that math was about solving problems, and so calculus increasingly made little sense in my mind. Perhaps if I had known what this book describes about math, I may have had a chance to get past the wall of calculus.
The first part of the book discusses abstractions and generalizations as one of the key goals of math. The second part of the book discusses Eugenia's field of specialty: Category Theory, and how the purpose of this meta-math (or math of math) is to simply math.
The final chapter brings all the earlier pages together as Eugenia summarizes the knowledge and makes a case to have her readers come away with the belief that math isn't hard. She does so by applying in her literary work the principles she discusses in this very chapter: she uses her discussions to bridge the knowledge and belief through understanding. So in the end I find that her math "principles" apply to not just math, but to cooking and to writing.
What is contained in this book is probably of most interest to someone familiar with high school math and onward. Many of the examples given assume a basic knowledge of algebra and geometry.
Eugenia alludes to math education a number of times in her book. Although this is not a book about math education, I believe that the reader can discover a vision for math education that she would like her readers to leave with. I think that this book will be an interesting and helpful volume for aspiring teachers and math educators, from elementary through high school and even into higher ed.
(This review is based on ARC supplied by the publisher through NetGalley.)
In the early part of the book Eugenia describes how many people find math difficult and drop away at different stages. For some, arithmetic is hard. For other algebra or geometry is where they drop away. For some it might be trigonometry. For others calculus. And so on.
In my own personal experience, I found that I could not get past the plateau of calculus. This book finally gave me insight into why: up to calculus, math was still primarily about solving problems/equations and finding the "right" answer. Starting with calculus and going further into advance mathematics, problem-solving and finding the "right" answer is no longer the goal. My belief was that math was about solving problems, and so calculus increasingly made little sense in my mind. Perhaps if I had known what this book describes about math, I may have had a chance to get past the wall of calculus.
The first part of the book discusses abstractions and generalizations as one of the key goals of math. The second part of the book discusses Eugenia's field of specialty: Category Theory, and how the purpose of this meta-math (or math of math) is to simply math.
The final chapter brings all the earlier pages together as Eugenia summarizes the knowledge and makes a case to have her readers come away with the belief that math isn't hard. She does so by applying in her literary work the principles she discusses in this very chapter: she uses her discussions to bridge the knowledge and belief through understanding. So in the end I find that her math "principles" apply to not just math, but to cooking and to writing.
What is contained in this book is probably of most interest to someone familiar with high school math and onward. Many of the examples given assume a basic knowledge of algebra and geometry.
Eugenia alludes to math education a number of times in her book. Although this is not a book about math education, I believe that the reader can discover a vision for math education that she would like her readers to leave with. I think that this book will be an interesting and helpful volume for aspiring teachers and math educators, from elementary through high school and even into higher ed.
(This review is based on ARC supplied by the publisher through NetGalley.)
January 3, 2016
So far, it's a great exposition of the things I love about math, at (what seems to be) a very relatable level for people who don't love math.
The style is a bit choppy, often jumping from one metaphor to another without smooth transitions, but still it's an easy and pleasant read. The metaphors themselves (for math or its concepts) are excellent, and I will steal some next time I teach :)
p.27: "if you try and use complicated math for a situation that doesn't call for it, you'll think the math is pointless. It's a bit like using the Dewey decimal system if you only own twenty books."
The book reminds me of the great math teacher blogs out there (such as Dan Meyer's), with a welcoming and thoughtful approach. It's nice to see high school teachers in the trenches sharing this perspective with a VERY abstract & academic pure mathematician.
~~~
Second half is a fun, simple introduction to category theory. I knew nothing about it before, and I'm still not fully clear but at least I have some intuition now. Many of the examples are from group theory / abstract algebra -- perhaps because it sounds like category theory grew out of studying groups.
Nice examples of various kinds of proof, and the links / distinctions between knowledge, belief, and understanding. She gives the reader two different proofs and then asks, "Which of these two arguments did you find easier to follow? Which was more satisfying?" (p.258)
Or she illustrates how sometimes, "the mathematical proof is often not something that will convince you why it is true. Instead, it might convince you that it is true. ... Proof has a sociological role; illumination has a personal role. Proof is what convinces society; illumination is what convinces us." (p.274)
This helps me feel better about all the dense, technical proofs I have to read for my PhD. Why can't they just give intuitive reasons? Not merely because intuitive reasons are hard to create, says Cheng, but also because (p.277) "Proof is the best medium for communicating my argument to X in a way that will not be in danger of ambiguity, misunderstanding, or distortion" ... even though "When I read someone else's math, I always hope that the author will have included a reason and not just a proof" :)
And indeed, if you're a young student in math class being asked to jump through un-illuminating hoops, it's easy to get jaded and see math as a bunch of arbitrary right-or-wrong rules to memorize, instead of a tool for understanding the world.
Throughout the book, she writes with great respect for (and encouragement towards) readers who felt unhappy with their math education and grew to hate it. She breaks down the myths about what math is, what it's for, and what success means in math -- myths that are unfortunately still perpetuated in many schools today.
p.277: "many people grew up feeling great antipathy towards math, probably because of how they were taught it at school, as a set of facts you're supposed to believe, and a set of rules you have to follow. You're not supposed to ask why, and when you're wrong you're wrong, end of story. The important stage in between the belief and the rules has been omitted: the illuminating reasons. An illuminated approach is much less baffling, much less autocratic, and much less frightening."
~~~
I'll admit that some of the food examples riled me a bit -- too much talk about losing weight, and too much patience with ridiculous fad diets. If your book is about breaking down a bad stereotype (of math), it shouldn't reinforce other bad stereotypes/obsessions.
But if you can stomach (*rimshot*) those parts, it's a worthwhile book with a nice vision of how math education ought to go and what it means to be a mathematician.
The style is a bit choppy, often jumping from one metaphor to another without smooth transitions, but still it's an easy and pleasant read. The metaphors themselves (for math or its concepts) are excellent, and I will steal some next time I teach :)
p.27: "if you try and use complicated math for a situation that doesn't call for it, you'll think the math is pointless. It's a bit like using the Dewey decimal system if you only own twenty books."
The book reminds me of the great math teacher blogs out there (such as Dan Meyer's), with a welcoming and thoughtful approach. It's nice to see high school teachers in the trenches sharing this perspective with a VERY abstract & academic pure mathematician.
~~~
Second half is a fun, simple introduction to category theory. I knew nothing about it before, and I'm still not fully clear but at least I have some intuition now. Many of the examples are from group theory / abstract algebra -- perhaps because it sounds like category theory grew out of studying groups.
Nice examples of various kinds of proof, and the links / distinctions between knowledge, belief, and understanding. She gives the reader two different proofs and then asks, "Which of these two arguments did you find easier to follow? Which was more satisfying?" (p.258)
Or she illustrates how sometimes, "the mathematical proof is often not something that will convince you why it is true. Instead, it might convince you that it is true. ... Proof has a sociological role; illumination has a personal role. Proof is what convinces society; illumination is what convinces us." (p.274)
This helps me feel better about all the dense, technical proofs I have to read for my PhD. Why can't they just give intuitive reasons? Not merely because intuitive reasons are hard to create, says Cheng, but also because (p.277) "Proof is the best medium for communicating my argument to X in a way that will not be in danger of ambiguity, misunderstanding, or distortion" ... even though "When I read someone else's math, I always hope that the author will have included a reason and not just a proof" :)
And indeed, if you're a young student in math class being asked to jump through un-illuminating hoops, it's easy to get jaded and see math as a bunch of arbitrary right-or-wrong rules to memorize, instead of a tool for understanding the world.
Throughout the book, she writes with great respect for (and encouragement towards) readers who felt unhappy with their math education and grew to hate it. She breaks down the myths about what math is, what it's for, and what success means in math -- myths that are unfortunately still perpetuated in many schools today.
p.277: "many people grew up feeling great antipathy towards math, probably because of how they were taught it at school, as a set of facts you're supposed to believe, and a set of rules you have to follow. You're not supposed to ask why, and when you're wrong you're wrong, end of story. The important stage in between the belief and the rules has been omitted: the illuminating reasons. An illuminated approach is much less baffling, much less autocratic, and much less frightening."
~~~
I'll admit that some of the food examples riled me a bit -- too much talk about losing weight, and too much patience with ridiculous fad diets. If your book is about breaking down a bad stereotype (of math), it shouldn't reinforce other bad stereotypes/obsessions.
But if you can stomach (*rimshot*) those parts, it's a worthwhile book with a nice vision of how math education ought to go and what it means to be a mathematician.
March 30, 2015
The math was a little interesting but the recipes deplorable.
April 21, 2017
Rambling, boring, and teaches nothing. I gave up.
April 10, 2022
Well, now I know that category theory exists. The second half of the book explaining category theory was more interesting than the first. I can’t say I fully understand what category theory is or how how it’s useful (and probably won’t be reading any more books about it) but I can say that it was an engaging introduction to it.
January 30, 2017
"When I read someone else's math, I always hope that the author will have included a reason and not just a proof." - Eugenia Cheng
Throughout this book, Cheng attempts to give reasons and not just proofs. I do have trouble deciphering proofs and Cheng makes the reader feel comfortable wherever his math has brought him to this point. She also has the hallmark of a great teacher--she explains the same math several different ways. This book is truly accessible whether you have degrees in mathematics or you just finished high school geometry.
In the first half of the book Cheng describes (or maybe, defines) certain topics in higher mathematics: topology, number theory, logic, algebra. The second half of the book attempts to describe category theory.
Don't expect in depth descriptions of topics in mathematics. Cheng's goal, I believe, is to tell you what math is ( a set of rules that can be changed under different circumstances) and what math isn't (one right answer.) For instance, when does 7 + 7 not equal 14??? And how Category Theory describes how it all hangs together. Read to find out.
Throughout this book, Cheng attempts to give reasons and not just proofs. I do have trouble deciphering proofs and Cheng makes the reader feel comfortable wherever his math has brought him to this point. She also has the hallmark of a great teacher--she explains the same math several different ways. This book is truly accessible whether you have degrees in mathematics or you just finished high school geometry.
In the first half of the book Cheng describes (or maybe, defines) certain topics in higher mathematics: topology, number theory, logic, algebra. The second half of the book attempts to describe category theory.
Don't expect in depth descriptions of topics in mathematics. Cheng's goal, I believe, is to tell you what math is ( a set of rules that can be changed under different circumstances) and what math isn't (one right answer.) For instance, when does 7 + 7 not equal 14??? And how Category Theory describes how it all hangs together. Read to find out.
January 30, 2016
The author shows how cooking recipes are similar to mathematics. It is a cute way to explore concepts of mathematics, but I thought that it lacked a focus. It did not meet my idea of a well written book. I believe that the use of a professional editor could have made a significant improvement to this book.
September 11, 2015
While most of the book is material I've known for a long time, it's very well structured and presented in a clean and clear manner. Though a small portion is about category theory and gives some of the "flavor" of the subject, the majority is about how abstract mathematics works in general.
I'd recommend this to anyone who wants to have a clear picture of what mathematics really is or how it should be properly thought about and practiced (hint: it's not the pablum you memorized in high school or even in calculus or linear algebra). Many books talk about the beauty of math, while this one actually makes steps towards actually showing the reader how to appreciate that beauty.
Like many popular books about math, this one actually has very little that goes beyond the 5th grade level, but in examples that are very helpfully illuminating given their elementary nature. The extended food metaphors and recipes throughout the book fit in wonderfully with the abstract nature of math - perhaps this is why I love cooking so much myself.
I wish I'd read this book in high school to have a better picture of the forest of mathematics.
More thoughts to come...
I'd recommend this to anyone who wants to have a clear picture of what mathematics really is or how it should be properly thought about and practiced (hint: it's not the pablum you memorized in high school or even in calculus or linear algebra). Many books talk about the beauty of math, while this one actually makes steps towards actually showing the reader how to appreciate that beauty.
Like many popular books about math, this one actually has very little that goes beyond the 5th grade level, but in examples that are very helpfully illuminating given their elementary nature. The extended food metaphors and recipes throughout the book fit in wonderfully with the abstract nature of math - perhaps this is why I love cooking so much myself.
I wish I'd read this book in high school to have a better picture of the forest of mathematics.
More thoughts to come...
June 15, 2015
Not really about baking, but there are a lot of cool anecdotes that make math sound logical and simple. I wish Ms. Chen was my high school math teacher, I might have actually cared about it.
April 6, 2017
I read this to learn how to apply Category Theory to computer programming and came away a little disappointed. I expected to become friends with Category Theory, but I feel more like I just waved to it on the way to work.
But I loved that baking was used as an analogy for math! I had never seen even one math-baking analogy, but this book has hundreds of them which are at least as illuminating and engaging as any stereotypically male analogy commonly used to illustrate mathematical concepts. Makes me wonder why baking isn't the go-to analogy for math! Dr. Cheng's analogies might be the strongest aspect of this book.
I started this book four times. First as a hard-copy which I only glanced at before returning to the library (I was busy).
Second as an audio-book while running. That worked surprisingly well for some chapters, but I missed a lot in other chapters and the dual challenge of pushing myself to run and visualizing things that really required pictures resulted in several lasting headaches. The audiobook should really be an abridged version containing only the chapters that work without pictures.
My third attempt was with the e-book, which was OK, except there were times I wanted to flip back to another section which I really don't know how to do easily with e-books. Also, some of the images of formulae were small enough to be hard to read.
The fourth time was with the paper book. I was determined to finish it on principle. I agree with the other reviewers that it was a little short on C.T. I love the metaphors, but I'd also love a little metaphor-free mini-reference or glossary as a summary. Like:
Something like that appears on page 120, but the word "group" is hidden in the final paragraph and there's no page number reference when "group" is mentioned later in the book. I'd like the same for Monoid ("group with no inverse" p.252), Field, Monad, etc., all collected together in one section. I can sort of get that in Wikipedia, but it tends to jump off the deep end too quickly for things I don't already understand.
I especially wished that the Sameness chapter had a little more information about the 5-branch trees that form a 3D shape (pp 234-235 in US edition). Are the squares starting or ending points? Are the trees the faces and the arrows the edges, or vice-versa? That looked like a fun project which had me sketching things out on scrap paper, but I needed just a little more help to make it work.
All of my non-audio disappointments were in the second half of the book and could probably be addressed with a companion web site or a second edition. I thought there were some very minor misprints in the American edition which of course I can't find right now.
So why did I give it 3 stars when it was so difficult and didn't meet my expectations? Because I found something I didn't expect, and I continue to find myself using Dr. Cheng's cooking analogies almost every week!
But I loved that baking was used as an analogy for math! I had never seen even one math-baking analogy, but this book has hundreds of them which are at least as illuminating and engaging as any stereotypically male analogy commonly used to illustrate mathematical concepts. Makes me wonder why baking isn't the go-to analogy for math! Dr. Cheng's analogies might be the strongest aspect of this book.
I started this book four times. First as a hard-copy which I only glanced at before returning to the library (I was busy).
Second as an audio-book while running. That worked surprisingly well for some chapters, but I missed a lot in other chapters and the dual challenge of pushing myself to run and visualizing things that really required pictures resulted in several lasting headaches. The audiobook should really be an abridged version containing only the chapters that work without pictures.
My third attempt was with the e-book, which was OK, except there were times I wanted to flip back to another section which I really don't know how to do easily with e-books. Also, some of the images of formulae were small enough to be hard to read.
The fourth time was with the paper book. I was determined to finish it on principle. I agree with the other reviewers that it was a little short on C.T. I love the metaphors, but I'd also love a little metaphor-free mini-reference or glossary as a summary. Like:
Group
An algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms: closure, associativity, identity and invertibility. For example, the set of Integers with the Addition operation is a group.
Something like that appears on page 120, but the word "group" is hidden in the final paragraph and there's no page number reference when "group" is mentioned later in the book. I'd like the same for Monoid ("group with no inverse" p.252), Field, Monad, etc., all collected together in one section. I can sort of get that in Wikipedia, but it tends to jump off the deep end too quickly for things I don't already understand.
I especially wished that the Sameness chapter had a little more information about the 5-branch trees that form a 3D shape (pp 234-235 in US edition). Are the squares starting or ending points? Are the trees the faces and the arrows the edges, or vice-versa? That looked like a fun project which had me sketching things out on scrap paper, but I needed just a little more help to make it work.
All of my non-audio disappointments were in the second half of the book and could probably be addressed with a companion web site or a second edition. I thought there were some very minor misprints in the American edition which of course I can't find right now.
So why did I give it 3 stars when it was so difficult and didn't meet my expectations? Because I found something I didn't expect, and I continue to find myself using Dr. Cheng's cooking analogies almost every week!
May 6, 2019
I learned some things about category theory from this book, which makes sense, because it was written by a mathematician brimming over with her passion for category theory. The author clearly loves cooking and loves math and mixes them up together in a mélange of words. Given its mathematical and logical underpinnings, I am surprised at how unstructured the book is. For me, this was an obstacle to understanding the ideas and to even finishing the book. It is peppered with anecdotes and analogies (many, though not all, to food). The ability to link abstract math ideas to concrete experiences is a gift. But I felt that there were SO MANY of them that I kept losing sight of the forest for the trees.
I have to wonder: who is the intended audience? I found it tedious to be walked through basic algebra and kept wanting to skip to the core message. And would someone who needed an explanation for how to convert a story problem into equations, or how to reduce fractions -- would that person even have picked up this book in the first place? It seems unlikely.
However, I did like these ideas:
1) People tend to think of math as hard because they've mostly only experienced it in the context of someone giving them a problem to do. They don't think of it as a tool they can use to make their lives easier.
2) The properties a number has derives from its context. We learn that 5 is prime, but this is only true in the world of the natural numbers. In the set of rational numbers, 5 is not prime!
3) "In a way, mathematics is like an emotion, which can't ever be described precisely in words -- it's something that happens inside an individual. What we write down is merely a language for communicating those ideas to others, in the hope that they will be able to reconstruct the feeling within their own mind." I would have expected her to say math is like an idea, not an emotion. An emotion? Fascinating :) (And yes - writing down math is a way to communicate, not a thing itself! Cool.)
The final chapter is the best. If you find yourself getting bogged down / losing interest, I recommend just skipping to that chapter.
I have to wonder: who is the intended audience? I found it tedious to be walked through basic algebra and kept wanting to skip to the core message. And would someone who needed an explanation for how to convert a story problem into equations, or how to reduce fractions -- would that person even have picked up this book in the first place? It seems unlikely.
However, I did like these ideas:
1) People tend to think of math as hard because they've mostly only experienced it in the context of someone giving them a problem to do. They don't think of it as a tool they can use to make their lives easier.
2) The properties a number has derives from its context. We learn that 5 is prime, but this is only true in the world of the natural numbers. In the set of rational numbers, 5 is not prime!
3) "In a way, mathematics is like an emotion, which can't ever be described precisely in words -- it's something that happens inside an individual. What we write down is merely a language for communicating those ideas to others, in the hope that they will be able to reconstruct the feeling within their own mind." I would have expected her to say math is like an idea, not an emotion. An emotion? Fascinating :) (And yes - writing down math is a way to communicate, not a thing itself! Cool.)
The final chapter is the best. If you find yourself getting bogged down / losing interest, I recommend just skipping to that chapter.
November 1, 2015
When you cook and bake, you are always looking at the ingredients, so it's easy to forget that the process with which you combine the ingredients is just as important. Maths isn't just about numbers (and variables, and shapes, and knots, and statements, ...). What you do with them is just as important. From the book: "There are many different ways of combining these simple ingredients [flour, butter, and water], and most of them will not result in puff pastry." The recipe for clotted cream only has one ingredient, so the process is everything! On the other hand, for porridge, the process is simply "boil ingredients".
There's also the question of what the ingredients list considers a basic ingredient. For example, in the recipe for Jaffa cakes, "small round flat plain cakes" is a single ingredient. Another recipe could have "small round flat plain cakes" as the output rather than the input.
Part one of the book, Mathematics, contains many of these enjoyable parallels between cooking and mathematics. It also explains when maths is useful in life, and when it definitely isn't.
Part two, Category Theory, follows the same format with each chapter starting with a recipe highlighting some feature about mathematics. In this part, the mathematics are more advanced. Somehow it seemed less coherent, and was less catchy. But maybe it's just the good first part, that gave me the expectation, that maths should be catchy! I think I understand category theory a little more now, but it's hard to say. But unlike the standard textbook on category theory I once started reading, I actually finished this book.
There's also the question of what the ingredients list considers a basic ingredient. For example, in the recipe for Jaffa cakes, "small round flat plain cakes" is a single ingredient. Another recipe could have "small round flat plain cakes" as the output rather than the input.
Part one of the book, Mathematics, contains many of these enjoyable parallels between cooking and mathematics. It also explains when maths is useful in life, and when it definitely isn't.
Part two, Category Theory, follows the same format with each chapter starting with a recipe highlighting some feature about mathematics. In this part, the mathematics are more advanced. Somehow it seemed less coherent, and was less catchy. But maybe it's just the good first part, that gave me the expectation, that maths should be catchy! I think I understand category theory a little more now, but it's hard to say. But unlike the standard textbook on category theory I once started reading, I actually finished this book.
April 6, 2018
Eugenia is a warm, engaging, intelligent woman who knows what she is talking about. I would definitely like to meet her. And she certainly conveys her huge enthusiasm for her subject. But I doubt that non-mathematicians will understand much of what she is saying. And mathematicians like me will say, "Yes, that's true, but where is she going with this?" It's like she's saying "Kittens are cute and cuteness is the essence of kittens!" Which is largely true, but not much use to anyone who has never seen a kitten, nor is it likely to impress a veterinarian. An introduction to category theory it is NOT.
If her point is that girls can do maths, then she has made it. And perhaps that IS what this book is all about.
If her point is that girls can do maths, then she has made it. And perhaps that IS what this book is all about.
July 3, 2016
3 stars only because, surprisingly, it wasn't advanced enough for me. I really wish it had a bibliography. Her website has a few interesting items, though. (I disagree with her that university lectures are a waste of time - at least in the humanities.)
Want to read
July 31, 2015Unfortunately math is not as much like pie or baking as I would have hoped from this title. I need someone to read this with me and translate it into english-major-ese for me.
February 21, 2016
really, about 7/10... Good sci-pop book, but I would prefer to have condensed version of it...
May 28, 2017
I have felt for a long time that we teach mathematics, especially in high school, in a way that fails to show what mathematics really is (it's not just about numbers, arithmetic, and, by extension, algebra). We tend to teach stuff that students do not relate to: "Two trains start at the same time from Chicago and New York City, and speeds of 30mph and 60mph, respectively. How long before they meet?" Why do we think that students care about such matters, and too often they seem contrived (and in this case old fashioned, because who uses trains in the USA?). Wouldn't it be better to try to engage students in the magic that mathematics can bring? And, yes, it can bring magic! But only if we try to show them how wonderful mathematics can be, and how diverse its applications are.
A few years ago, I taught Computer Science at a local college. The Computer Science department was, as it often is, in the Mathematics department (which, if you think about it, isn't an obvious place for it). There was a great debate among the Mathematics faculty about whether to teach Mathematics in a rigorous way, or instead to teach an application-oriented approach. This was mostly driven by the choice of textbook, and the textbooks of the time for the "rigorous approach" and the application-oriented approach were very different from each other. In particular, the application-oriented books were significantly watered down from those showing the rigorous approach. I felt that we should be teaching Mathematics somewhat rigorously, but with a definite bias to its applications because students, for the most part, were only interested in how they might use Mathematics in their lives. If it seemed too far away from their personal experiences, they lost interest and motivation very quickly. It seemed a real loss that there were seemingly no mathematics books that combined the two "approaches".
In the rigorous approach, mathematics was taught with a very strong emphasis on proofs. That was not how I was taught mathematics, probably because, in high school, I studied physics and mathematics at the same time, and mathematics was seen as a set of techniques used in physics. Time and time again, we would learn something in Physics, and, pretty much contemporaneously, a topic in Mathematics that could quickly be applied to Physics. We never doubted that Mathematics was relevant to our world. But an English Lit, or History, major would, I recognize, be a rather different kettle of fish.
Later, at University, where I was majoring in Physics, and, since I was at a British university, the subjects I studied were quite limited: Essentially, Physics, Pure Mathematics, and Applied Mathematics. Applied Mathematics turned out to be sort of a more formal study of Physics -- especially Mechanics (I remember lots of ladders leaning against walls, etc.). Pure Mathematics was rather more formal, but I still don't remember lots of formal proofs -- but I do remember so-called epsilon/delta proofs, which I never seemed to understand the relevance of. Perhaps I would today, with a little more experience under my belt?
So, when I encountered this intriguingly titled book, I wondered how successful the author would be at conveying the true nature of Mathematics, using cooking and recipe analogies. I believe she did a great job! She tries hard to show that Mathematics isn't just numbers/digits/arithmetic/algebra, and also how a mathematician looks at the world, and how to solve a problem, prove a theorem, etc. One thing that does impress me is the diversity of references to applications and mindsets; the author is very well-read and well-prepared. She clearly looks at the world and sees opportunities to apply mathematics to so many different aspects of life, and refers to quite recent events and characters. (She was born and educated in England, and holds tenure at the University of Sheffield, so many of her examples have a British flavor.) I found her approach very refreshing. She begins almost every chapter with a cooking recipe -- a real one -- and then uses analogy to compare what she typically does when cooking that recipe with how she approaches mathematics.
Some people seem to have thought that they should review this book on the quality of these recipes -- they basically seem to have missed the entire point. It's the analogies that are important.
The author studies Category Theory, which I had not previously heard of. Apparently, "... category theory uses abstraction to make it possible to state and prove many intricate and subtle mathematical results in these fields in a much simpler way." (https://en.wikipedia.org/wiki/Categor...) . Since Mathematics uses abstraction to seek out commonality in order to generalize concepts and apply them to other aspects of Mathematics, I suppose you could look at Category Theory as the Mathematics of Mathematics (see the title of the book). It seems that even mathematicians are not too familiar with (or are suspicious of?) Category Theory; there aren't too many Category Theorists around.
Anyway, the author uses analogy in a very effective way. She positively oozes enthusiasm about her mathematics, and her cooking. She is also really interested in the popularization of Mathematics -- in other words, trying to get more people to understand what Mathematics really is, how it can be useful to people in their everyday lives, and how to engage and interest people in Mathematics who wouldn't typically think it was "for them".
The book has two parts:
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
and:
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
Sounds a little dry to you? The chapter titles certainly do, but her writing makes things very accessible, and often amusing. And, at times, she brings in topics you would never expect.
Part I is all about explaining Mathematics using cooking/recipe analogies. I found it to be very effective, and readable by just about anyone.
Part II is about Category Theory, still using cooking/recipes and analogy. Admittedly, things get a bit heavier here, so perhaps need more effort to read.
Towards the end, she talks about how she feels we could make the teaching of mathematics more effective, and more appealing to more students, instead of turning them off, as seems so universally true. The problem is a massive one, because, even after we accept that it should be done, and agree on a way to do it, it would involve (IMHO) a complete re-education of mathematics teachers at just about every level of mathematics teaching. But just because we might not be able to do a complete revamp of the system doesn't mean that we shouldn't be examining how to improve things, perhaps in a more incremental way.
I believe this book should be read by almost everyone; math-phobes (of which there are legion), math lovers (because the book brings some fresh perspectives on how to think about math), and -- perhaps most especially, teachers of math and math curricular creators, to help them create better ways of teaching math and conveying its many beauties and fascinations to all students.
A few years ago, I taught Computer Science at a local college. The Computer Science department was, as it often is, in the Mathematics department (which, if you think about it, isn't an obvious place for it). There was a great debate among the Mathematics faculty about whether to teach Mathematics in a rigorous way, or instead to teach an application-oriented approach. This was mostly driven by the choice of textbook, and the textbooks of the time for the "rigorous approach" and the application-oriented approach were very different from each other. In particular, the application-oriented books were significantly watered down from those showing the rigorous approach. I felt that we should be teaching Mathematics somewhat rigorously, but with a definite bias to its applications because students, for the most part, were only interested in how they might use Mathematics in their lives. If it seemed too far away from their personal experiences, they lost interest and motivation very quickly. It seemed a real loss that there were seemingly no mathematics books that combined the two "approaches".
In the rigorous approach, mathematics was taught with a very strong emphasis on proofs. That was not how I was taught mathematics, probably because, in high school, I studied physics and mathematics at the same time, and mathematics was seen as a set of techniques used in physics. Time and time again, we would learn something in Physics, and, pretty much contemporaneously, a topic in Mathematics that could quickly be applied to Physics. We never doubted that Mathematics was relevant to our world. But an English Lit, or History, major would, I recognize, be a rather different kettle of fish.
Later, at University, where I was majoring in Physics, and, since I was at a British university, the subjects I studied were quite limited: Essentially, Physics, Pure Mathematics, and Applied Mathematics. Applied Mathematics turned out to be sort of a more formal study of Physics -- especially Mechanics (I remember lots of ladders leaning against walls, etc.). Pure Mathematics was rather more formal, but I still don't remember lots of formal proofs -- but I do remember so-called epsilon/delta proofs, which I never seemed to understand the relevance of. Perhaps I would today, with a little more experience under my belt?
So, when I encountered this intriguingly titled book, I wondered how successful the author would be at conveying the true nature of Mathematics, using cooking and recipe analogies. I believe she did a great job! She tries hard to show that Mathematics isn't just numbers/digits/arithmetic/algebra, and also how a mathematician looks at the world, and how to solve a problem, prove a theorem, etc. One thing that does impress me is the diversity of references to applications and mindsets; the author is very well-read and well-prepared. She clearly looks at the world and sees opportunities to apply mathematics to so many different aspects of life, and refers to quite recent events and characters. (She was born and educated in England, and holds tenure at the University of Sheffield, so many of her examples have a British flavor.) I found her approach very refreshing. She begins almost every chapter with a cooking recipe -- a real one -- and then uses analogy to compare what she typically does when cooking that recipe with how she approaches mathematics.
Some people seem to have thought that they should review this book on the quality of these recipes -- they basically seem to have missed the entire point. It's the analogies that are important.
The author studies Category Theory, which I had not previously heard of. Apparently, "... category theory uses abstraction to make it possible to state and prove many intricate and subtle mathematical results in these fields in a much simpler way." (https://en.wikipedia.org/wiki/Categor...) . Since Mathematics uses abstraction to seek out commonality in order to generalize concepts and apply them to other aspects of Mathematics, I suppose you could look at Category Theory as the Mathematics of Mathematics (see the title of the book). It seems that even mathematicians are not too familiar with (or are suspicious of?) Category Theory; there aren't too many Category Theorists around.
Anyway, the author uses analogy in a very effective way. She positively oozes enthusiasm about her mathematics, and her cooking. She is also really interested in the popularization of Mathematics -- in other words, trying to get more people to understand what Mathematics really is, how it can be useful to people in their everyday lives, and how to engage and interest people in Mathematics who wouldn't typically think it was "for them".
The book has two parts:
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
and:
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
Sounds a little dry to you? The chapter titles certainly do, but her writing makes things very accessible, and often amusing. And, at times, she brings in topics you would never expect.
Part I is all about explaining Mathematics using cooking/recipe analogies. I found it to be very effective, and readable by just about anyone.
Part II is about Category Theory, still using cooking/recipes and analogy. Admittedly, things get a bit heavier here, so perhaps need more effort to read.
Towards the end, she talks about how she feels we could make the teaching of mathematics more effective, and more appealing to more students, instead of turning them off, as seems so universally true. The problem is a massive one, because, even after we accept that it should be done, and agree on a way to do it, it would involve (IMHO) a complete re-education of mathematics teachers at just about every level of mathematics teaching. But just because we might not be able to do a complete revamp of the system doesn't mean that we shouldn't be examining how to improve things, perhaps in a more incremental way.
I believe this book should be read by almost everyone; math-phobes (of which there are legion), math lovers (because the book brings some fresh perspectives on how to think about math), and -- perhaps most especially, teachers of math and math curricular creators, to help them create better ways of teaching math and conveying its many beauties and fascinations to all students.
August 26, 2023
A wonderful approach to de mystifying any fears to the subject by an applied mathematician. Great perspectives. I also learnt that is a very good pianist.
Awesome.
Awesome.
June 15, 2019
This was a fun and interesting book that I quite enjoyed. It tied in a lot to the mathematics and physics work I'm currently doing at the university.
September 21, 2019
How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics
How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics
By Eugenia Cheng
Who is Eugenia Cheng?
Eugenia Loh-Gene Cheng is a British mathematician who specializes in a fringe area of mathematics referred to as Higher-Dimensional Category Theory. She is also known for her support of popular mathematics. Among her many publications are The Art of Logic and, my personal favorite, Beyond Infinity. Professor Cheng attended school at Roedean and is a graduate of The University of Cambridge with her Thesis: Higher-dimensional category theory: opetopic foundations (2002). She graduated with both a BA and a PhD.
Who will this book appeal to?
This book could appeal to anyone; perhaps with the exception of those traumatized by ill intentioned or professionally inept math teachers. Those that are the exception may still enjoy this book. Eugenia has taken the everyday practice of baking and uses it as frame to hang mathematical theories on, to make the mathematics more accessible to a wider audience, and to simplify the theory for the common man. These theories are not new concepts, however, they may be fresh concepts to you. It is a skillfully woven discourse with Category Theory at its heart. Of course, there may be some people who will not understand the basic concepts, but I believe the majority of people who read this book will learn something that may benefit them.
In this book
Having read How to Bake Pi, I’ve noted the Professor is a skilled and gifted educator. She takes the art of teaching mathematics to a whole new level. Her ability to enlighten the audience is due in part to her: familiarity with her subject, and her varied methods to demystify the subject; while simultaneously encouraging an enthusiasm for math that most people never knew they had.
I enjoyed the humor and the lucidity of her delivery. The mathematical logic is there throughout the text, but it is softened through: clear, lucid, and work-a-day explanations that aid the reader in exploring the world of math.
In conclusion
I found this book to be engaging, warm, effusive, and fun. Ultimately, Eugenia has proven that it isn’t what you teach, but how you teach that makes the difference.
May 23, 2016
An extremely engaging celebration (and defense) of research in pure mathematics. For math lovers, Eugenia Cheng, "the best young female category theorist in South Yorkshire" (p. 248), has prepared a tasty morsel on practically every page. And for those who aren't math lovers? "Whatever you think math is... let go of it now. This is going to be different." (p. 3, emphasis/ellipsis original) A few examples follow.
Flipping to a random page (22), I find the chapter title "Road Signs: Abstraction as the Study of Ideal Versions of Things." Describing a picture of a white bar in a red circle, Cheng writes, "This `No entry' sign is entirely abstract: it doesn't look like the thing it is representing at all. (What does `No entry' look like?) But it's also more important -- you will probably encounter more of these in your driving life that the one warning you there might be deer crossing the road." No wonder, then, that abstraction deserves study.
Later, Cheng presents evidence that math is easy. "This is the crucial point: we make things easy by ignoring the things that are hard. Mathematics is all the parts we don't have to throw away." (p. 146) That's why your math text doesn't ask you to answer questions like: "I am very happy. How will I feel if I go bungee-jumping?" (p. 145)
It is sad, if not surprising, to see Prof. Cheng write, "For most of my career I've been much less myself at work, for fear of drawing too much attention to the fact that I'm female in an extremely male-dominated environment. I tried to be as unfemale as possible, to avoid any prejudiced accusation that my being female was making me a worse mathematician." (p. 170) I find it uplifting, though, that she uses this experience to illustrate the fact that "the number 5 takes on different characteristics depending on what context we're in. Category theory seeks to highlight the context you're thinking about at that moment, to emphasize its importance and raise our awareness of it." (p. 172) This is the best popular summary I've ever read of that consummately abstract discipline.
I fear two classes of people may choose not to pick up this book: mathematicians, who may feel the conceit is too cute, and non-mathematicians, who may hate the idea of a book about math. They will be missing out on a delicious treat.
Flipping to a random page (22), I find the chapter title "Road Signs: Abstraction as the Study of Ideal Versions of Things." Describing a picture of a white bar in a red circle, Cheng writes, "This `No entry' sign is entirely abstract: it doesn't look like the thing it is representing at all. (What does `No entry' look like?) But it's also more important -- you will probably encounter more of these in your driving life that the one warning you there might be deer crossing the road." No wonder, then, that abstraction deserves study.
Later, Cheng presents evidence that math is easy. "This is the crucial point: we make things easy by ignoring the things that are hard. Mathematics is all the parts we don't have to throw away." (p. 146) That's why your math text doesn't ask you to answer questions like: "I am very happy. How will I feel if I go bungee-jumping?" (p. 145)
It is sad, if not surprising, to see Prof. Cheng write, "For most of my career I've been much less myself at work, for fear of drawing too much attention to the fact that I'm female in an extremely male-dominated environment. I tried to be as unfemale as possible, to avoid any prejudiced accusation that my being female was making me a worse mathematician." (p. 170) I find it uplifting, though, that she uses this experience to illustrate the fact that "the number 5 takes on different characteristics depending on what context we're in. Category theory seeks to highlight the context you're thinking about at that moment, to emphasize its importance and raise our awareness of it." (p. 172) This is the best popular summary I've ever read of that consummately abstract discipline.
I fear two classes of people may choose not to pick up this book: mathematicians, who may feel the conceit is too cute, and non-mathematicians, who may hate the idea of a book about math. They will be missing out on a delicious treat.
August 22, 2016
In the genre of general audience books that attempt to explain math, Eugenia Cheng has written an intriguing and often successful volume. Probably more than any other undertaking I've read, Cheng's book wonderfully and clearly describes what doing theoretical mathematics is like (especially on the algebraic side). She has a nice chapter on the benefits and pitfalls of logic, and she does an excellent job of illustrating the processes of abstraction and generalization, both with her cooking examples and a fair number of mathematical examples. (A note: the mathematics needed here to follow the examples is mostly at the high school level. If you feared quadratic equations in algebra class, some part of the books might be tough going.) I haven't seen anything else that does so much to explicate mathematics as process.
Now, the cover, the title, and the subtitle leads one to think that cooking will be heavily involved. It's not. I found the title to be little more than a gimmick. While the recipes that start each chapter often help Cheng make her points by acting as metaphors, I would not call this (as the subtitle does) an "edible exploration". If you're coming to this as a foodie, I think you will be disappointed.
The book is really about category theory, not cooking. I first ran into category theory in my graduate school days, when I was pursuing a higher degree in mathematical logic. Category theory, at the time, seemed to be parallel to mathematical logic --- another attempt to describe the underpinnings of mathematics, but supported by algebraists who had turned abstraction up to 11. I basically ignored it, having cast my lot with the thrills of first order logic. But Cheng makes a nice case for the uses of category theory and makes excellent use of the visuals that categories can provide. My biggest concern, however, is that she just barely gets going by the end of the book. There's a nice ending chapter on the difference between proving something and understanding the proof, a cry for greater understanding, and a claim that category theory helps that understanding, but no final payoff on how and why category theory helps.
Still, this is wonderfully readable and a great insight into how mathematicians reason. If you come for the recipes, stay for the mathematical process.
Now, the cover, the title, and the subtitle leads one to think that cooking will be heavily involved. It's not. I found the title to be little more than a gimmick. While the recipes that start each chapter often help Cheng make her points by acting as metaphors, I would not call this (as the subtitle does) an "edible exploration". If you're coming to this as a foodie, I think you will be disappointed.
The book is really about category theory, not cooking. I first ran into category theory in my graduate school days, when I was pursuing a higher degree in mathematical logic. Category theory, at the time, seemed to be parallel to mathematical logic --- another attempt to describe the underpinnings of mathematics, but supported by algebraists who had turned abstraction up to 11. I basically ignored it, having cast my lot with the thrills of first order logic. But Cheng makes a nice case for the uses of category theory and makes excellent use of the visuals that categories can provide. My biggest concern, however, is that she just barely gets going by the end of the book. There's a nice ending chapter on the difference between proving something and understanding the proof, a cry for greater understanding, and a claim that category theory helps that understanding, but no final payoff on how and why category theory helps.
Still, this is wonderfully readable and a great insight into how mathematicians reason. If you come for the recipes, stay for the mathematical process.
August 7, 2015
I read How to Bake Pi in hopes that ingredients, dessert recipes, and baking would help elucidate math for me, and this worked for the most part. Some of the food analogies are necessarily a bit forced, and I had trouble relating some of them to the math being discussed, but that was most likely a failing on my part.
One thing that stands out in Dr. Cheng's book is her ability to clearly define and talk about math terms that I've heard, been taught, used, but never completely understood (or perhaps I've forgotten). She thoroughly discusses concepts like abstraction, generalization and axiomatization in ways that even I could understand, before writing about her own field of category theory in the second part of the book. Things got a bit murky there for me; I kept wondering, “What is category theory?” even while reading that it is “the mathematics of mathematics.” This is probably because I'm a reader and student that needs concrete examples that I can ponder and examine, but I'm not sure category theory or Dr. Cheng can provide that.
What I liked best about How to Bake Pi is Dr. Cheng's enthusiasm for her subject matter, that she seems to really care about explaining mathematics to non-mathematicians, that she made me think and also raised many other questions, ideas, and areas of interest for me. Even if you may not care about math or think math is difficult, reading How to Bake Pi may change your mind in an interesting and enjoyable way. Like the author says (http://cheng.staff.shef.ac.uk/illogic...), “Mathematics is easy, life is hard.”
One thing that stands out in Dr. Cheng's book is her ability to clearly define and talk about math terms that I've heard, been taught, used, but never completely understood (or perhaps I've forgotten). She thoroughly discusses concepts like abstraction, generalization and axiomatization in ways that even I could understand, before writing about her own field of category theory in the second part of the book. Things got a bit murky there for me; I kept wondering, “What is category theory?” even while reading that it is “the mathematics of mathematics.” This is probably because I'm a reader and student that needs concrete examples that I can ponder and examine, but I'm not sure category theory or Dr. Cheng can provide that.
What I liked best about How to Bake Pi is Dr. Cheng's enthusiasm for her subject matter, that she seems to really care about explaining mathematics to non-mathematicians, that she made me think and also raised many other questions, ideas, and areas of interest for me. Even if you may not care about math or think math is difficult, reading How to Bake Pi may change your mind in an interesting and enjoyable way. Like the author says (http://cheng.staff.shef.ac.uk/illogic...), “Mathematics is easy, life is hard.”
August 16, 2015
When I first saw a review of this book it sounded very intriguing. Then it took a couple of months to get from the library, and a few weeks to get around to reading it. My understanding is that the book was focused on explaining mathematical concepts using reference to food and cooking. There are a number of recipes, and recipes are used to explain some broad concepts. What I didn't realize is that this book is really about Category Theory of mathematics, or the effort to define math concepts in an even simpler manner. And what I got from the book is that, despite all the rhetoric of math being the universal language, it is actually relative to our experiences and understanding. It is dependent on context, and full of assumptions and rules so that it will maintain logical relationships despite real world variation.
Along the way Dr. Cheng provides some fun examples and exercises, some tasty-sounding recipes, and some entertaining anecdotes. I particularly enjoyed the stories about when she told people at parties what she did and the strange substitutions made by online grocers.
Overall, I thinkit is a pretty accessible book, though it is best if the reader has had algebra, trigonometry and geometry in order to understand what she's getting at. I didn't read it deeply, but then I didn't need to. I do intend to try out one or two of her recipes though.
Along the way Dr. Cheng provides some fun examples and exercises, some tasty-sounding recipes, and some entertaining anecdotes. I particularly enjoyed the stories about when she told people at parties what she did and the strange substitutions made by online grocers.
Overall, I thinkit is a pretty accessible book, though it is best if the reader has had algebra, trigonometry and geometry in order to understand what she's getting at. I didn't read it deeply, but then I didn't need to. I do intend to try out one or two of her recipes though.
May 17, 2015
Everyone should read (eat) this book!
I can't believe how good this book is for illuminating what mathematics is. I have spent most of the past forty-five years trying to find the words to communicate what Eugenia Cheng has so masterfully done in this book. Whenever I get a chance in the future to talk about mathematics I will steal her metaphors and examples. I will also be recommending the book to all of my colleagues in education as well as students. I could not stop reading and wondered if she could continue, chapter after chapter, to come up with examples to make her case. She succeeded right up to the end. I am a little sorry now that I did not pursue Category Theory with more diligence when I first encountered it in the 60’s, but I may look into it again at this late date.
I can't believe how good this book is for illuminating what mathematics is. I have spent most of the past forty-five years trying to find the words to communicate what Eugenia Cheng has so masterfully done in this book. Whenever I get a chance in the future to talk about mathematics I will steal her metaphors and examples. I will also be recommending the book to all of my colleagues in education as well as students. I could not stop reading and wondered if she could continue, chapter after chapter, to come up with examples to make her case. She succeeded right up to the end. I am a little sorry now that I did not pursue Category Theory with more diligence when I first encountered it in the 60’s, but I may look into it again at this late date.
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