Book Review-How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics By Eugenia Cheng
Good and gentle introduction to mathematics and Category Theory though baking recipes.
I had started reading one of Eugenia Cheng’s other books The Art of Logic: How to Make Sense in a World that Doesn't (Cheng, The Art of Logic: How to Make Sense in a World that Doesn't, 2019) a few years ago. I was much of the way through it, but it just did not gain traction with me. Maybe it was the topic, or it may be that I just wasn’t in the mood for it, or it may be that I just started paying more attention to the next shiny glittery lure that was in front of me. I vowed that I would return to it someday. That someday may be soon because I not only enjoyed this book: How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, I started to think differently at the end of the reading experience than at the beginning of the reading experience.
I had not intended to read this book, but I was thinking about the ideas of abstraction and generalization in the everyday context, that is, not in the mathematical context. I was confusing myself and trying too hard. I asked my friend, a mathematician and philosopher, for some reference to unconfuse myself. She recommended this book, with the thought that going through reading about the rigorous and strict definitions of the two terms in a narrow context could remove the detritus of overthinking. Remembering my failure with Cheng’s other book, I dawdled a little, but I decided to read more diligently, and also because I believe that my critical reading skills had improved since I had been working on both my reading and thinking habits.
The book is divided into two parts, the first part is devoted to explaining the tools of mathematics, which is what I was interested in; the second part is devoted to explaining the tools of Category Theory, or as the author explains in the introduction: the mathematics of mathematics. As an engineer, I was trained in applied mathematics, but mathematics is not something that can be parsed easily into distinct parts and studied in a segregated manner, so I was exposed to some part of theoretical mathematics. I was not particularly interested in theoretical mathematics then as my only foray into thinking mathematically was a course in Real Analysis, which I dropped quickly. It never made sense to me. Indeed, I was assiduously devoted to learning engineering at that point in my life. It wasn’t until much later in my life that theoretical mathematics became interesting.
My strategy for this book was to diligently read and think about the material in the first part of the book and then maybe skim over the second part about Category Theory. I was previously aware of the phrase Category Theory, but I did not even understand what the area entailed.
Each part of the book is bookended with chapters that first introduce the orthodox definition of the topic, Chapter 1 is titled What Is Math and Chapter 8 is titled: What Mathematics Is. This structure gives the reader a methodical progression through the topic addressed by each part of the book. Chapter 9 and 15 do the same with Category Theory. It is a very clean and methodical structure.
The unique part of the book, which I had been remiss in mentioning is that each chapter opens with a recipe. Not just any recipe but a recipe that Cheng feels is illustrative of the concept that she is trying to explain in each chapter. It is a clever way of introducing the subjects by analogy, although the baking part is partially lost on me because I am not a baker, but she does not limit her analogy making and making connections to just baking examples, she works very hard to make connections with disparate topics to clearly explain, in plain language, some very profound ideas. I am appreciative of her efforts because the analogies helped me in deciphering the topics. There were times when I thought the baking idea was slightly distracting, but then I would read a chapter where it helped. So, I took the bad with the good and I was generally happy with the device.
I went through Part 1 rather quickly and was able to put the material together, the book served its purpose as my friend had suggested. As I had decided on apriori, I skimmed through the second part. Much to my delight, I found the subject to be less intimidating than I had assumed. Since I had become accustomed to the way Cheng had structured the book, following along with the structure and trying to dig into the granularities of Category Theory became much more interesting and less challenging. I am still a rank amateur when if comes to Category Theory, I am, however, an interested and motivated amateur now. A definitive sign of my interest and motivation is that I am beginning to delve into Cheng’s latest book: The Joy of Abstraction: An Exploration of Math (Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life, 2022). When I told my friend who had recommended the book, she gleefully replied: Hah, gotcha. Yes, indeed.
I would conclude that this book is a gentle but helpful introduction to how mathematicians think and do math. As a reader, I attained an understanding of the tools of mathematics and Category Theory, I am not able to wield those tools proficiently yet, but I am becoming much more proficient with these tools, which is all that had asked for. I came in wanting to read one book, now I am reading a second, much denser and more granular book about a topic that I had no interest in learning, and I am committed to re-reading a third book that I had previously abandoned. that is a pretty strong recommendation.
References
Cheng, E. (2019). The Art of Logic: How to Make Sense in a World that Doesn't. NYC: Profile Books.
Cheng, E. (2022). The Joy of Abstraction: An Exploration of Math, Category Theory, and Life. Cambridge UK: Cambridge University Press.