In her book, How to Bake Pi, Eugenia Cheng takes the reader on a two-part journey, exploring the wonder behind the concept called mathematics. If "pi" wasn't enough of a hint, then the reader shortly realizes upon reading the Prologue that this text does not actually tell the reader how to bake the delicious desert that has a crust on the top and bottom, with some, usually fruit flavored, filling on the inside. Rather, the title comes from the series of recipes the author supplies at the opening of each chapter, which she then uses to relate to mathematics in some way, shape, or form.
What is math?
Like stated earlier, Eugenia Cheng breaks apart her book into two sections. In the first half of the book, she spends 156 pages (at least in my copy) answering the most simple question: What is math? Or maybe not so simple as she introduces mathy words like abstraction, generalization, axiomatization and more that make any non-math-geek cringe. Do not worry, for Cheng uniquely defines each by breaking down the process to the simplest form. As a reader, I was impressed with how capable I was reading her text and understanding the point she was trying to get across. That's because Cheng uses real-life, everyday encounters to explain the most complex of mathematic processes. For example, each chapter begins with a recipe. Sometimes the recipe was very vague in the ingredients it offered, or extremely detailed in the method of making the treat on hand. In either scenario, Cheng used the recipe to explain the process of axiomatization or some other ten-plus character word. As a result, the reader (no matter what math background they may have) is more likely to continue reading as oppose to quitting after fifty pages due to complex material.
As Cheng comes to a close in her writing of this section, she defines math as the "study of anything that obeys the rules of logic, using the rules of logic" (143). Seem redundant? She has lots of textual evidence that supports this definition, it is now up to you to read her text to fully understand why she defines "math" in such a way.
What is category theory?
Eugenia Cheng, after defining math in the first half of the book, then moves on to define category theory, a term that I was unfamiliar with prior to picking up this book and reading it. If the definition of math did not make you want to read the text, the way in which Cheng defines category theory will make you drop all tasks on hand and find yourself a copy. In seven words, Cheng defines category theory as the "mathematics of mathematics" (162). Do better help you wrap your mind around, let me present a quote within the text. It is a little bit of a spoiler of the contents of the first half revolving math, but it will better engage your brain at what Cheng means by category theory.
"In the first part [of the book] we saw that mathematics works by abstraction, that it seeks to study the principles and processes behind things, and that it seeks to axiomatize and generalize those things. We will now see that category theory does the same thing, but inside the mathematical world. It works by abstraction of mathematical things, it seeks to study the principles and processes behind mathematics, and it seeks to axiomatize and generalize those things" (162).
Some deeper mathematical thinking is introduced in this half of the book, bringing up lots of ideas I have previously explored in my math past, whether that be in a high school class, or college course. Once again, the way in which Cheng breaks down category theory, exploring it in relation to structure, sameness, universal properties and more, is done in such a way that draws any reader, not matter how math-smart. For example, for as long as I can remember, I have struggled with modular math. I have never fully wrapped my mind around the process and have consistently struggled through many course (both in high school and in college). In the text, Cheng uses modular math in relation to a clock, a physical object every human is aware of. I can now say, that I understand the meaning behind modular math, THANK YOU CHENG! This isn't the only example, throughout the text, I found myself often saying, "Man, I wish I was taught it this way in (insert math class name here)" or "If only (insert math concept) had been explain to me this way, I would have understood so much more." It really is amazing how Cheng masterminds her ideas into simple language. As a result of such efforts, I walked away from this section of the text with lots of new information regarding category theory.
Four out of five starts
After reflecting on the Eugenia Cheng's book, How to Bake Pi, I really cannot complain. I recommend this book to my math colleagues, to my friends, to any looking to explore the crazy subject we call math. The way in which Cheng pens the text is extremely engaging and easy-to-read. While many of her chapter contained lots of subheadings that often did not relate with one another, Cheng did her very best to break down the aspects of math into the most distinct parts and succeeded in writing in an understandable way. Your job now is to drop everything and go find a copy now and start reading. No matter how your personally feel about the text, at least you have several recipes on hand to try. A win-win situation for all!
My name is Abby Niemiec and I am in the midst of my final year as a undergraduate student at Grand Valley State University. I am a double major in Mathematics and Education, with my minor focusing on Elementary Education. Within this blog, I will be sharing mathematical ideas, perspectives, thoughts and much more! Stay tuned...and enjoy the read!