Review: How to Bake Pi by 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 how the bechamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng’s work on category theory, a cutting-edge “mathematics of mathematics,” that is about figuring out how math works.

Combined with her infectious enthusiasm for cooking and true zest for life, Cheng’s perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let’s look for the answer in the kitchen.

I know this is not going to be a review or a book that everyone is interested in reading. Math is not exactly the most popular subject. But the thing is, Eugenia Cheng is well aware of this. She knows that you might not like or understand math, but she is on a mission to make math fun. Rather than expect readers to know and like math the way she does, she meets her readers where they are at in order to share the power, beauty and fun mathematics has to offer. I love this book because it’s a joy to see my love of math shared with a wider audience.

In a mere 280 pages, Cheng introduces her reader to many forms of mathematics as well as the way mathematicians think. But no matter how abstract, Cheng’s writing remains witty and approachable. How does she do it? Through cooking, of course!

While most of us may think cooking and math have little to do with each other beyond measuring the ingredients, Cheng has a unique perspective. Being a prolific baker as well as a mathematician, she sees the connection between math and food everywhere. For example, associativity, the mathematical property that a+(b+c) = (a+b)+c, can be compared to the way ingredients mix together — or fail to. When you make a cake, you can start by mixing the sugar and butter, then add the eggs, or you can start by mixing the butter and the eggs before you add in the sugar. The order doesn’t particularly matter because the ingredients are associative. But if you want to make custard, you have to add the egg yolk and sugar together before adding the milk. If you add the sugar and milk first and then add the egg yolk, you will not get custard. So the ingredients of custard aren’t associative. This connection to cooking is what Cheng uses to introduce her readers to math concepts which may have previously seemed scary.

Importantly, Cheng’s explanations do not end with cooking. The entire book is filled with analogies comparing math to parenting, the high jump, and legos. This means that even if you aren’t a baker, you are bound to find interpretations that make sense to you. Cheng is constantly connecting math to the everyday world around us, illustrating just how ingrained in us these mathematical principles are, regardless of whether or not we think of them.

One of the many secrets Cheng shares with us is although math may be difficult, it is actually there to make things easier. Most of us hated word problems in school so much that they have now become a popular joke. Who buys 60 watermelons and 30 zucchinis? But math allows us to ignore the unimportant information (that we have watermelons and zucchinis) and focus on the important information (60+30). Math takes a complicated sentence and turns it into a simple equation.

The second half of the book focuses on Cheng’s area of specialty: category theory. If mathematics is about making hard things easier, Cheng terms category theory the “mathematics of mathematics” because it makes the study of math easier.

Category theory studies not just mathematical objects themselves, but in relation to other objects. The same way a list of cities becomes a map by showing us where the cities are in relation to one another, category theory combines different areas of math into one by studying the relationship between them.

But we can’t just look at any old relationships, we have to focus on useful relationships. Category theory’s job is to keep the useful bits of mathematical information and remove the useless, much in the way math does with a word problem.

I find Cheng’s perspective insightful and illuminating. She is able to verbalize something I understood but was unable to voice: the process of stripping away the useless information to make an equation is generally the difficult part of math. But once you get past that, math can be satisfyingly simple.

No reader is going to walk away from this book with the ability to do math they couldn’t do before. If that is what you’re looking for, I recommend a textbook. But you will walk away with a sense of awe for the beauty of math, and delight in the fun of it. It’s a perfect book for anyone who wants a flavor of what higher mathematics is all about, as well as for mathematicians to hear a fresh perspective on viewing and teaching mathematics.

If this review feels a bit heavy on the math, that is because I wrote it for a class. If you glazed over the math parts, the tldr is that I really love this book. I think Cheng does a great job of explaining the all the things that I love about math to a wider audience. It is exactly the kind of book I want to share whenever somebody asks me what a mathematician actually does. So if you are ever interested in reading about math, this is the book to pick up.