How to Bake Pi uses analogies to cooking and baking (and lots of other everyday things) to explain some fairly advanced mathematical concepts. These work nicely, especially for someone like me who hasn’t done anything beyond calculus 2, and that over 10 years ago. The invention of an olive oil plum cake recipe for example becomes a way of explaining generalization (how can something be called a ‘cake’ if it is not completely really a cake) and the mathematical practice of proof by contradiction (proving something true by proving the opposite as wrong. There are also analogies involving things like transportation, long distance running, and online dating, in addition to the more traditional algebraic looking bits and diagrams with arrows and shapes. The genius of this book is putting the easier to understand stuff first, so that the explanation with the traditional numbers and letters and arrows is easier to follow.
I have two problems with the book overall. First, my complaint is that this book is supposed to be about something called category theory, yet I still don’t know quite what that is beyond what I could have guessed from the label ‘category’. There’s lots of analogies, so I know what elements of category theory are like, but I’m not really sure what the whole thing is in terms of advanced math. For example, vegan and gluten free brownies help show a goal of category theory which “is to take slightly subtle notions of sameness and make them precise” and “Category theory highlights the relationships between things, so it enables us to look for more subtle notions of ‘sameness’ than equality via these relationships.” This much makes sense, but it does not provide an actual definition. Apparently, category theory also makes hard math things easy, but to a non-mathematician, that probably means something entirely different than it does to the author.
I also take a little bit of issue with the author’s argument that the reason most people think math is hard is because of how it’s taught. While this reasoning may be true in the sense of the level of detail concerning how mathematical processes work often used in the classroom, it ignores the fact that most instructors at nearly every level have to cover a certain amount of material, which means they likely don’t have the time to take with the in-depth analyses that would be necessary, and second, it ignores the simple fact that some people would not have an easy time with the formal logic behind the math. It’s not the most exciting thing in the world to everyone, formal logic is not easy or straightforward in a lot of ways, and it seems like the author forgets this. As a university teacher, she must teach, but I have to wonder when the last time she had to teach non-math majors or high schoolers. These two groups would likely not care or have the time/patience to spend with the in-depth background she suggests would help people appreciate math more.
Overall, this book has some good things that can’t always be sustained. The splitting up of ideas was a good move to present the subject to lay-people, but that also makes the book hard to read for a long period of time. Because the structure is fragmented, out of necessity and I understand the decision, it’s hard to read through several sections at a time because they are so stop-and-go. I love the recipe analogies, but even these don’t always work out. Using jaffa cakes as an example of the need for detail in terms of description and the concept of ‘from scratch’ forgets that a lot of Americans don’t know what these cookies actually are to begin with. I do, and they are wonderful, and I’m glad to see them here, but it seems a little ironic that an example concerning the need for full information violates that very principle itself.