On "Cakes, Custard + Category Theory"

Posted on April 18, 2016

I am not a mathematician, and this is probably the only regret of my life. When I was young I was too lazy to work seriously enough in High School to be accepted at one of the “Grandes Écoles”. Or rather I was way too much interested by role-playing games to spend time doing homework. And I must say maths were quite boring in High School and Preparatory School, not even talking about Business school’s math which barely went beyond basic arithmetics…

Things would probably have been quite different had I been taught math by Eugenia Cheng, the author of Cakes, Custard + Category Theory and one of the presenter of the famous Catsters series, among other talents.

I have read, or more precisely tried to read, many books about category theory but I know I still only have an intuition about very basic things, e.g. what is a category theory, composition of morphisms, units, simple limits… The more abstract - and important - concepts (adjunctions, Yoneda lemma, topoi, sheaves…) are still inaccessible to my understanding: To state it in Eugenia’s terms, I know them but I don’t understand them.

Cakes, Custard + Category Theory is a math books for non-mathematicians, a book that tries and - to my humble opinion - somehow succeeds in giving lay people some ideas on why maths are important, interesting and fascinating. More importantly it also succeeds in giving intuitions on what is math and category theory and on connecting the dull, formal and painful external aspect of maths most people see with the deep, complex, beautiful and sophisticated ideas behind that rude shell.

The book is divided in two parts, Mathematics and Category Theory which shares a common underlying structure: Each small chapter is introduced by the recipe of some cake, some classical and some invented by the author, and each part ends with a tentative explanation of what is math or category theory. Through the various chapters, Eugenia threads mundane life examples, recipes, cooking metaphors with actual mathematical questions in order to convey to the reader intuitions on what things like monoids, groups, morphisms, associativity or equivalence are. Mathematical notations is mostly restricted to sidebars and does not clutter reading.

I am not usually a great fan of analogies which more often than not obscure rather than illuminate the thing they are supposed to explain. But this book is written in a such a way that it mostly avoids this pitfall1:

• Eugenia’s style is so lively and entertaining one cannot but avidly read the book and reach for the next chapter till the end,
• She manages to motivate mathematics, not as a mere tool one uses to solve more or less complex problems, but as a way to ask profound questions about the way we think and the world we live in.

The key question in maths and category theory is then not how but why.

Proof has a sociological role ; illumination has a personal role. Proof is what convinces society ; illumination is what convinces us. 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 they will be able to reconstruct the feeling in their own mind.

1. Although I myself enjoy cooking very much, I was not that much convinced about the whole recipe meme…↩︎