Ignorant and unprofessional.

Surprising words to describe a math book, eh? Well, that is the sort of surprise you'll get when you pick up this book to learn about category theory.

Let's start with Ignorance. Early on, the author attempts to demonstrate the usefulness of category theory by showing that it enabled her to understand why poor white people get told they have "white privilege": you see, there are (in order of privilege, most to least) Privileged White People, then there a Privileged People, then there are White People, then there are People.

I don't want to get into class warfare here, but combining racial warfare and class warfare as the author does requires some response. Let's assume, for the same of argument, that the wealthy or "privileged" are the enemy of the people, as Marxist theory tells us they must be. There is no indication that white wealthy people are any better or worse (in terms of morality or of material wealth) than wealthy nonwhite people; in fact, any familiarity with the wealthy of India, China or Saudi Arabia (to name just the most frequently encountered non-white wealth holders) will reveal that they are as wealthy as the whites, and are just as ruthless, vicious and rapacious in the acquisition and retention of that wealth.

So let's leave the race component out of it, eh? It is the 21st century; it should not need to be stated that any generalization based on race is absolutely wrong, even (need I say *especially*?) when it is popular or politically expedient to do so. The author comes from an academic environment, of course, and the news is rife with stories (backed up by anecdotal evidence provided by friends and colleages) that this sort of atavistic thinking is pervasive in academia right now. To which my only reply is, yeah, they tried to sell this crap to us in college in the 90s as well, but we weren't stupid enough to fall for it. Racism is racism is racism, end of story full stop. If you find yourself bringing up race in the course of making an argument, maybe back up a step and rethink your assumptions.

Enough of that diatribe. What about Unprofessional?

Well, a hundred or so pages later, the author chucks in some no-doubt-joking aside that all while males look the same to her. I mean, fine, it's not unusual to make that sort of a joke, though usually it's over beers and placed in the context of a humorous anecdote about how you embrassaed yourself with a complete stranger. Not, you know, apropos of nothing in the middle of a book on mathematics. Shall I even go into the accusations of racism and sexism that would erupt if a white male made the same comment about asian females? I shall not. At this point I set the book aside, and have not picked it up in the months since. It just doesn't seem worth the aggravation.

So, Ignorant for racist reasoning, Unprofessional for including this sort of thing in a *math* book. Save it for some echo-chamber academic discipline, like gender studies.

But what about category theory, you say? What does the book say about that?

Indeed.

Well, it's hard to say. The author seemed at great pains to discuss her personal preferences and beliefs, but didn't seem to to get around to talking about category theory, or why it is worth learning, or how it differs substantially from Groups and such as covered in a book or course on abstract alegbra. I have now started three books on category theory, and not a single one has managed to convey what is unique or interesting about category theory.

In this book's favor, the *approach* is good, and narrative coverage of mathematical topics (as in Mike Cohen's Linear Algebra book, among others) is sorely needed for those of us who do not spend three-quarters of our reading time on equation-heavy monographs. Perhaps a complete rewrite, maybe one not assuming TOTAL ignorance of abstract mathematics on behalf of the reader (I mean come on, it is category theory, you're not going to have too many truck drivers in the audience) would produce a useful work. ( )

Eugenia Cheng, in The Joy of Abstraction, shows how the pragmatic uses of mathematical thinking does not preclude the fun of it.

This is the third of her books that I have read and, as I have come to appreciate, it both taught me a great deal as well as entertained me. No, not like a film might, more like when your mind begins to grasp something and it is entertained by how many ways there are to use that new information. While Cheng says that How to Bake Pi isn't necessary for understanding this book, I can say I was glad I had read it. I do agree, it isn't necessary, but it sure helped with my comfort level while reading this one.

This is mathematics, but not like we learned in school. This is engaging, creative, and, yes, fun. This leads the reader to some new ways of thinking, mathematical thinking, that can affect every aspect of your life. Her enthusiasm is contagious.

Since this real math made more accessible for non-mathematicians, there will be sections that may require rereading. The reward, however, is well worth the extra time to make sure you get the big picture. That said, because the big picture is probably what most readers want, some sections can, I think, be skimmed without losing the view. I also, at least for myself, think this will be a work that will get richer with subsequent readings. My plan is to give it a couple of months to ferment in my mind then revisit it.

Highly recommended for everyone from creative types to those in the mathematics-based fields (science and engineering as well as math). Since this is as much about mathematical thinking as it is category theory itself, the benefits go far beyond just learning about a field of mathematics.

Reviewed from a copy made available by the publisher via NetGalley. ( )