★★★☆☆ Infinity for lovers of shoes and baked goods

Beyond Infinity: An Expedition to the Outer Limits of Mathematics

Eugenia Cheng

I started this book by mistake. I heard a presentation by Eugenia Cheng at The Perimeter Institute for Theoretical Physics, in which she told us a little about Category Theory. Category Theory is a field of mathematics I have never studied, and her talk got me interested. So I thought I would read her book about Category Theory. That is something I may someday do, but today is not that day. Cheng's Category Theory book is The Joy of Abstraction: An Exploration of Math, Category Theory, and Life. If I had been paying attention, I would have realized that Beyond Infinity: An Expedition to the Outer Limits of Mathematics is not it.

But it's a short book, so upon realizing my mistake I thought, "Well, why not? It'll be a quick dip into Cheng's writing." So, I read it. I confess myself disappointed. Cheng is a very chatty writer -- she talks a lot about herself personally, and I just couldn't relate. For instance, this

Let’s assume the cookies are circular and perfectly even. I was once criticized in public for assuming this about scones, and accused of using factory-made scones. For the record, I do make my own scones, and I’m perfectly aware that nothing on earth is perfectly round and even, but it’s a good enough approximation for a math discussion

I do not make my own scones. I cannot imagine feeling compelled to defend myself against the accusation of using factory-made scones, or even using the verb "accuse" in this context. Elsewhere she speaks of counting her shoes as an approach to visualizing infinity. She mentions with incredulity acquaintances who have "only" four pairs of shoes. I imagine that Cheng includes these personal asides in an attempt to make herself more relatable. The effect on me, however, is the opposite of that -- she feels like an incomprehensible alien, except when she's talking about mathematics, when she becomes human.

I was honestly not terribly impressed by her explanations of difficult mathematical concepts. She didn't make them easier to understand than the usual more formal explanations. (In my opinion, Ben Orlin's books are a better starting point for a nonmathematical reader seeking to understand difficult mathematical ideas.)

There are two mathematical concepts discussed in Beyond Infinity that I was not previously comfortable with: ordinal infinities and Category Theory. Having read it, I still don't understand them. Now, Category Theory only comes up as an example of multiple dimensions -- Beyond Infinity is not intended to explain Category Theory in any depth, so it can't be fairly criticized for failing to do so. Ordinal infinities, however, are very much a part of what Beyond Infinity is about.

In summary, if you prefer to take your math with baked goods and plenty of shoes, this might be the book for you. For me, except for the math, it was like a book written by an alien. I understand that The Joy of Abstraction is more mathematician-oriented, so I haven't given up on that yet.

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