I’m disappointed that so many people seem underwhelmed by the autobiographical parts of this book and feel that they are ancillary to Frenkel’s purpose. I disagree: they are, in fact, the heart and soul of Love & Math. Without them, this would be a fairly intense treatise on deep connections between abstract algebra, algebraic geometry, and quantum physics. With them, Frenkel demonstrates how the study of mathematics and a devotion to thought for thought’s sake, to fulfil human curiosity helped him personally through anti-Semitism and Soviet persecution. In some ways I was reminded of remarks Neil Turok makes in The Universe Within (if I am remembering correctly) about the state of education in many African countries depriving us of staggering potential intellects. How many people, poor or Jewish or otherwise unprivileged, were not as lucky as Frenkel happened to be?
Frenkel’s personal recollections are also interesting because they provide a glimpse into the lifestyle and community of professional mathematicians. This is not something most people think about, even people who are scientifically-minded. There are a few famously reclusive or otherwise lone-wolf mathematicians out there (though I think that most of them at least maintain some kind of correspondence with a few respected colleagues), but for the most part, twentieth and twenty-first century mathematics is very much a group endeavour. Frenkel describes how he helped to organize new research in the Langlands Program by gathering together mathematicians from various institutions to hear their input. Belying the stereotypes, mathematics is a very social world.
Ultimately, of course, the personal parts of the story are essential to Frenkel’s explanation of why he loves math. Again, I must disagree with those reviewers who pan this book because it doesn’t inspire them to love math … that was never the aim. Neither the book nor Frenkel are naive enough to believe that, I think. But I suspect one reason many people react the way they do when one reveals one’s mathematical inclinations is genuine bewilderment over the idea that a “normal” person could actually love math. As Frenkel points out, even when mathematical achievements are depicted in popular culture, the subject is always a social outsider.
(In a way, it’s similar to this whole idea of left brain/right brain people. “Oh, you’re a left brain person!” and, when people find out I teach both math and English, “You’ve got a weird left and right brain thing going on!” But the truth is, a lot of people in “left brain” positions that require logical reasoning are also very creative and passionate and linguistic—and a lot of “right brain” thinkers are also organized and calculating. Humans are diverse, and the stereotypes and categories we create are not that good at classifying us.)
The autobiographical elements also humanize what might otherwise be a fairly involved book. When Frenkel talks about loving math, he isn’t pulling a Cabinet of Curiosities here. Don’t get me wrong: I’m all for books explaining elementary math. But I’m pleased that Frenkel tackles much higher-concept, abstract mathematics in a nonetheless accessible and approachable way.
I’ve forgotten a lot of my undergraduate math, I am sorry to say. One day I’ll delve back into ring theory and group theory for some fun. I’m pleased by how much I do remember, however. I recognized a great deal of what Frenkel explained, even though some of it still managed to escape me. So when I say Love & Math is accessible, I’m not claiming Frenkel is going to help you comprehend abstract algebra. Rather, he demonstrates some of the concepts that power abstract algebra through some clever diagrams and explanations, and he connects abstract algebra to quantum physics.
I particularly enjoyed this latter endeavour. I knew that symmetry was one of the most significant aspects of group theory, but I didn’t understand the specific ways in which group theory actually underlies a good deal of the interactions between subatomic particles. So that was cool. There are many points where Frenkel basically explains the math behind the physics, then says, “Oh, and mathematicians figured this out long before physicists came along and discovered the math was useful.” That’s not to say math is more important than physics (that’s just, like, self-evident), but I love that we can build these models in math without any reference to the physical world … and then somehow, these models become useful in explaining the physical world. That is just mind-boggling.
As an educator, I also sympathized with another remark Frenkel makes, rather early in the book. He compares the teaching of math in high schools now to the prospect of teaching art by having students paint fences. That is, we barely get to scratch the surface of what mathematics is in high school. Frenkel speaks of quadratics with the disdain only a pure mathematician could muster. But it’s true: I don’t blame students for thinking that math is boring, because the topics we drill into them and the way we do it tends to communicate that fact. You really don’t need to know the quadratic formula—not in the days of Wolfram Alpha—but symmetry? That’s not only important but beautiful as well.
Honestly, Love & Math is not going to make you love math, and it was never supposed to. It’s not going to teach you group theory or representation theory, and you probably won’t have any clue what a Riemannian Surface or a Kac–Moody Algebra is after reading the book. (Maybe you’ll understand what a group is, in some way.) If you’re really interested in learning those things, there are books and videos and courses and wikis to help you out.
Instead, Love & Math is one mathematician’s story of how he fell in love with math, how it saved and defined his life, and how he feels honoured and awed that he has had the chance to give back to the mathematical community. Frenkel goes so far as to make a weird surrealist movie about loving math … and that is not my thing, but it’s clearly his thing, and I’m all for people doing their thing. So you go, Frenkel. And while you do that, hopefully some of the people who read this book come away with a better understanding of what it might mean to love math, even if they don’t quite share that feeling themselves.