Whenever I go shopping, I don’t struggle too much to resist the temptation to buy a new T-shirt or a CD. However, my willpower becomes very weak in bookstores, especially in the popular science section. This time I gave in again and came home with Edward Frenkel’s “Love and Math: The Heart of Hidden Reality”.
I have to admit that I hadn’t heard about this UC Berkeley professor before. My level of ignorance must have been unbelievably high because how could one miss a scientist starring nude in the film he co-directed?! His movie “Rites of Love and Math” told a story of a mathematician who found the mathematical formula for love. As Nobel realised that his ground-breaking discovery might cause harm, the main character of Frenkel’s film wants to keep his idea in secret. He decides to tattoo it on his lover’s body.
Like the film, Frenkel’s book is aimed at non-mathematicians. His goal was to show the beauty of mathematics to people who never had a chance to discover anything beyond basic calculus. He focused on describing the problem he’s been working on for over a decade: the Langlands program. This idea, known also as the Grand Unified Theory of mathematics, was proposed by Robert Langlands in 1967 in the letter to André Weil. He suggested how to find connections between many fields of mathematics and physics that seemed to be unrelated before.
I devoured first chapters in one evening. There is more than maths in this book; Frenkel described his childhood and studies in the USRR. I wasn’t aware that Jewish last name could prevent such a genius from studying mathematics at the university. It did. We learn how he discovered the beauty of maths, having been “converted” – he wasn’t very fond of this subject at school. His narration is intertwined with clear descriptions of somewhat complicated mathematical ideas such as symmetry, definitely understandable to anyone.
I also liked the idea of extended annotations to each chapter. In some cases the author makes a brief statement and explains the topic further for those interested, so I was able to read the proofs that could scare a non-mathematician. Also, not every idea was relevant to the main topic but I’m glad that Frenkel included some curiosities in the annotations.
The author is able to use surprising analogies and examples. For instance, he wanted to show that scientists sometimes reduce dimensions in the problems they analyse. It would make sense if we wanted to describe the movement of a cup served by a stewardess in a moving plane. From an outside observer’s point of view, it doesn’t matter what exactly the stewardess’ arm is doing because the plain movement dominates it completely.
This book had a big potential. However, the second part disappointed me. The author seems to be so fascinated by the Langlands program that he forgot who he was writing for. In my opinion Frenkel completely failed to make his explanations clear even to mathematicians, not to mention laypeople. At least he lost me – and I’m familiar with most of the concepts he introduced. In order to understand last chapters, I would have to read some heavy textbooks, dig into scientific papers and spend hours on Stack Exchange. It is not too encouraging for readers without any mathematical background.
To sum up, I believe that the idea of “Love and Math” was interesting. I would recommend reading first half of it – but better skip the second part unless you’re an expert in Galois groups, Abelian class field theory, Frobenius automorphisms, conformal field theory… All of them. However, I’ll give Frenkel the second chance and if he ever publishes a new popular science book, I’ll read it. In the name of Love… and Math.