Love and Math: The Heart of Hidden Reality in Science and Inquiry

Sep 27, 2016 David Rubenstein rated it liked it

Shelves: memoirs, mathematics

I wanted so much to love this book, but it was difficult. About half of the book is about Frenkel's life; and it was fascinating. The other half, interleaved with his memoirs, are descriptions of Frenkel's mathematical work and discoveries. I had a great deal of trouble following the descriptions of the math. I am superficially familiar with many of the concepts, but it just gets more and more complex. Toward the end, especially, I became quite confused.

Frenkel grew up in a small town in the Sov I wanted so much to love this book, but it was difficult. About half of the book is about Frenkel's life; and it was fascinating. The other half, interleaved with his memoirs, are descriptions of Frenkel's mathematical work and discoveries. I had a great deal of trouble following the descriptions of the math. I am superficially familiar with many of the concepts, but it just gets more and more complex. Toward the end, especially, I became quite confused.

Frenkel grew up in a small town in the Soviet Union, a two-hour train ride from Moscow. Initially interested in physics, Frenkel's father introduced him to a mentor who showed him how modern physics, especially quantum mechanics, relies on some very modern concepts in mathematics. In that way, Frenkel got hooked on math.

When he was in high school, starting to think about college, Frenkel applied to the math department at Moscow State University. It was explained to him that he had no chance of being admitted. He had a Jewish last name, and anti-Semitism would prevent his admission. Frenkel applied for admission anyway, and he was grilled mercilessly during an oral entrance exam. The examiners found excuses to refuse him admission.

So, Frenkel went to undergraduate school at a different college, one that did not discriminate so much. Nevertheless, he attended lectures and seminars at Moscow State University. He didn't have a college ID, so he scaled the fence to get in! The Soviets put tight controls on photocopiers. While in undergraduate school, his research papers were secretly copied and smuggled out, and reached mathematicians around the world. One day, Frenkel received an invitation from the president of Harvard University to come to Harvard on a fellowship grant, and become an assistant professor. At that point in time, he didn't even have a PhD!

What I did get out of the math descriptions, is the inner beauty of math. Vastly different areas of math can be connected, through hidden connections, as if by magic. This attracted Frenkel to the Langlands Program, a grand unified theory of mathematics. Now a vast subject, the program tries to connect number theory, harmonic analysis, geometry, representation theory, and mathematical physics. Riemann geometry is the cornerstone of Einstein's Theory of General Relativity. It contains hidden connections with number theory. Frenkel's career goal is to establish connections between the dualities in physics and the dualities in mathematics.

In the last chapter, Frenkel spent a sabbatical in France, writing and producing a short film. He also co-stars in the film, titled Rites of Love and Math. The trailer is on a site on YouTube.com. In this allegorical film, a mathematician discovers a mathematical formula for love. He realizes the formula's importance, and that it could be used for good as well as for evil. He tattoos the formula on his lover's body. The film was screened at many film festivals to wide acclaim, but also received a lot of controversy.

You can read the book and skim or skip through the math. Frenkel does a good job of describing the hidden connections and beauty of math. But he leaves the average reader lost in the details. ...more

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