Love and Math
By Edward Frenkel
Basic Books, New York, NY, 2013
You’ve probably seen those late night TV ads for Zumba or P90X or a dozen other fitness programs. Ever notice how everyone in those ads already looks slim, sculpted & sexy? And you think, “As if!” As if any of these people would ever need this or that program.
Well Love and Math: The Heart of Hidden Reality is a little like Zumba for math. The author, Edward Frenkel, tries to convey the breadth and beauty of modern mathematics to a general audience, even people who just plain hate math. It’s a valiant attempt, but if you don’t already love math, and haven’t already studied some pretty advanced math, this book is unlikely to win your heart.
I do have an undergraduate background in math and so some of the material in the early chapters was familiar to me. I could build on that knowledge to follow the story through the middle chapters. But I got lost around the halfway point and just started skimming through the technical details.
It’s not a bad book; it’s just that Frenkel is trying to explain some really advanced, abstract concepts and in order to understand them you need to build up a foundation of knowledge.
Think of it this way: Pretty much all the math you learned in school, up to about 10th grade, was known to the ancient Greeks 2,500 years ago. If you studied calculus in high school or university your mathematical knowledge took a giant leap forward to the late 1600’s. The math used to describe Einstein’s theory of relativity was actually developed back in the mid-1800s. Well, Frenkel tries to bring you right up to date, exploring mathematical developments into the last decades of the 20th Century.
The mathematical heart of the book focuses around the Langlands program, which some call the Grand Unified Theory of mathematics. This program is a coordinated research effort started by Robert Langlands at Princeton University involving several generations of mathematicians around the world. They are seeking the underlying connections between seemingly disparate areas of mathematics.
I won’t attempt to describe the math in detail because I really didn’t understand a lot of it, but here’s a small example. Take a look at this equation which Frenkel uses throughout the book:
We’re trying to solve the equation. For example, the integers x = 1 and y = -1 are a solution. Plug in those numbers and the equality holds true. So is x = 0 and y = 0. If you plotted the integer solutions to this equation on a graph they would form a set of disconnected points, like mountain peaks poking up through the clouds.
Not all the solutions are integers. The equation also has solutions that are fractions, or what mathematicians call real numbers. If you plot all the real number solutions they might form a curve like a ridge line running along mountain tops.
Taking this example just one more step, the equation also has solutions in the complex number field. Complex numbers involve the square root of -1. Plotting all the complex number solutions yields a surface, like the contour map of a mountain range.
They look different, yet these integers, real numbers and complex numbers are all solutions to the same equation, just like the peaks, ridges, and slopes are all part of the same mountain range.
OK, that’s a really simplified example of what the Langlands program and much of Frenkel’s career are all about. They’re trying to find the underlying structures which unify entire branches of mathematics.
* * *
Love and Math is actually a two-part journey, part mathematical, part autobiographical. The autobiographical journey is much easier to follow.
Edward Frenkel was born in Russia in 1968 and grew up in a small town about 70 miles from Moscow. He was denied entrance to the Soviet Union’s pre-eminent mathematics program at Moscow State University because he is Jewish. So he attended a second tier university whose admission policies were less discriminatory. Nonetheless he attracted the attention of some of the leading mathematicians of the day and managed to publish a couple of noteworthy papers.
In early 1989, at the age of 21, he was awarded a Harvard fellowship. He has lived in the US ever since and today he’s a professor of mathematics at UC Berkeley.
Had he been allowed to develop as a mathematician in the Soviet Union, and later Russia, allowed to study and teach and research, he would have brought knowledge, leadership and prestige to his university and country. Instead, Berkeley and the United States have been the main beneficiaries.
Frenkel faced discrimination because of his religion. In other places, people are discriminated against because of their race, gender, sexual orientation or whatever difference the local majority finds objectionable. The result is always the same. Not only does the discriminated minority suffer, but the majority, denying themselves the full participation and contribution of the minority, is worse off too.
While the mathematics may be difficult to follow, what does come through loud and clear in Love and Math is the utter self-defeating stupidity of discrimination.