Mathematician Edward Frenkel of the University of California–Berkeley wants to expose the beauty of mathematics, inspire awe at its power, and challenge his colleagues to wield it for good. His new book is Love and Math: The Heart of Hidden Reality.
What is wrong with the way most of us are introduced to math?
The way mathematics is taught is akin to an art class in which students are only taught how to paint a fence and are never shown the paintings of the great masters. When, later on in life, the subject of mathematics comes up, most people wave their hands and say, "Oh no, I don't want to hear about this, I was so bad at math." What they are really saying is, "I was bad at painting the fence."
So what is it really like to be a mathematician?
You don't discover something beautiful every day. Most of the time, you work on something for weeks or months, only to realize that it doesn't work. But you never give up, you go back and try to analyze the data that you have, and try to see the analogies and connections to try to come up with a new hypothesis. Then you try to test that.
What is the ultimate goal of all these efforts?
Another analogy is solving a jigsaw puzzle. Imagine that somebody gives you a puzzle, but they don't give you the box, just the pieces. You take those different pieces and try to put them together to create something of value, something beautiful and powerful. You can think of mathematics as the grand project of building this enormous jigsaw puzzle, with different groups of people working on different parts. Then, every once in a while, somebody finds a bridge between two parts, a way to assemble pieces together so that big chunks of the puzzle connect.
You work on the Langlands program, which aims to discover those connections. Why do we need them?
From the outside, mathematics might look like one big lump. In fact, it is a huge subject that has many different subfields: algebra, number theory, analysis, geometry, and so on. In the world of mathematics, they look like disconnected continents. But the Langlands program connects different fields and, by doing so, tells us something about the unity of mathematics. It offers a glimpse of something beneath the surface that we don't understand.
It also reveals links between abstract math and the structures in physics. Could the entire universe be based on math?
I believe that physical reality as we know it and the world of mathematical ideas are two separate worlds, and neither can subjugate the other. For example, we talk about the standard model of physics, which has been very successful in predicting a whole range of phenomena. Of course, the discovery of the Higgs boson last summer was a big trial for the standard model. But from a mathematical perspective, it is just one of a tremendous class of models. We don't observe the others in our reality, but do they exist? Well, one can argue that they do in the ideal world of mathematics.
How well does this ideal world connect to our real, physical universe?
Sometimes you have some beautiful mathematics which comes out of the real world. We all know the story of Newton, an apple falling on his head. But another possibility is that within the narrative of mathematics, he discovered something about the real world. So, there is a sort of back-and-forth connection between the two. Neither controls the other. I think that the way to make progress in physics is to use this connection, to use experiments, but also to use the awesome powers that mathematics gives us to come up with new ideas. And that, I think, is a good illustration of this subtle interplay between the physical and the mathematical worlds.
You were fascinated by math and quantum physics from an early age. How did growing up in Soviet Russia influence your pursuits?
By the time I was 16 years old, I was very passionate about mathematics. Just a couple of years earlier there was someone in my life, a professional mathematician, who opened the world of mathematics to me, this magic, beautiful universe. He did for me what I now hope to do for other people with my book.
But then there was a seemingly insurmountable obstacle. Because of some absolutely stupid policies of anti-Semitism, I was not accepted into university. The doors were closed in front of me.