Edward Frenkel, a mathematics professor at the University of California, Berkeley, has emerged in recent years as a high-profile celebrator and explainer of mathematics. His book “Love and Math” (Basic Books, 2013) was a New York Times bestseller, which is particularly impressive considering that the book delves into such abstract topics as “the Langlands Program,” an effort to uncover hidden links among diverse branches of math.
Frenkel, who recently started a website edwardfrenkel.com, is a passionate proponent of better math education and communication. Math-centered technologies such as 3D printing are making math increasingly central to society, he emphasizes, and governments and businesses use math in many ways that affect people's lives, for example in inflation calculations that play into public and private benefits and contracts.
The global financial crisis, Frenkel argues, was sparked in substantial part by improper use of mathematical models by financial institutions. More generally, in his view, financial professionals and clients alike have much to gain by taking a greater interest in math—and much to lose by not doing so.
I asked Frenkel to discuss some intersections of finance and math in an email interview, which appears in slightly edited form below.
Research: You wrote in “Love and Math” that “the global economic crisis was caused to a large degree by the widespread use of inadequate mathematical models in the financial markets.” Do you see signs that lessons have been learned, in how the models are constructed or used?
Edward Frenkel: Surely, people are now more aware of the dangers of misuse of mathematical models. But memories tend to fade away, so I am afraid we will go through such calamities again and again, unless major structural changes are made. One [thing] that troubles me is this extraordinary gap between those who create mathematical models (the so-called “quants”) and the decision makers. It is clear that in the past many of the decision makers didn't fully understand those models, nor did they try to understand. I think the attitude was “as long as the models work and we make profit, we’ll be fine” rather than “let's find out what these models are actually doing.” And that's very dangerous: Mathematics is a powerful weapon that can be used for good and for ill.
The film “Margin Call” provides a good reference point for this phenomenon; the higher up the executives, the less they know about these models. “I don't get any of this stuff,” they say, with defiance and pride. This creates a disaster for their firm and the financial markets. The person who sounds the alarm is the one who understands math, but his bosses don't pay attention until it's too late. And then, after the crash, those decision makers were blaming the “quants.” How convenient!
Are we going to learn from this lesson? Are we going to reduce this gap? There are many other urgent issues that need to be addressed, but this one is very important, in my opinion.
Are you worried about a brain drain, in which the financial sector draws mathematical talent away from other fields?
I don't know about the “other fields,” but I can speak about the “brain drain” of mathematical talent from academia. I am very worried about the cause of this drain, which in my view is the general deterioration of our higher education. There are fewer and fewer well-paid jobs available, and there is less freedom and more politics in academia, especially around the job decisions (often, by the time a person reaches tenure, he or she has been put through such a grinder that they can hardly remember why they got there in the first place). No wonder that, seeing all this, many bright Ph.D.s decide to abandon academia and search for more exciting and higher paid endeavors elsewhere. Let's create better conditions for self-fulfillment and higher paid jobs in academia, and then more of them will stay.
What are some math concepts or techniques you’d like financial advisors to know more about, and why?
I think what's really important is not a particular method or technique, but just a general awareness of what mathematics is about. I realize that this is very difficult, given the sorry state of affairs in our math education. The way mathematics is taught at schools today is akin to an art class in which they teach you only how to paint a fence or a wall, but never show you van Gogh or Picasso.
It's important for all of us to realize that mathematics is a much bigger and more fascinating subject than we have been led to believe. Especially today, when our lives are controlled more and more by mathematical formulas and algorithms. This applies to all of us, but especially to the financial advisors who are on the forefront of this brave new world.
There are of course some concrete concepts and techniques [the learning of] which can be beneficial. But what's even more important, I think, is general curiosity and absence of fear of math. For example, “Fibonacci retracement” is a widely used method of technical analysis. One can just keep blindly using the formula, or one can ask: What does this formula mean? I bet if you know what it means, you’ll be able to use it more wisely.
How can clients use math to get better results in dealing with financial services companies?
Again, I believe that just a general awareness of mathematics is very important. Would someone with a rudimentary knowledge of mathematical statistics ever invest in a questionable Madoff-style “scheme” knowing that it reported the same percentage of profit year after year? I doubt it. Unfortunately, the prevalent attitude today is “math is too hard, I won't get it.” The reason I wrote my book “Love and Math” was precisely to open the doors to this subject for everyone. To demystify it and at the same time show how beautiful it is.
Will math be even more important in the future to understanding the economy and financial markets?
Absolutely. The tendency has been more and more math in more and more areas. But especially our economy and financial markets are now becoming dependent on more and more sophisticated mathematics. It's our destiny. We should utilize the awesome powers of math, but also take responsibility to avoid any abuse of this power. It's not mathematical models that lead to crises; it's the humans who misuse these models.