Dr. Jameson Graber Shares About Earning an NSF CAREER Award

April 19, 2022

My mathematical journey began quite early on. I don’t remember a time when I didn’t love mathematics. That love was never exclusive. When I was little, it often went hand in hand with an interest in physics. As a teenager, I began to have more of an appreciation for the liberal arts, especially philosophy and, later on, economics. Mathematics remained for me the most attractive because of its complete transparency: if I wanted to know why something was true, I could prove it.

I completed my B.S. at Washington and Lee, a small liberal arts school, majoring in mathematics and physics. I am grateful to have had a broad and rigorous introduction to various academic disciplines in college, and I still believe it is a good model for the university. Nevertheless, by the time I began my Ph.D. studies at the University of Virginia, I was prepared to pursue “pure” mathematics, since what enthralled me most was the beauty of abstract theorems rather than the messy particulars of “real world” problems. Thus, my present day affiliation with “applied” mathematics might seem surprising. Let me explain.

To begin with, “pure” and “applied” mathematics are not well-defined concepts. In graduate school, my first love was the abstract world of functional analysis, through which I was soon introduced to partial differential equations (PDEs). Yet PDEs, as it turns out, typically fall under “applied mathematics.” This seems to be especially true in France, where I did my first post-doc after completing my Ph.D. By the time I took that job, I had unwittingly become an “applied mathematician,” even though my primary interest in proving abstract theorems had never changed in the slightest.

At the same time, it was in France that my other intellectual interests began to converge with my mathematical career. In college I had begun reading a lot about economics and politics, mostly from a layman’s perspective. In France I discovered “mean field game theory,” which meant that I could now study PDEs directly related to economic and political questions. This confluence of personal and professional interests was exciting, and I was lucky to get in near the ground floor of this newly emerging branch of mathematics.

Ever since, most of my work has been devoted to mean field games. I do this research primarily because of how cool the math problems are, but I also enjoy explaining how relevant it is. Imagine a bunch of people are invited to a party; they all want to know how many people are going before they accept the invitation, but that depends on how many will end up accepting—this is a mean field game! We see these sorts of “games” all the time—in the global economy, in our political systems, even in city traffic.

I have embraced the label “applied mathematician” for a few reasons, but one in particular stands out: I’m interested in how mathematics can contribute to discussions of social issues. How we address these issues always depends on some theory of why social structures exist. Mathematics can, among other things, check the internal logical consistency of these theories, sometimes with surprising results. Thus I argued in my recently successful NSF CAREER grant proposal, which will fund five years of my ongoing research. While most of my work is indeed technical and difficult to explain to non-experts, I try to keep this core message as the guiding theme.

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