When visiting the Curie Museum in Paris this May, I became aware that much of Marie Curie’s later work was devoted to the medical uses of radiation. Here was one of the most brilliant scientists of all time, two-time nobel prize winner, with a clear view towards the applications of her theoretical work. While I had heard of her interests in nuclear medicine before, I was fascinated to see on display in the museum early devices used to treat cancer with radiation.

I was raised on a diet of pure mathematics; as a graduate student, even the hint of applications was enough to dissuade me from further studying a topic. This might explain my early fascination with mathematical logic and the foundations of mathematics.  As I matured as a mathematician, I came to truly realize the power of applications in my own work. This was especially true in my research on real-world complex networks like the web graph. The web graph has nodes consisting of web pages, and edges corresponding to links between pages. The link structure of the web was a strong driver of Google’s early PageRank. Complex networks include the web graph and many other networks such as Facebook or protein networks in a living cell. Several of my papers and one of my books focuses on the theory of complex networks, which has evolved into a rich discipline over the last 15 years.

What I re-discovered around 2001 or so, (indeed, a fact which many generations of mathematicians knew before me) is that the study of real-world phenomena often give rise to major new directions in mathematical theory. Random graph models are a good example. Before complex networks, random graph theory focused on a few beautiful but non-realistic models. Now there are dozens of random graph models which match very well observed properties of complex networks. New models are still popping up, and many require new tools to analyze rigorously. Most of these models would not exist if it were not for the applications that drove their design.

Ryerson’s coat of arms made me think about the intersections of pure and applied mathematics:

The motto “Mente et Artificio”  translates from Latin as “With Mind and Skill.” Someone recently presented me with a modified translation: “Mind and Action.”  Ryerson itself focuses on innovation, which I view broadly not just as commercial innovation, but the innovation of ideas. Madame Curie herself would approve!

Anthony Bonato