Career Path

I was born in Los Angeles, California, USA in 1976. For my schooling, I attended Temple Emanuel preschool, Hawthorne Elementary School, Beverly Hills High School, California Institute of Technology (BS, Applied Mathematics, 1998), and Cornell University (PhD, Center for Applied Mathematics, 2002). I then was a postdoctoral scholar in the School of Mathematics at Georgia Tech (with a semester away at MSRI in Berkeley), with an affiliation with the nonlinear-science group in the School of Physics, and then a postdoctoral scholar in the Center for the Physics of Information at Caltech. In fall 2007, I joined University of Oxford as a University Lecturer (i.e., a junior faculty member) in the Mathematical Institute. I became a full professor in 2014 and moved to UCLA (in my home town!) in 2016.

When I started my frosh year at Caltech, I thought that I was going to major in computer science and eventually earn a PhD in computer graphics and work with computer games. I had decided in elementary school that I was going to do this. However, at Caltech, I soon discovered — despite my love of games and my associated interests — that I was much better at mathematics than at computer science. As a frosh, I even had considerable trouble with an elementary computer-science course. (It seemed like it was easy for other people, but it certainly wasn’t easy for me!) I eventually dropped the course (it’s the only course that I ever dropped) and decided to major in applied mathematics, which at Caltech is a separate department from mathematics. Many professional researchers in applied mathematics start out in theoretical mathematics (at least for their undergraduate degree) and then become more applied at some point. Many other researchers in applied mathematics start out in the sciences (such as in physics) and become interested in more theoretical questions. In my case, unusually for a research mathematician in the US, all of my degrees are in applied mathematics (from programs that were in engineering divisions). It’s surprising that my road to applied mathematics — which seems to me to be the most direct road — is actually unusual in the US. This road is common in other places, such as in the UK.

My road to a professorship has been mostly straightforward, with (of course) my share of good luck and privilege. I think that I’ve experienced fewer obstacles than many other people, although I have faced several challenges. Almost all paths to a university professorship — no matter how straight and narrow they may seem — have nontrivial challenges. One of my notable challenges is that my PhD thesis advisor didn’t treat me properly, and we had a falling out and were no longer on speaking terms within about a year after I graduated. After starting my first postdoctoral position, I could no longer get any reference letters from him, and apparently it is rare to apply for faculty jobs without a reference letter from one’s PhD advisor. However, I got past this situation, received helpful advice and good mentorship from several people, and now am the beneficiary of survivorship bias.

Research Interests and Mentorship

My initial interest in nonlinear systems arose from visual enjoyment, especially of bright colors and complicated patterns. Some of my childhood sketches reflect these tastes (see Fig. 1). (These sketches were also influenced by things that I saw during my migraine headaches, for those of you who study such things and are wondering.) In high school, these tastes led to an interest in fractals when I found about them. However, in college, I discovered that what really fascinated me was trying to understand (1) the mechanisms that can produce such interesting patterns and (2) the real-life and human-made systems that create them. Since then, my research interests have branched out into many fields of science that one study using dynamical systems and other methods.

Figure 1. Two pictures that I drew on index cards when I was about 6–8 years old.
(It’s no wonder that I developed an interest in nonlinear systems.)

I am interested in numerous mathematical and scientific phenomena, and I am always looking for new research topics to try. More or less, I am doing a weighted random walk through problem space. Topics that I have studied (with more than 200 papers so far) include quantum chaos (on which I did my PhD thesis), classical billiard systems, Bose–Einstein condensates, granular crystals, granular networks, social networks, plankton dynamics, coupled oscillators, cow synchronization (for real!), punctuation time series, financial networks, multilayer networks, network clustering, spreading processes on networks, opinion dynamics, topological data analysis, and many others. Many of these topics include dynamics and/or networks, and the “Snowbird” applied dynamical-systems conference is what I consider to be my home conference (see Fig. 2). It’s a great community of people and topics. I even still interact regularly with several people who I met at my first Snowbird conference in 1999.

Figure 2. Mason and several of his mentees having dinner at the Snowbird conference in 2019.

I am especially motivated by mentoring junior scholars, which was the key aspect of my ambition to try to obtain a faculty position at a top PhD-granting institution. It was my direct goal to have a career as a mentor of scientists, and I was highly motivated (and occasionally bloody-minded, but in a complimentary way) to work hard (sometimes way too hard) to attain it. I am now privileged to have mentored many wonderful people, including more than a dozen postdocs, 25 completed PhD students (with several more in progress), more than 35 Master’s students, and over 100 undergraduate students. I am still looking for my first graduated PhD grandstudent. (I want grandstudents!) My students are what drive me, and they have also led me to new research topics through their discoveries. For example, my research on bounded-confidence models of opinion dynamics (which now includes many papers) started out with a project by Oxford undergraduate Flora Meng, who is the one who found out about these models and told me about them in the first place. My current emphasis on topological data analysis (TDA) also arose largely from student interests. I initially intended to do one project on TDA, but student after student kept wanting to work with me on TDA, so now I study it a lot. I have also worked with many great senior people and I have learned a lot from them, but mentoring is where my heart is and the source of my keenest scientific joys.

I have managed to get through almost this entire article without saying many concrete things about my research itself, but that is what my website is for. If you are interested in research details, you can find my scholarly works at my “boring, professional webpage” (https://www.math.ucla.edu/~mason/), as my mentor Predrag Cvitanovic’ once encouraged me to create. The website that it replaced had many bright colors. :)

I love academia and science, though of course the academic, mathematical, and scientific communities have their share of problems. I hope that some of my mentoring and other efforts have helped improve things, and I heartily look forward both to my mentees’ exciting research and to the ways in which they will improve the mathematical and scientific communities. I want my mentees to continue to do excellent mentorship and research, be warm and kind-hearted, and not take any crap from anyone.