Arlie Petters is the Benjamin Powell Professor and Professor of Mathematics, Physics, and Business Administration at Duke University. He has done ground-breaking work in the mathematics and physics of gravitational lensing. Petters also serves as Chairman of the Council of Science Advisers to the Prime Minister of Belize and has received numerous awards and honors.
Prof. Petters, you have by any standards achieved outstanding academic success. You hold an endowed chair and have joint appointments in mathematics, physics, and business at a top research university — Duke. You have received numerous awards, prizes, and honors and have an outstanding research and publication record. Yet if you go back to the early part of your life in the 1960s and 70s, your prospects did not look quite so promising. Born in Belize, transplanted to America, what were those early days like for you? Looking back, do you see any seeds planted in your life that could help explain your future success?
Oh boy, those were humble times—the toilet was an outhouse, we had no running water, baking was done on a fire hearth, etc. Things improved when my mother immigrated to the U.S.A. and she sent money and parcels for us back in Belize. During that time, I was raised by my grandparents, who, by the way, were not educated beyond elementary school. Probably due to the humility of the time, I spent extended periods in our little yard staring at how ants march along, at the beauty in the patterns of leaves and flowers. I remember being captivated by the grand cloudscapes in our tropical skies. At night, the few lamp posts in the town created little light pollution, allowing for a breathtaking view of millions of stars sparkling across the dark sky. It was precisely these encounters with the grandness of nature and its penetrating beauty that stirred my curiosity and gripped me deep within. Interestingly, I also had a similar experience in high school with the mystery and beauty that permeated the subjects of mathematics and physics. These deep experiences were what set me on the path to become a mathematical physicist.
And, perhaps, the most important observation that fortified me internally was that I realized this grand reality is there for all of us to access, rich or poor. No one had any special privileges to it. We are all in the same boat in the face of the mystery of existence!
You did your undergraduate at Hunter College. How significant was your experience there? How well did your high school education prepare you for Hunter? Did you thrive there from the get-go or did you first have to get some “leveling” work out of the way? It’s obvious that you must have done extremely well at Hunter since it served as a springboard to graduate work at MIT. How well did Hunter prepare you for MIT. What was the crucial transition in your education when you realized, “Hey, I can do this. I’ve got a future here”?
I attended Ecumenical High School in Belize and Canarsie High School in Brooklyn. They gave me a fantastic grounding for college (I was an Arista student). Hunter was an educational turning point. I recall it to be a vibrant, intellectually diverse melting pot! I felt like the sky was the limit. In fact, from those childhood days in Belize, I had the constant encouragement and nurturing of my grandparents and the constant reminder that no one innately has any extra privileges to existence. So, even though I came from “the Third World,” I never allowed any subtle assaults on my intellectual abilities to infect my psyche. Someone may try to squeeze the confidence out of me, but I always resiliently expanded right back out like a stress ball!
What I loved about Hunter is that they allowed me, as an undergraduate, to enroll simultaneously in a B.A./M.A. program in mathematics and B.A. program in physics, both of which were paid for by a Minority Access to Research Careers fellowship and a Minority Biomedical Research Support program. I was like a kid in candy store. I gobbled it all up! And more!
Equally important, I also had excellent mentors at Hunter College—e.g., Daniel Chess, Steve Greenbaum, Bob Morino, Ed Tryon, and Jim Wyche. They were my coaches during an intellectually formative period.
Could you describe your graduate education at MIT? What role did it play in your intellectual and scientific development? You have appointments in mathematics and physics. How much of each discipline did you study at MIT — were you more on the math or physics side? Was your entire graduate education at MIT or did you also do some of your graduate studies elsewhere? How did your graduate work lay the foundations for your main current research, which is in gravitational lensing?
From my college days, I was struck with the interdisciplinary bug. So when MIT’s acceptance letter said that they would tailor my Ph.D. program to allow a simultaneous exploration of mathematics and physics through a mathematical physics concentration, I was sold! To add icing on the cake, after two years of course work and the passing of my General Exam, MIT allowed me to complete my thesis research at Princeton via an exchange scholar program. I had the benefit of being trained by both institutions during my graduate school years.
At Princeton, I was introduced to the astrophysics of gravitational lensing by my thesis advisor there, David Spergel (astronomer). My MIT advisor, Bertram Kostant (mathematician), then guided me on mathematical matters. It was during graduate school that I started developing a mathematical theory of gravitational lensing.
What is gravitational lensing and why is it important? Briefly, what is the history of the field? What have been your key conceptual breakthroughs in it? You have written and are also in the process of writing some texts in this area. How are these impacting the field?
In a nutshell, gravitational lensing is the action of gravity on light, analogous to how a glass lens deflects light. The phenomenon made Einstein a household name in 1919 when his prediction for how much the sun’s gravity will bend light from background stars was confirmed. I’ll share two examples of my contributions to the subject. I developed a mathematical theory of lensing by solving a series of challenging theoretical problems in the subject. The resulting mathematical theory brought an innovative conceptual framework for handling generic properties of lens systems, which are universal features that are independent of choice of lens models; provided new analytical techniques for solving some key problems about image counting and lensing behavior near caustics; and produced theorems that gave insights into complex scenarios like multi-plane lensing that could not be penetrated using physical intuition. For example, the work can be applied to determine the presence of dark matter substructures in galaxies. Another example of my contribution was in a joint paper with the astronomer Keeton at Rutgers. We developed a theory of gravitational lensing by microscopic braneworld black holes that gives a way to test whether our universe has a 5th dimension, i.e., whether physical space has an extra dimension beyond length, width, and height.
The book “Singularity Theory and Gravitational Lensing” by myself, Levine, and Wambsganss was a tome (over 600 pages!) and is currently the main reference for the mathematical aspects of weak-deflection gravitational lensing. With co-author Werner, I am in the process of writing another monograph on lensing. This new book will be a natural continuation of the former one since it takes up strong-deflection gravitational lensing, which is lensing by the powerful gravitational fields of black holes, including supermassive black holes like those at the center of our galaxy.
You also work in the area of mathematical finance. Given your mathematics background, mastering the technical side of this field was no doubt easy for you. And yet, given that your main focus of research is in so seemingly esoteric a field as gravitational lensing, it seems rather odd that you would also work in mathematical finance, a field that is very practical and of especial interest in the current economic climate. It appears that with this work in finance you are also trying to inspire entrepreneurship in your native Belize. Please explain what’s prompting your interest in finance.
On the surface it looks strange, indeed. But mathematics is the great unifier! It is the underlying structure that links finance with stochastic gravitational lensing. For example, the probability distribution that stock prices follow is called geometric Brownian motion. This is the same distribution that appears in the cosmos for the distribution of shear in galaxy lenses. Now, that’s cool!
My interest in finance goes back over ten years. In fact, Dong and I have been working for the past few years on a textbook, “Mathematical Finance with Applications,” aimed at students who plan to take up careers in that sector. I have been testing out parts of the manuscript at Duke with undergraduates in Arts and Sciences and MBA students in the Fuqua School of Business. My approach to finance also has a mathematical-physics current in that I dissect financial models by isolating their central assumptions and conceptual building blocks, showing rigorously how their governing equations and relations are derived, and weighing critically their strengths and weaknesses.
With regards to Belize, I believe that the understanding of and facility with finance is core in any emerging economy. This can range from basics like setting up net present values for companies to the sale of carbon credits. By injecting more quantitative financial analyses and model building in the decision making process, Belize stands to benefit as it steers its economic course.
Belize, the country of your birth, is a gorgeous land. Yet its capital resources are limited and its population is small (only a third of a million). You are a celebrity there. You’ve founded a research institute there to encourage the training of budding scientists, and you are working with Duke’s business school to promote entrepreneurship and innovation not only in Belize but also in developing nations. Can you elaborate on these activities and outline your vision for transforming Belize (and the developing world more generally).
I am a strong proponent of the application of science, technology, and innovation to advancing national development. Developing nations must be unrelenting in their human capital investments. That is the core transformational tool from Third World to First World.
What advice would you give to bright young people who find themselves in circumstances similar to those of your early years? How would you encourage them to pursue a life of learning? What pitfalls do they face? What should be their incentives for pursuing academic excellence?
Absolutely never give up! Resiliency is the trait that will keep you focused on your goal as you execute in the face of challenges, even when they appear unfair. Without a doubt, you must develop your cognitive and emotional intelligences to their utmost potential. This kind of excellence is no longer an option! It is mandatory for success in our highly competitive global environment.
And, as you attain success, don’t forget where you came from! Give back to your community. Help to create excellence in the next generation. Not even the most profound mathematics and physics can quantify the vast fulfillment and meaning you would receive from giving back!