Giovanni Leoni is a Professor of Mathematics at Carnegie Mellon University. He received both his Ph.D. and Masters in Math from the University of Minnesota. Today, he explores the calculus of variations, along with partial differential equations and geometric measure theory. In 2001, Leoni won the Premio Giuseppe Bartolozzi award from the Italian Mathematical Society. This award is given to the best Italian mathematician under age 34.
What events in your life have contributed to where you are today with your career? How would you describe your interaction with math during high school?
I grew up in a small rich town in Italy. My family owned a cheese shop, which, for the standards of my city, was not cool. I was the bookish type and shy. I spent all my time reading fantasy books, and I always felt like I did not belong. My dream was to leave. I was fascinated by the United States. I don’t know why. During high school and college, I did part-time jobs and saved enough money to pay for a summer program to study English in the US. I went for a month in a college in Olympia, in Washington state.
It was a beautiful experience. The sense of freedom, meeting students from different cultures, realizing that the rules of ”normal” behavior where I grew up were not universally accepted, the breathtaking nature in the state of Washington and Canada changed my life. So at the end of college, I decided to apply for a Ph.D. in the United States.
In high school, I loved math and not just math but also any subject that used logical thinking. This included Latin (translating to and from), chemistry (balancing chemical reactions), technical drawing. It was like a complicated game where you had to understand the rules and apply them. I was also lucky to have incredible math teachers. That made a huge difference.
Please describe your specific field of study and what it is that sparked your interest.
I work in the calculus of variations. The calculus of variations is a branch of analysis that studies extrema and critical points of functionals (or energies). A functional is a mapping from a function space (for example, the space of continuous functions or the space of differentiable functions)
to the real numbers. What I liked about it is that it has beautiful applications from physics, materials science, engineering, and computer science.
In your list of papers, you have collaborated many mathematicians across multiple institutions. How do these groups form and what are particular moments from these collaborations that you cherish?
Typically, you go to a conference, and some of the talks are particularly intriguing or closely related to what you are doing. So you start talking with the speaker, and sometimes you click. By that, I mean that you either find a common problem that you are both interested in or just like the person and decide to work together. Then there are your Ph.D. students and postdoctoral fellows. You continue to work with some of them after they leave your institution.
What is it like to attend a mathematics conference?
Ha! You sit for many hours listening to boring talks. But then one out of ten of those talks turned out to be fascinating either because the speaker is impressive or the problem is amazing. That makes it worth it. After a few years, it becomes a way to see your friends who live all over the world. And there is the traveling part. You see different countries and cultures. You get to visit beautiful places and try new foods.
What advice would you offer to youth today looking into pursuing mathematics?
If you are in the US, start reading math books. Sadly, the way calculus is taught in many high schools takes away the beauty of math. It is too much like a cookbook where you follow recipes without understanding the theory behind it. So take a serious book in analysis or algebra with a lot of proofs and start reading it. It will be difficult but worth it.