Faculty Profile: Dr. Peter Nandori

By: Raquel Leifer  |  November 2, 2022
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By Raquel Leifer, Features Editor

Each month, the YU Observer aims to highlight a YU faculty member. For the October 2022 edition, the YU Observer is highlighting Dr. Peter Nandori, PhD. 

RL: Please introduce yourself.

PN: Hi! I was born and raised in Hungary. I got my PhD in mathematics from the Technical University of Budapest. I moved to the U.S. right after graduation, which was nine years ago. I worked as a Courant Instructor at NYU for two years and another four years at the University of Maryland as a Brin Fellow before coming to YU.

RL: How long have you worked at YU?

PN: A little more than three years.

RL: What do you like most about working at YU?

PN: I like being in the classroom because my students are curious, hardworking and take their studies seriously. It is a real honor to be part of some of their most important years. I also like the fact that the classroom sizes are relatively small, and I get to know my students better. I used to teach classes of 200+ students at other universities, which was very far from optimal for both students and professors.

RL: What made you passionate about your field?

PN: As a young student, I liked mathematics, physics, and computer science. Perhaps I was also inspired by the fact that my parents taught similar topics, namely physics and geometry at an engineering school. I chose to pursue mathematics because it seemed the purest of all. You do not need a lab or even a computer to pursue mathematics. The only thing you need is your imagination.

RL: Is there anything interesting you are currently working on?

PN: A general area of mathematics that I work on is dynamical systems. One specific system that I study a lot is mathematical billiards. These billiards are similar to the usual billiard game, except that the shape of the billiard table can be very different; perhaps even infinite. They can be studied just for fun but are also of interest in statistical mechanics, where people try to derive macroscopic laws of physics, such as the heat equations, from microscopic models of heat conductions; a simple one being billiards. In a joint work with Xingyu Liu, a math PhD student at the Katz school, we are studying the long flight in high dimensional billiards. For example, consider a space of at least three dimensions and cut out periodically situated identical non-overlapping spheres. What is left is our billiard table. A frictionless particle may fly for a very long time if its velocity vector happens to point in the direction of an infinite chamber inside the table. We are trying to prove that if a very long flight takes time T, then typically the next flight is of length T to the power 1/the dimension of the billiard table.

RL: Do you have any advice for students interested in a career in your field?

PN: Most students know about the engineering face of mathematics. What I mean by this, is that both in high school and in introductory college math classes, students mostly see formulas that are useful for a particular set of problems, often engineering applications. It is important to realize that mathematics is much more than that. For example, mathematics can be viewed as an art- many mathematical objects have truly spectacular beauty. It is also a philosophical field, most notably mathematical logic. I truly believe that nearly anyone could benefit from taking mathematical classes beyond the required ones as if you have not seen art and philosophy in math yet, you are missing real beauty. Another comment is that mastering the strict logical arguments in mathematics is invaluable in many professions way beyond math, such as law, politics, sciences and even music. For students who have already decided to study mathematics, my first message is that they chose well. Then, please stay curious and patient. Sometimes it takes hours to read one page of a graduate level book but it is well worth it. Hard work always pays off.

RL: What makes your field special?

PN: Mathematics has its roots in axioms: statements that we all accept. These are usually very simple, one example being the existence of the empty set. Anything beyond axioms has to be derived from the axioms only using strict formal rules of logic. The fact that everything is very objective distinguishes mathematics from many other scientific disciplines. If we prove  something new, that will remain valid forever and cannot be overwritten by fancier results in the future. Another specialty of mathematics is the diversity of its applications. For example, I teach probability theory and statistics. It is hard to overestimate the importance of these subjects in our modern world in computer science, machine learning, economics, physics, biology, etc.

RL: If you could bring in any guest lecturer, alive or deceased, who would it be, and what would they speak about?

PN: Hillel Furstenberg, a prominent mathematician who is a YU alumnus. He was awarded the Abel Prize, which is informally known as the Nobel Prize of mathematics (note that there is no actual Nobel Prize in mathematics). YU students should be proud of his achievements, and I believe that he can serve as a role model for everyone. He already produced genuine mathematical proofs as an undergraduate student at YU (for example, a topological proof of the fact that there are infinitely many prime numbers). He gave a lecture at YU about five years ago, but this was before my time and so I was not there.

RL: What is one thing you want students to know about you?

PN: I am happy to chat with anyone at any time about the beauty of mathematics. You can just stop by my office if you want to talk. I hope that my students know this, so this is a message mostly for those students that I have not met yet.

RL: Is there a particular book you would recommend that everyone read?

PN: I personally find studying the life of famous mathematicians fascinating. I used to read about them a lot when I was a student but nowadays I have less time for that. I encourage everyone to look up the stories of, for example, Srinivasa Ramanujan and John von Neumann. If you don’t have time, just look them up on Wikipedia, but of course there are more in-depth books.

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