Po-Shen Loh GS ’10 is a professor of mathematics at Carnegie Mellon University, where his research studies the intersection of probability theory, combinatorics, and computer science. A former silver medalist at the International Math Olympiad (IMO), Loh became the head coach of the U.S. IMO team in 2013. In 2015, under his coaching, the team finished as the overall winner for the first time since 1994, and went on to win again in 2016, 2018, and 2019.
Loh is the lead developer of NOVID, a pandemic-response app that uses the principles of game theory and network theory to fight the spread of COVID-19 and future infectious diseases. As opposed to contact-tracing after an individual has become sick, NOVID informs its user the proximity of the spread of a disease so that they can protect themselves before becoming infected.
In a video interview, Loh spoke with The Daily Princetonian about his unique teaching style, how math instruction in America might be improved, and NOVID.
The Daily Princetonian: What are your fondest memories from your graduate school days in Fine Hall?
Po-Shen Loh: It's very inspiring to be learning in a place surrounded by some of the great people that you have read. I had a really good experience because my Ph.D. advisor [Benny Sudakov] spent an enormous amount of time building with me. Actually, we met every day. Before, I was primarily just a person who did problems. And through the course of my Ph.D., I learned how to choose what is worth working on, and then driving a whole lot of energy to beat that. There are questions that aren’t super important that would take two years to solve, so, what you should do is to figure out what are the actually important questions.
DP: Along with Steven Strogatz ’80 and Alex Kontorovich ’02, you are one of several prominent math communicators with Princeton roots. One thing that makes you three unique is that you are educators, communicators, and researchers all at the same time. How does your Princeton background shape your roles as all three?
PL: The people you named are all communicators, but we also all have some fairly serious mathematics backgrounds. Let’s take an analogy with the entertainment industry. You have some people who are singers, you have some people who are songwriters, and you have some people who are both singers and songwriters. The good thing about people who go through this Princeton route is that you get the songwriters and the singer-songwriters; the songwriter is always a part of it.
DP: How has your experience as an educator and communicator influenced how you teach math to your own children?
PL: I don’t teach math to my own children. The thing is, first of all, my wife is really good at teaching. I’m one of these people who thinks that the exact skill is less important than the ability to invent and the ability to keep working on something that's very hard for an extended period of time. I’m not one of those people who says, “Okay, let’s go drill a bunch of math concepts.” What we actually care about is that if you see some analytical tasks that you’ve never seen before, can you actually invent a new approach to it? Since that was already happening with our children, I didn’t really have to do anything, so I guess I’m lucky.
DP: People who spend their careers at places like Carnegie Mellon or Princeton tend to live in a much higher level of mathematics and physics than the general populace. Do you ever think about how the instruction of math and arithmetic at the grade school level can be improved all around America?
PL: I am completely convinced that huge numbers of people could actually become very creative mathematically, but that’s just not how they are learning. I don’t want to blame the teachers; they have a job to teach a curriculum set by someone else. I do something very different. I’m interested in helping people learn. If you see something you don't know how to do, now what? Most people don’t have experience doing that. The curriculum is focused on making sure people know how to do this and how to do that. In terms of changing the curriculum for this, I’m not entirely sure how easy it is to do in a classroom setting.
DP: With that being said, do you think that it might be a good idea to think up some alternatives for the traditional classroom setting?
PL: See, I’m a funny guy, I think that the classroom setting teaches a lot of things that are also very useful outside the curriculum, like how to talk to people and how to interact in a group. My attitude is that if you wanted to learn this mathematical creativity, you can just do that outside of the classroom, right? You can do that at home. But what you can’t do at home is to be in a room with 30 kids. Interpersonal skills are very important. Communicating in the context of math and science is also very important. So, I think there is a lot of value in the in-school experience.
DP: You’ve been a part of the university system for several decades now. Do you think the general curriculum for instructing math is due for a change in any substantial way?
PL: I think the curriculum is very good. The content is very good. My way is to adjust the teaching style. There are many teachers who actually have a lesson plan with examples they’ve prepared before class. I will come into a class and ask the students to come with all of the theory. I will just ask them, “Do you guys have any ideas about how to solve this?” It’s a very improvisational style of teaching. It’s like improv comedy, and improv comedy is all about dealing with it on the spot. The way my exams work is that I tell the students I’ll give them all the exams I’ve previously given in this class, but they will get an exam no one has seen before.
DP: Where do you see yourself 10 years from now?
PL: Nowadays, I’m working on the intersection of mathematics and public health. My immediate goal for the next five days is to make our concept we’ve invented to fight pandemics become the standard way used to control deadly pandemics for the rest of civilization. The point of the concept is not even the [NOVID] app. The important thing is the game theoretic principle upon which the app was built. If a deadly pandemic with a 50 percent fatality rate happens in my lifetime, then there is a 50 percent chance that it’ll mark the end of my lifetime! Instead of using contact tracing to stop the spread once someone has already gotten sick, the principle is to help people recognize it as the infection creeps closer to them, so that we can leverage people’s selfish behavior.
DP: Is math invented or discovered?
PL: I think it’s discovered. I think there’s a lot of concepts out there waiting for us to see how they are related to each other. If we met aliens, they probably would have many similar observations as us. For example, take the circle, if you defined ℼ through the circumference, which is 2ℼr, then why is the area of the circle also using ℼ? That’s kind of cool. Whether the aliens call it ℼ or something related, it has to be the same constant appearing in both formulas, so my point is that these kind of things will be discovered.