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Princeton University’s valedictorian for the Class of 2023 is Aleksa Milojević, a mathematics major from Belgrade, Serbia, who has focused on combinatorics while at Princeton and has already written three papers. In addition to earning 16 A pluses at Princeton, he has been a recipient of the Freshman First Honor Prize, the Class of 1939 Scholar Prize, and the Shapiro Prize for Academic Excellence — twice. Milojević spoke with PAW about his Princeton experience, about solving math problems no one has solved before, and about the many friendships he’ll bring with him after graduation, with classmates from around the world.
Julie Bonette: Hello, I’m Julie Bonette, writer and assistant editor for Princeton Alumni Weekly. Welcome back to the PAWcast. This is the Commencement edition. Today, I’ll be speaking with Aleksa Milojevic, the valedictorian for the Class of 2023.
Aleksa, a mathematics major from Belgrade, Serbia, has focused on combinatorics while at Princeton and has already written three papers. In addition to earning 16 A pluses at Princeton, he has been a recipient of the Freshman First Honor Prize, the Class of 1939 Scholar Prize, and the Shapiro Prize for Academic Excellence — twice. He directed the Princeton University Mathematics Competition for more than 500 high-school students and was an early inductee of Phi Beta Kappa. After graduation, he plans to pursue a PhD in combinatorics from ETH Zurich, but first he’ll deliver the valedictory address at Princeton Stadium on May 31.
Welcome, Aleksa, and thanks for joining me today.
Aleksa Milojević: Thanks for inviting me.
JB: Absolutely. So, I know your grandfather was a math teacher and your parents were engineers. Do you think you were destined for this line of study?
AM: I’m honestly not sure. I mean, especially being here at Princeton with so many different, you know, fields that I had the opportunity to explore during my undergrad, I think it was very easy for me to end up in any other field. But I guess at level of high school it started becoming obvious because I went to a specialized math high school and then I did a lot of math competitions and somehow at that point I started directing myself. But I definitely had many other passions during elementary school.
JB: If you weren’t studying math, what do you think you would be focusing on?
AM: In elementary school I had this love for history and somehow during my time here I think it combined slightly with literature. So during my time at Princeton I really enjoyed 19th-century Russian literature. And then I think I would be either like a historian of literature, I don’t know if there is such a thing, but definitely either history major or a literature major, focusing on some earlier part of the tradition, either one of these two.
JB: Hmm. What do you like most about math?
AM: About math as a science, I think it’s very precise? So you are told the rules and then you know, the rules doesn’t, don’t change through the game. There’s no, nothing’s unexpected. I think at least in terms of the proofs, you are, we always know what the proofs needs to satisfy before we can call it approved. And I think that sense of definiteness and just being clear what’s enough and what’s not enough to prove your is something very, very valuable. You’re never lost — is this enough, is this not enough? You know, we always know exactly what’s enough.
JB: And now that you’re coming to the close of your Princeton experience, when you reflect back, what stands out?
AM: So definitely many math classes, but I think I’ve heard this many times and I think it’s definitely come true that the classes that you remember the most are not the classes in your major but rather the one-off classes that you take in other departments. So I’ve taken three classes now in Russian literature, which I enjoyed very much and that’s definitely something that I’ll remember throughout.
JB: Wonderful. Tell me about some of your challenges on your Princeton journey.
AM: So definitely one of the big challenges that came early on was COVID because it hit somewhere halfway through my freshman year. And then there was some adapting obviously as everyone else did, just some time difference, being away from everyone. So that was the first challenge and then readapting back. I think given that we were here only for a couple of months, we didn’t really get a feel for campus as much as some older students did. And then it was like rediscovering it all over again during COVID and during the first semesters when we were timidly coming back to campus. And then this year when actually everything started going normally. So definitely there’s been a trajectory there.
JB: Yeah, definitely. Have you found some favorite spots here on campus?
AM: So given that I’m a math major, I really enjoyed spending time in Fine Hall. I think there is a really nice common room and a community build around it. There’s the daily math and cookies at 3:30, so I tend to go to that every day and that’s been one of the highlights, I think, for me this year.
JB: Any professors stand out?
AM: Definitely a couple of them. I think my junior paper advisor, Professor Noga Alon was very influential to my home Princeton experience because he first taught two of the classes that I took in my freshman-sophomore years. Then I did a junior paper with him my junior year and now my senior year I’ve been something like an undergraduate course assistant for two of his classes. So I think we’ve had a very, very deep relationship at least while I was here.
And then obviously my senior thesis mentor Peter Sarna, who’s also an amazing professor and an amazing inspiration, at least for me, this year to learn the topic surrounding my senior thesis and so on.
JB: I know you’ve studied a couple of different branches of math while you’ve been here. Can you tell me about that and which one’s your favorite?
AM: I think early on I started doing combinatorics perhaps because combinatorics doesn’t require you to have as much background before coming into the research. So you could essentially do research maybe after a couple of months of studying the problem as opposed to, for example, number theory, which I did later on. And even now I don’t think I’m at the level of doing research there, but I definitely think that both combinatorics and number theory are immensely interesting.
And then I think it’s good to know as many areas as you can because you never know when ideas from one field of math can be used in another. And the biggest breakthroughs I think over the decades in math have been exactly coming from that interplay between different fields and just using ideas from one field into the other and vice versa.
JB: And I understand for your thesis you kind of switched tracks a little bit. Can you tell me about that?
AM: For my thesis I did something closer to number theory and even a little bit of algebra geometry, which was completely different from what I’ve been doing for my junior paper. And I think that’s been a part of this somewhat intentional push to try to broaden out and to learn some more different areas. Because I think when one does a Ph.D. in math, people tend to specialize into one area exactly. And undergrad is pretty much the last time we had the opportunity to explore very broadly different areas without any pressure to produce papers or anything. So I think I’ve been just trying to use my undergrad for that.
JB: Nice. How valuable do you think a math major is?
AM: From Princeton? I think if one wants to do academia or wants, wants to go into academia, I think it’s very valuable precisely because of the close interactions that you can get with professors and if you step out and if you try to reach out to them, I think they’re very open to both collaborations and just mentorship. So I think that’s amazing. And then also the community here, both undergrad and grad students at the math department I think are amazing. So I think for me at least, it’s been very valuable.
JB: I’ve noticed that there’s been a little bit of a decline in math learning during the pandemic. Do you have any thoughts on how we can maybe address this gap and what is the future of the field of mathematics?
AM: I definitely agree that math is very useful. Whether one ends up doing math or doing something else, I think just the way of thinking that math develop in, in a student is very important. And I think that’s why being an educator is very important.
Now I’m not sure that they have a very valuable thoughts for how to improve math education because, in starters I don’t even know exactly how it works in the U.S. because I come from a different system and it works completely differently there. And then the other thing, I think I’m not, I don’t even have enough knowledge to say anything about how to teach kids, but I think it’s definitely very important to try to get across that way of thinking that, you know, logic and trying to argue things step by step and not just, you know, guess the answer. So I think that’s perhaps the most valuable thing even though maybe the students want to remember the exact way to solve a quadratic equation or whatever. I think at the end of the day that way of thinking is the most important one.
JB: I know you’ve started to give back with your time with young people, especially the Princeton University mathematics competition and tutoring. Tell me why that’s important to you.
AM: I think one of the big things that got me into math science in general were the competitions that I went to in high school. So I always felt indebted to these people who organized these competitions who wrote problems for them, who graded, who made all these things possible for me, who prepared me for these, who showed me actually all the problems and math behind these problems. So I really felt the need when I, once I graduated from high school, to somehow get involved on the other side because I really felt I had some debt to repay. And I feel my engagement with the PUMaC, the Princeton University Math Competition, has been at least one way to do that. The other way has been of course tutoring. I’ve been doing some tutoring both here at Princeton and back home in Serbia online during COVID and so on for people going to math competitions for high schoolers. So I think both of these have been very meaningful to me.
JB: You have lived in different parts of the world. How do you feel like that adds to your overall perspective?
AM: I think the perspective, at least for me, these four years of living in the U.S. have been amazing. I think it really broadens your perspective, especially having the opportunity to meet so many diverse people, so much diversity in the student body here at Princeton. It’s — I think it’s a unique experience. Honestly, I don’t think I would’ve experienced something like that had I stayed in Serbia and that’s why I think it’s very valuable to switch countries as often as you can, essentially. I mean I’m going for my Ph.D. to Switzerland, to Zurich, so I think that’s going to be yet another side and yet another story. So I’m really looking forward to that as well.
JB: Yeah, congratulations. That’ll be exciting.
AM: Thank you.
JB: Looking past that, what do you hope your job is in a couple of decades?
AM: Well, it’ll be very nice if I had a position in academia and if I somehow could work as a professor somewhere. But that’s definitely not the only option. I’m also open to going into industry or, I don’t really have any particular job that I am set on doing. I think I’ll just try to enjoy my work, whatever it is. And then as soon as I don’t enjoy it I’ll probably switch it up.
JB: But before then, you have a couple more days left as a Princeton student.
AM: That’s right.
JB: Tell me a little bit about what clubs or groups you’ve been involved with here, besides the ones that we’ve already mentioned.
AM: I think my freshman year I’ve been involved with the Princeton Triangle Club, the theater group here on campus. Over the years, unfortunately due to Covid, partially, I started getting less involved in that. But I think that’s been a very fun experience to, again, that’s one of the things why Princeton is so unique to me. I think because as a math major who doesn’t have any background in theater, I still had the opportunity to be a part of a theater group and help them build their set or whatever and just see how things work behind the stage. I think that was, that was a really big experience for me.
JB: Very cool. Any others that you want to mention?
AM: I don’t think I have any others which are particularly standing out, but—
JB: Sure, sure. You’re going to be delivering your address in a couple of days here. Do you have a theme for your classmates or a message that you want to send?
AM: I didn’t actually think about it cause my speech is not due for maybe a week or so, so these days it’s been a little rough for me. But apart from that, yeah, I, I think, I mean generally the message that they try to give anyone to anyone who asks for advice here at Princeton is just to make sure that they’re enjoying what they’re doing. Because I think here at Princeton it’s sometimes easy to get caught up in all the requirements that we need to do and, you know, I need to do this for that and it’ll be good for my CV if I had this requirement and that certificate, and so on. And I think if you don’t enjoy your time here at Princeton, then I don’t think it’s worth it.
JB: Hmm. But now you’re almost done.
AM: That’s right.
JB: What was your reaction to being named valedictorian?
AM: I was honestly a little surprised. I definitely didn’t expect that. I didn’t know how to react when I was told that, but definitely very happy. I think, I mean, it’s the biggest academic honor that one can get here at Princeton, so I feel incredibly lucky to have it. I think having gone through the process and everything, I realized that luck also plays a factor in me getting it, and I consider myself incredibly honored and lucky to have it.
JB: What did your family think?
AM: Oh, they were surprised and I guess very happy as well. I mean they were very proud of me, I guess.
JB: Are they going to be able to come to the ceremony?
AM: My mother and sister will come, looking forward to that.
JB: Definitely. Awesome. That’s so cool. Is there anything you do differently if you could start Princeton over again?
AM: Probably worry a little bit less about my assignments. I don’t know. Other than that, I mean, of course I’d spend more time with friends, but I think I tried that during Princeton as well. I’m not sure if I have anything else.
JB: Fair enough. I also noticed in the University article that announced you were a valedictorian, that it mentioned that you actually kind of solved problems that some of the Princeton faculty have posed here. Can you talk a little bit about that? What’s it like to kind of go toe to toe with the faculty while you’re still a student?
AM: Oh yeah, that’s been very interesting. I, I consider myself very lucky to have had the opportunity to work on that problem and to solve it in the end. So actually the way that came about is that I was a part of the undergraduate research experience in the University of Duluth, Minnesota. And my mentors were actually graduate students from Princeton who were working together with their adviser at the time. And they wrote this paper but they couldn’t complete all the questions that they had and they’ve let out some questions unanswered. And then of course with the help of some other people who gave me some inspiration, I tried looking at these questions and modifying their arguments slightly. I managed to solve it, but I think at least my argument is very much builds on their arguments and on their ideas from their paper. So I don’t think it’s any kind of like competitiveness or anything. I think it’s just collaboration to just try to answer some interesting questions in math.
JB: How has that been for you? Has it been a joy to kind of rise to that level?
AM: Oh yeah. I think doing research in math is incredible fun. I think just that feeling of not being able to solve the problem at first and you know, it’s not like a problem on the test that, you know, the teacher knows the solution, but you just have to figure it out on the test. Generally, like, no one knows the solution to this problem. No one even knows if it’s like solvable or true or anything. So just trying to find your way around it and trying to convince yourself in the first place that it is true and then later on trying to actually provide like a formal proof, I think that’s been a very rewarding process. Very, very much different from just taking a math test.
JB: What’s been your favorite memory over the course of your Princeton career?
AM: I think I mentioned some of them in the interview that I did for the valedictorian story. I think a very warm memory that I have is the first semester after we were allowed to come back on campus, the restrictions were still there and COVID was still very much a thing. But that idea that we could come together and I think that’s perhaps the semester where we did it with the most joy and with the most, I think, intention, just trying to hang out together. I mentioned the story when my friends bought me a cake for my birthday and that’s been an amazing memory for me. But also all the other times that we just came out to hang out or just take a walk because usually we couldn’t hang out in the rooms because we had restrictions on that. We were just trying to get together and finding ways to do that. I think that’s, that’s been something that definitely stuck with me during Princeton.
JB: What do you think you’ll bring with you after you leave Princeton? What lessons or memories or takeaways?
AM: I think I’ll definitely bring many more perspectives than I came in with. I think just the friends that I met. I actually met mostly international friends, so it’s, I think I know people from like 20-plus countries which are like close friends of mine. And then just being able to look at different issues from different perspectives and from different cultures, I think that’s something that I really built here at Princeton.
JB: Is there anything else that I didn’t ask you that you wanted to talk about?
AM: I don’t think so.
JB: Well Aleksa, congratulations again on all that you’ve achieved and thanks for speaking with me today.
AM: Thank you.
PAWcast is a monthly interview podcast produced by the Princeton Alumni Weekly. If you enjoyed this episode, please subscribe. You can find us on Apple Podcasts, Google Podcasts, Spotify, and Soundcloud. You can read transcripts of every episode on our website, paw.princeton.edu. Music for this podcast is licensed from Universal Production Music.