Ivan Bortnovskyi

BIG Scholar 2024 | IMO Medalist

Major and Institution
Mathematics at Churchill College, University of Cambridge
Achievements
IMO Bronze 2023
Country
Ukraine
One Aspiration
To explore mathematical physics
Hobbies
Observing deep sky objects through a telescope
Ivan Bortnovskyi

BIG Scholar 2024 | IMO Medalist

Ivan likes the structured nature of math, particularly algebra and number theory because they involve applying standard methods. He is eager to explore topics like math analysis and topology at university. An amateur student of the cosmos, he likes the sense of discovery he gets when observing planetary nebulae and galaxies through his 20 cc telescope.
We caught up before he started university (interview edited for length and clarity):
GTF: How's your summer going, and what have you been up to?

IB: Quite all right. I'm finally relaxing from the exams that finished in June. It's finally maybe the year where I do not have any Olympiads or tournaments or summer camps where I need to prepare. So, like I am left completely by myself and I can maybe enjoy my hobbies and try new things.

GTF: What are your hobbies outside of mathematics?

IB: My main hobby is astronomy, specifically amateur astronomy. Back in Kharkiv I used to have a 20 cc telescope and I tried to watch for deep sky objects, planets, and any other stuff. I have a list of very dim and small objects like a planetary nebula in Pegasus or the other galaxy in Fiscus. They are not generally well known, but they have interest within amateur astronomy circles.

I also watch for meteor showers or just try to estimate the brightness of some variable stars. Every new object that I see through my telescope is like a small discovery, although it was seen and photographed by many people before. I have been quite interested in astronomy since middle school. So I was just enjoying watching some kind of astronomy films and reading some random stuff about planets and stars.

And then when I first got a small telescope, I started actually practicing astronomy, observing different objects, improving my skills. Gradually, I felt like the first telescope was not enough to observe the number of different objects because the higher the diameter of the telescopes, the dimmer objects you can see and therefore like the bigger number of objects you can observe.

So, I got the bigger telescope that I talked about. Eventually, it became my main hobby and at some point I even bought a solar film, with which I was able to observe some solar spots on the sun.

GTF: How long have you been participating in Math Olympiads, and how has your approach changed over time?

IB: I think that I started participating in Math Olympiads since fifth or sixth grade. It all started with regional competitions where I managed to get bronze or silver medals. Then I was invited to a very popular set of math circles in our city, where we had both theory and practice lectures, solving Olympic problems.

Over time, I began attending summer camps where we spent two or three weeks of intense study, which eventually led to international competitions. Compared to my early participation, I’ve become more calm and confident when entering Olympiads, though I still get anxious at national or regional levels because anything can go wrong, and I might not qualify for the next stage. With more experience, I’ve learned to expect what comes at each particular stage.

GTF: What keeps you interested in Math Olympiads, and do you have a favorite topic?

IB: I just enjoy math and how well it’s structured. Unlike learning a language, there aren’t weird exceptions or illogical rules. My favorite topics are algebra and number theory because they involve applying standard methods.

I don’t really like combinatorics because it’s less about knowing methods or theorems and more about coming up with ideas. I’m not sure that’s something you can train. Some people can, but I don’t like it as much.

Recently, I’ve found myself less interested in competition and more in learning math for enjoyment rather than competing. The stakes are always high in Olympiads, and I know some of my friends have also gotten tired of the competition.

GTF: How are you feeling about starting university? Are there any specific topics you're looking forward to exploring?

IB: I’m excited about university life because I think it will finally be the place where I can study the math topics that I really enjoy. For the last two years, I’ve been studying in a UK high school, and while the program is different from Ukrainian math lessons, it still involved a lot of repetition. The math exams often just follow known algorithms, where they change the numbers and you substitute them into calculators. It can get quite boring, especially by A-levels.

In terms of what I’m looking forward to, I already have some favorite topics, like math analysis and topology. A few of my friends and I have learned parts of this theory in a small group, and I really enjoyed it from the first lessons. I’m also interested in exploring mathematical physics since I was involved in physics tournaments for about four or five years. I don’t want to give up physics, and I think mathematical physics could be a way to connect the two subjects.

GTF: You also participate in physics competitions, do you see any connection between how you approach math and physics?

IB: I’ve been involved in physics tournaments for quite a while, though not in the Physics Olympiad. I did participate in some city and regional competitions. The main difference between a tournament and an Olympiad is that in tournaments, you’re given about 17 problems to work on over three or four months. You have to explore them, conduct experiments, write theory, and prepare a presentation. In the tournament, you then present your work and defend your methods, kind of like in a physics fight or similar to math tournaments, where you have an opponent, reviewer, and reporter.

In physics, people often ignore certain strictness in proofs that are crucial in math. For example, in the physics tournaments, we were using differential equations and integration without fully understanding them or deriving them properly. In physics, many things are simplified or ignored, like frictional forces, because if you accounted for everything, the equations would be unsolvable. So, the methods mathematicians and physicists use to solve problems can be quite different.

GTF: What advice would you give to someone starting out in Math Olympiads?

IB: Practice more and do not expect that a miracle will come up in the next Olympiad you participate in. It’s possible to devote a lot of time but not be successful. Just continue and don’t give up.