This interview, with a graduate student in Ukraine, was conducted by Mark Saul on 17 February 2024. It speaks for itself.

Questions: Let’s start with you. Where did you grow up? Go to School?

I have always lived in Kyiv. I found my love for mathematics early, and went to a special mathematics school here. I then got a master’s degree in mathematics, and am now a Ph.D. student at the Institute of Mathematics at the National Academy of Sciences of Ukraine here.

I discovered mathematics as a child, through reading books on extra-curricular mathematics. Games and puzzles. And now one of my jobs is creating such puzzles. The mathematics we studied in school was easy for me.

I remember my father explaining to me what a fractal was. He did it by asking me what the measurement was of the coastline of Great Britain. The more finely you measure a coastline, the longer it gets.

In seventh grade, I participated in a team math competition. It’s a contest between two teams. The teams are given a list of questions, and must challenge each other to present solutions. It was my turn to present for my team, up at a blackboard. I had to calculate the length of a diagonal of a rectangle with sides 3 and 4. This may seem too simple to us now, but at the time I didn’t know the Pythagorean Theorem. Nor did my opponents. But I did remember seeing a Youtube video about 3,4,5 triangles. So I was able to present a solution, and became a hero for my team.

Question: What role has mathematics played in your life?

Mathematics has always played a central role. It helped me to find a boyfriend, the love of my life. We connected through mathematics. And of course now I make my living doing mathematics. I am working on the development of a Museum of Mathematics here in Kyiv.

Question: Talk a bit more about this museum.

It’s a big project. We are planning numerous exhibits. I am the main content consultant for the project. It was they who found me, because they knew of my enthusiasm for the subject.

I now have three jobs. I teach courses for the institute: Calculus, Linear Algebra and Introduction to Mathematics for the Kyiv School of Economics. But my main job is for the Junior Academy of Sciences in Ukraine. This is my work on the museum of mathematics. Also I do a lot of face-to-face work with pre-college students. Mostly in high school. I try to make the work interesting. It’s mostly extra-curricular work, of the sort that first attracted me to mathematics.

Question: So some of your work now is with school age children growing up in a war-torn country. What role do you think mathematics—or your work in mathematics–plays in their lives?

Students have to live with the war. For my students, school is not all that interesting. It’s easy for them. My courses help students to not to worry about tragic events in lives. I help them to focus on interesting mathematics instead. And also it helps me. I like to give positive energy to kids, and they return it to me. We help each other.

I conduct my courses in Zoom. Sometimes there are air raid sirens. We stop the lectures. I tell them to go to shelters. They can’t listen to me while missiles are flying. It’s not much fun.

I also teach calculus in the Kyiv School of Economics. Lectures are on-site, and we have air raid shelters nearby. It’s actually made somewhat comfortable to teach there, even during an air raid. We just go to our shelter classroom, two floors underground. There are no windows. Only walls, chairs, and a whiteboard. We continue our studies, but it is difficult to concentrate on the mathematics when we know that missiles are flying. We are constantly checking the news to see what is happening.

I am happy to be in Kyiv, because it’s relatively secure here. It’s a lot harder in other cities. And we have many students here who come from cities which have been destroyed. Some of these students have lost their homes or their families. When air raids begin, they may have panic attacks. We get training in how to stabilize their psychological situation.

I often meet with my Ph.D. supervisor. We discuss graph theory, but sometimes we stop and think: “Why are we doing this now? There’s a war going on. Why are we characterizing different sets of vertices while people are fighting for us?” It can get a bit depressing.

Question: What are some of answers to “Why are we doing this?”

We are in our own place, and we make all we can of our situation. Of course we help our soldiers. There’s a big volunteer network in Ukraine. Every tenth person is volunteering for the war effort. We collect money and buy things for our soldiers. We also help support migrants from other towns. We don’t do the fighting, but we do our jobs. We continue our research. And we help our soldiers as much as we can.

Mathematics calms me down. Why do we do mathematics? At the moment we don’t know why. But maybe someone will use it, eventually. Mathematics is like an art. I feel like I’m painting a picture. This must be yellow, and here must be red and there green. It comes from the heart. Our study appeared out of nowhere. It was one simple problem for a math circle, and we generalized it.

My mother doesn’t understand why I chose mathematics seven years ago, or what I’m actually doing. What are these mathematical problems? They don’t seem to have any application. Better for you to go to work in a store.

But I know that I have mathematical intuition. My supervisor saw it and helped me to find my way, to find my topic where I can use my mathematical power. In this way I build a little bit of graph theory with my theorems and propositions. I feel like I’m connected with something great. At the moment we don’t know why are we doing this, but in 200 years someone will use our research. Mathematics is big, big, strong thing, and I’m connected with this big strong thing.

Question: Do you impart any of these feelings to the kids?

Well, it’s very much the same thing for kids. The same motivations. These students don’t get enough math in school. They get a little, but they want more. They want to see the whole picture.

I invite them with words like “You don’t meet these ideas in school. Here’s something different and interesting in math.” They get internal motivation to learn something new, and they understand that math is not boring and simple.

I ran a course on mathematical logic two years ago. I had seven students. But I found that people all around Ukraine are interested in mathematics. Now I have more than 100 students in my courses. It makes me happy and proud. I look forward to the feedback at the end of the course, because I know that students enjoy it. They find that mathematics is useful, and also beautiful.

Question: As a student, did you have exposure to this sort of extra-curricular mathematics?

My school mathematics teacher and his colleagues organized a cultural exchanges with a German ‘gymnazia’ for talented students. We traveled to Germany, lived there and attended a math camp for a week. Every day we solved problems and learned mathematical topics. We had three such exchanges. They were fascinating. Motivating and eye-opening.

Question: What do you learn from your students?

In my course on mathematical logic, I start with set theory. In teaching a certain proposition about sets I asked a student: Why do you think the proposition is true?” One girl gave an interesting answer, using the contrapositive of the statement, which we were not scheduled to discuss for five more days. Students often think differently. I like to give homework which requires them to write out their answers. Not short answer questions. It takes a lot of time. But I see how they think and admire their intelligence.

Doing mathematics in wartime presents its own difficulties. We don’t have much support from the government, which is busy prosecuting the war. Sometimes I feel as if I’m playing in the orchestra while the Titanic is sinking. We don’t have opportunities for cultural exchanges. We cannot even travel inside the country. Train schedules are irregular and if there is an air raid there’s no place to hide. So people try not to travel.

Here in Kyiv we have it good. But on other regions, closer to the border with Russia, they don’t have regular water or electricity. We in the capital are relatively safe from that.

Mathematics gives me strength. It’s the mainstay of my life. If I didn’t have mathematics, I don’t what I would do. It’s this idea that my world is connected with something great. The war is present now, but mathematics is eternal. The war cannot affect it. We cannot say that Euler was right in 1736, but now he is wrong.

(At this point in our discussion the electricity went out. Katya and I finished our conversation in the dark. She later sent me a reassuring email message. There were no bombs, and she and her family were safe. The lights came back about an hour after our conversation.)

AFTERWORD

In the spring of 2022, I (Mark Saul) was working with Tatiana Shubin and other American mathematicians of Ukrainian origin. Hearing of the horrors of war in Ukraine, we decided to do what they could do best to help out—bring mathematics to Ukrainian teachers and students.

We had been working on a similar program for Native American youth, called the Bluebird Math Circle, and thought that an adaptation of the materials we had been developing might also serve the Ukrainian audience.

Within a few months, we made contact with the Ukrainian Junior Academy of Sciences, and through them with a number of teachers and educators in Ukraine. We started the Sunflower Bluebird Math Circle, a program for teachers offering unusual or advanced mathematics that the teachers could use with their students.

The structure was designed to reach as many students as possible. Teachers participated in a Zoom math circle session. Materials for each session were sent to the Ukrainian group in advance and Katia did an excellent job translating everything into Ukrainian. She was also doing synchronic translation at the Zoom meetings to help teachers whose English wasn’t strong enough. After a session, teachers tried out the materials with their students. They created videos and recorded feedback. Two weeks later, they shared their experiences.

But this description does little to describe the true nature of the program. The circumstances under which teachers work are terrible. Wifi and electricity sometimes fail, and even heating of indoor spaces cannot be relied on. Sometimes teachers tuned in from ‘warmup centers’, places around Ukraine where people can be warm and have access to wifi. And pretty often some teachers had to log off in order to go to a bomb shelter. It was heart wrenching for us to hear siren wailing and a teacher saying apologetically and calmly, “Sorry, there’s an air raid warning, I have to go but will check the rest of the session online when possible.”

Despite all these hardships, the teachers who attend find energy, enthusiasm, and sheer will power to do the best for their students. What they are doing is far beyond what is expected in their profession. They want to use mathematics to bring joy to the lives of their students, students who otherwise had little joy in their lives these days.

Teachers tune in from all over Ukraine, from cities, towns and small villages. Some teach in elementary school and others in high school or college. The world has heard about the heroism and bravery of the soldiers in Ukraine, but these teachers are brave heroes in their own right.