Translation. Region: Russian Federation –
Source: Peoples'Friendship University of Russia
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Professor Daria Apushkinskaya of the S. M. Nikolsky Institute of Mathematics at RUDN University has had a long career in science. Today, she teaches mathematical analysis, differential equations, and introduction to mathematical modeling at our university, and also serves as chief research fellow at the "Mathematics for Promising Young People" scientific development center.
In her work with students, she draws on the experience gained over years of studying and teaching in various countries and the traditions of the legendary Leningrad School of Mathematics. Her students achieve excellent results in international competitions. In 2025, they took second and third place in the International Mathematics Competition, and this year, at the Olympiad in Bukhara, they won two gold, one silver, and three bronze medals. In honor of Mentor Day in Russia, we're sharing more about Daria Evgenyevna.
First mentor
Daria Evgenyevna considers three people to be her main mentors in mathematics. The first is her schoolteacher, Valentina Aleksandrovna Pivanova.
"She taught me from fourth to eighth grade. And I'm incredibly grateful to her for one day, at a regional pedagogical meeting, she approached the director of the correspondence mathematics school at Leningrad University and asked her to send me an invitation to that very school," says Daria Apushkinskaya.
The invitation arrived, the entrance problems were solved, and then came an invitation to the Leningrad State University summer mathematics school. From there, the path led to boarding school No. 45—one of four schools founded by the eminent mathematician Andrei Kolmogorov. After that, according to the professor, admission to the Faculty of Mathematics and Mechanics at St. Petersburg State University was quite easy.
At the Faculty of Mathematics and Mechanics of St. Petersburg State University, which Darya Evgenyevna graduated with honors in 1990, her mentor was Professor Nina Nikolaevna Uraltseva.
"I came to her in my third year, wrote my coursework in my third and fourth years, then wrote my thesis under her supervision and defended my PhD dissertation. And then we began working together; she was my doctoral dissertation advisor. And our collaboration continues to this day, despite Nina Nikolaevna turning 92 this year. We published our last joint paper in early 2025," says Daria Apushkinskaya.
She also names her “scientific grandmother,” Nina Nikolaevna’s supervisor, Olga Aleksandrovna Ladyzhenskaya, as her “mentor.”
Reflecting on what these great women taught her, Darya Evgenievna says: "First, the best way to deal with all the problems that arise in life is work. This is truly true, and it has actually saved me during difficult turning points in my life. They also taught me not to be afraid to argue, not to be afraid to defend my opinion. If you're sure you have to fight, then fight."
The teachers also instilled in them a love of problem solving. According to Daria Evgenyevna, their inexhaustible interest in mathematics, even at an advanced age, keeps them on their toes.
The value of postdocs and international experience
From 1996 to 2000, Daria Evgenievna worked as a postdoc at the Australian National University, the Mittag-Leffler Institute in Stockholm, and the Research Institute of Mathematics and Mechanics at St. Petersburg State University. Since 2001, she has been at the University of Saarland in Germany. She believes that the postdoc system is crucial for the development of young scientists.
"This system was devised so that someone who grew up under the influence of their academic advisor and followed their lead could, by moving for a while to another country, another university, another scientific school, escape their influence a little and try to prove themselves independently. This experience, in addition to new knowledge, also provides new connections and contacts. Knowing how to survive in a new country is a very useful skill when you arrive with just one suitcase, which you still need to pack properly. Everything around you is new, you have to start practically from scratch – this spurres you on and mobilizes your body's strength," says Daria Apushkinskaya.
In her opinion, despite the difficulties, we should now strive to send students to other universities for postdocs and to accept interested candidates. This broadens a young scientist's horizons and connections.
International experience also helps in her work with RUDN students, as Daria Evgenievna has become familiar with various educational traditions.
"This allows me to take a little bit of what's good from each system. To diversify exams in some places. For example, Germany had a wonderful system of surprise tests. I sometimes use it. Or a combination exam, consisting of two parts: a written part, which tests one aspect of your understanding of the material, and an oral presentation. When you see different educational systems, you can always borrow something good, something interesting, and thereby enrich your own," says Daria Apushkinskaya.
Find and support talent
While teaching at the RUDN University Mathematics Institute, Daria Evgenievna has the opportunity to observe students "at the entrance."
"If, during an exam or a conversation, I sense that someone might succeed, I usually suggest they try participating in some kind of competition. It's clear who's better suited to Olympiads, who's better suited to an industrial project. Some might find working with schoolchildren more interesting. Everyone is different, and I don't have a set formula. I observe and encourage them to try. It's a completely experimental activity, a testing ground," says Daria Apushkinskaya.
In case of failure, Darya Evgenievna tries to support: “We wipe away tears, I calm them down, I say that this is not the last competition, there will be more.”
At the same time, she emphasizes that she is demanding of those who undertake the work.
"If someone takes on something, it's best if they do it to the fullest extent of their abilities. If they decide to attend a club, they go, and don't make excuses like they overslept or the weather isn't right. If they come to work on a project, you want them to work regularly," says Daria Apushkinskaya.
The main thing is to have interest. Answering the question about professional secrets, Daria Evgenievna draws an unexpected parallel.
"I work according to the principles of a German swimming club. By a twist of fate, I ended up a licensed swimming judge and for many years accompanied a youth swimming team to competitions in Germany. When it came to building the Olympic movement, I tried to model it after a sports club: we have free admission—anyone can come to a class, there are no special tests. The main thing is interest," says Daria Apushkinskaya.
All competitions are divided into several groups: open to everyone (a kind of showcase), more rigorous selection (where she consults with coaches and nominates participants), and those where the organizers make the selection themselves. The formats of the classes also vary: explanations of new material, complementing lectures and seminars; selection tests before major Olympiads, to observe young people and discover new stars.
"We're always experimenting. And I'm really excited about our young coaches, former Olympic athletes, who are sometimes playing coaches, and sometimes have matured enough to be coaches only. We're constantly trying new formats, new methods, different organizations. It's all a living organism. We try it, it's successful, and then we implement it. If not, we try again. Basically, it's a trial and error process," says Daria Apushkinskaya.
Daria Evgenievna considers participation in Olympiads, especially distance and international ones, to be an excellent tool for developing soft skills and digital literacy.
"Digital literacy is when students are forced to contact the organizers themselves, set up the system, and contact them if there's a problem. And soft skills… There's this wonderful thing about Olympiads called appeals. You have to prove the jury was wrong. This is where you develop your ability to convincingly convey your point, while trying to keep within your boundaries, remembering that you're representing a university and a country. Sometimes you have to do this in English, which isn't your native language," says Daria Apushkinskaya.
In addition, team competitions teach teamwork, distribution of tasks, and the captain to feel like a leader.
"Choosing a team captain is always a painful process, especially if you're fielding multiple teams. The ability to perhaps put aside some personal ambitions and collaborate effectively toward a common goal is a useful skill for the future," says Daria Apushkinskaya.
About students in Russia and Europe
Answering a question about differences between students, Daria Evgenievna notes that good students are the same everywhere, but the differences are visible at the level of weak ones.
"In Europe, for example, in Germany, students are expelled more harshly. If you have a course in mathematical analysis, on average, 40% of the original class survives after the exam and re-examination. There's also a rule: if you fail an exam three times, you can't study that subject again in Germany. This teaches students to take exams more seriously. European students are a little more responsible, but it must be acknowledged that they're older on average—20-21 years old, compared to 17-18 in our country. Simply because of their greater life experience, they take their education a little more seriously," says Daria Apushkinskaya.
Olympic Preparation Today Preparing students for international competitions is always challenging, and approaches change little. However, Daria Evgenievna notices a trend.
"Recently, there's been a significant bias toward linear algebra and combinatorics, which I don't think is right. When organizing our competitions, we try to cover a full range of mathematical disciplines. Otherwise, our approach doesn't change much. We have a rough idea of what the problems might cover. Five problems on the first day, five on the second. It's a bit like ski wax: if we guess right, we don't. If we guess right, the result is slightly better; if we don't, the result is worse. Something like that," says Daria Apushkinskaya.
When asked what she considers to be the main result of her work, Daria Evgenievna answers:
"I'd say: a person who's found their place in life. A person who's found their calling. Mathematics is vast, and I try to suggest to someone where they should try, what area of mathematics to pursue, if they ask such a question," says Daria Apushkinskaya.
She also considers success when a student is "dragged off to their firm" by the examination committee after defending their bachelor's thesis. Or when a student comes up with a solution to a complex problem or successfully defends their dissertation. But there's another, special outcome.
"I think it's really important for the students to develop a sense of camaraderie and a sense of belonging that will support them even after they graduate. When our older students get together, cook dinner, and discuss their goals—I think it's wonderful. We've helped people bond. We've helped them build a team, a collective," says Daria Apushkinskaya.
And he adds that the success of a mentor lies in students who go further than him.
"I really love how our senior Olympiad participants come up with absolutely wonderful ideas. A competition like 'Integra' (the integration competition) was entirely our students' idea and their implementation. We constantly receive feedback on how to better organize training sessions and what else we can do with the club. The students already know how to do it, better than I do. This is probably the most important result of our work—that our students go further and become better than us," says Daria Apushkinskaya.
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