'Mathematics Is So Fascinating That I Never Ask Myself Whether It Will Be Useful in Life’
In an interview, Sania Pushkar, a member of the first graduating class of the Faculty of Mathematics, talks about why she loves math, what she’s up to now, and what she’ll remember most about studying in the Faculty of Mathematics at HSE University.
How did you fall in love with mathematics?
This is not difficult for a person who grew up in a family where everyone holds a degree in Mathematics. I have memories from my childhood about trying to guess the number of rice grains in a tin or calculate an optimal route to the nearest metro station. And, of course, the amazing lessons we had at home. For instance, my grandfather’s sister Elena Kozlova is the author of a math book for kids ‘Tales and Clues’. She also taught us some math. This is what she would do: she would tell us a bit from Pushkin’s ‘The Tale of Tsar Saltan’ and show us the Princess-Swan painting by Mikhail Vrubel to go with the tale. Then she would give us a problem in which the Princess-Swan wanted the number of water lilies in the pond to double, and the question would be: When did the pond get half-filled with water lilies if it was fully filled on day 12. With lessons like that, how could we not fall in love with mathematics? But then again, when your family members are such talented teachers, you can fall in love with any discipline.
But frankly, I think the word ‘mathematics’ you used in your question sounds different to me, someone who has recently earned a degree in mathematics, than it sounds to the professors who taught me. School- and university-level mathematics lead to different mathematical constructions and exercises for understanding them. The average time it takes to complete such an exercise is several minutes, but in mathematical science, solving a problem takes months or years of painstaking labor, which will not necessarily yield a positive result. It is one thing to be addicted to that sense of gratification you get from solving a problem—this is how it was for me—and it is an entirely different thing to be so passionate about mathematics that you want to spend years of your working time trying to work out a solution to a problem. I never developed this kind of passion; I was only fortunate enough to witness it.
I believe that much of my love of mathematics has to do with its structure and consistency. I was lucky that back in my school years, I was given an answer to the question: ‘Why do I need to know so many seemingly unrelated mathematical concepts?’ The teacher outlined for me a certain inner structure of mathematics and its applicability to other disciplines, and then I decided I wanted to learn it and fell in love with it.
How did you end up at the Faculty of Mathematics?
My story with the Faculty of Mathematics started when I was admitted there during my last year of high school, but then I changed my mind. It was 2008, the department was in its early years, I was young and got a bit scared. Instead, I enrolled in the Department of Mechanics and Mathematics at Moscow State University. When mid-term exams ended, I got bored, so I went to visit my favorite classmate and friend Vlada Kazantseva at the new mysterious Faculty of Mathematics of HSE. I remember that literally after the first lecture I was texting my parents letting them know that I was transferring to HSE. And that's how it all worked out.
I was both lucky that I changed my mind just in time and that I had participated in an Olympiad to enter the Mathematics Department and got admitted. I was also lucky that I had been brought up in the classical mathematical tradition, in the broadest sense, in all its beauty. It was only much later that I understood that it is a unique phenomenon to see people, who were able to fully dedicate themselves to this kind of labour with great results and work with such dedication to bring up a new generation.
What stood out most for you during your studies? Did you have any favorite professors?
During my student years, the Faculty of Mathematics was entirely different from the way it is now, as I understand. In my first year, for example, we were cooped up in three lecture halls in Myasnitskaya Street; we had, perhaps, eight professors, being a group of twenty five students. For me, this period was the most memorable one. Everything felt like home: our classes, the time between classes, and the students. Alexey Nikolaevich Rudakov gave us tangerines when we gave correct answers to his questions about the sliding rule, and we would often run to the basement-level cafeteria to buy HSE’s famous pastries, which are now a thing of the past.
To me, the Mathematics Faculty for bachelor’s students is a romantic gathering place for young people who share a passion about a certain subject, which is, perhaps, rather vague, but definitely has nothing to do with any career aspirations. This goes especially for the very first students of the tiny faculty. This is something that I remember well, since back in those days, there was no promise of future glory, no ratings, graduate admissions, huge grants, or summer schools. All this came later.
My classmates were the kindest and most pleasant people, and the general vibe was very supportive. They were not the most ambitious people I’ve ever known, but they were really involved. I think now that I would enjoy teaching them math.
As a side note about our course and competitiveness: my classmate, Denis Shishkin, has just become a professor of economics at the University of San Diego in California. He is perhaps the first faculty alum to become a professor. There are only a handful of graduates of my year left at HSE, excellent researchers and teachers: for example, Nina Sakharova and Inna Mashanova. They all were taught by someone and learned to teach that heroic group of people of the Mathematics Department back in 2008—2009.
We heard a lot of stories of students choosing the field of mathematics for their term paper, thesis, or even future academic career because of an outstanding lecturer in this particular subject. Basically, that was never the case for the Faculty of Mathematics. You could choose everything based on your preferences.
What did you do after graduation? And why did you choose the field that you did?
Halfway into my bachelor’s programme, I already knew that pure mathematics was not what I really wanted to do. But I knew that if I used the technical skills taught I gained at the Faculty of Mathematics, the sky would be my limit in whatever areas I wanted to devote myself to. However, I was unable to choose a particular field. I was reading books on neurobiology, microbiology, algorithms, anthropology…I can’t seem to remember it all now. I was torn. Then, as advised by Vladlen Timorin, my academic research supervisor, I submitted an application to a doctoral programme in applied mathematics. This was a really valuable piece of advice, and I’m glad I followed it. Since then, I’ve been working in various fields, where I equally needed my bachelor’s degree in mathematics and my master’s degree in applied mathematics.
I wanted to go study at a university abroad. Choosing where to go was complicated. Finally, I found myself enrolled at a department that offered the most diverse curriculum. Out of the universities where I was admitted, I felt that the University of Maryland had the most to offer. I decided not to go to Cornell University. The University of Maryland is a place undervalued by people in Moscow. There are a lot of research institutes there, offering a vibrant applied mathematics environment. All the professors were highly engaging, and the those who graduate from the programme go on to have fascinating careers in the field all over the country there. I follow their work with a great deal of interest.
Selecting a particular application field was no easy feat. When I was a student of the Faculty of Mathematics, we were offered a programming module or two, there was no minors system in place yet, no practice of enrolling for courses offered by other departments, and there was no Faculty of Computer Science yet. So, I really had to learn a lot of applied stuff to figure out what I could do and how. But once I was at the University of Maryland, I was lucky to take a course in complex systems and a seminar on applied dynamic systems. The seminar dealt with topics such as, for example, animal movement models, bird flocking or fish schooling behavior, i.e., simple elegant examples in which a mathematical model is used to help figure out what is going on. This kind of research was the field I really wanted to be in.
In actual fact, what I was doing was not far from what they were doing in the Faculty of Mathematics. My academic research supervisor was Michelle Girvan, a co-author of Edward Ott, one of the authors of chaos theory, which is a perfectly mathematical field. But I was engaged with a rather experimental task: explosive percolation in graphs. This provided a model for gene networks. It was an interesting and beautiful task: it turns out, chaos provides a plausible explanation of how things in a cell can go increasingly wrong due to some local mutations. Therefore, this was the subject of natural selection. I spent most of my time simulating evolution and conducting experimental research (i.e., in a mathematical laboratory) to validate the hypotheses related to it. But I also had a chance to have a look at the human gene networks data and try to apply my theoretical knowledge in this area.
What kind of research are you doing right now? Who do you collaborate with?
Generally, I did not specialize in any particular area. If possible, this is how I would like to continue. I would say that right now my main focus of interest is data-driven matters, and the bulk of my work deals with data analysis and simulation.
Let me tell you a few words about some of the projects I’m working on. There was a period of time at Rutgers University, when I was dealing with evolution of certain types of proteins. To put it in a nutshell, every protein is a sequence of amino acids, i.e., literally a set of points in 3-dimensional space. Biology research scientists are able to scan proteins and obtain relatively accurate coordinates of these points. The task my laboratory was handling boiled down to trying to figure out how similar these sets of points were for various proteins and how the process of evolution could unfold, based on such knowledge. This was a compelling task, which introduced me to a world of microbiological disciplines, some of them very technical. Well, I never thought that after school, I would ever refer to a 3-dimensional (solid) angle in serious discourse.
I’m currently working at a laboratory at Northwestern University, and what I’m doing now is already driven by my own interests. Being able to decide for myself what tasks pique my interest is an important milestone for me. I hope everyone can have this ability in their life.
I’m working with data obtained from pictorial arts, with the information one could gather when looking at a picture. This may shed some light on the author’s individual style. I’m part of the group led by Lois Amaral, and I’m feeling privileged to be a member of the team. This is a shining example of a place where people are inspired by their own interests, and they therefore enjoy working on their projects. The laboratory implements projects in linguistics, psychology, biology, and sociology: any field where you need to know your subject matter well and be able to apply analytical methods to find answers to your questions.
What do you like most about your research?
That would be primarily my freedom of choice. However, it is quite possible that there are also non-science related jobs that have the same quality.
In the eight years that have passed from the day I completed my bachelor’s programme, I have worked at four universities (the only one not mentioned here is Brown University). It’s important to me that it is my conscious choice to continue working in academia. The benefits of academic work are fairly obvious to those who have studied at a university, including freedom, beauty, the search for truth, not to mention the honor.
But academic work has its challenges, too, which are not usually discussed with those who have only just embarked upon this path. This is the race for publishing, which sometimes really negatively impacts results, or the culture of exploiting young scientists. We should hope that one day, this will change for the better. Let me say that not all of this necessarily happened in mathematics departments; however, these problems are not solely characteristic of other fields.
What are your plans for the future?
I'd like to have some time to think about a lot of things, to try going deeper into various areas of applied mathematics. Honestly, I'd like to study more.
What advice would you give to our applicants, students, and graduates?
I have not just advice, but rather something that I would have liked to formulate for myself earlier. This is about how mathematics can unwittingly lead to dissonance when you want to know something outside of it, and how I prefer to deal with it.
Mathematics is an old discipline. The latest of what we study in schools and in required courses that are part of the bachelor’s programme was discovered about a hundred years ago, and let those who know correct me if I’m wrong. Reading contemporary articles on mathematics is very difficult and in most cases, such articles may only be understood by experts in a specific area of knowledge. This is what makes the difference between mathematics and many other sciences or disciplines that are currently enjoying wide popularity such as economics, sociology, biology, linguistics, psychology, political science, and ecology. The questions these fields are trying to provide answers to are normally discussed in everyday life. But the theory behind these matters is commonly unknown, for these subjects evolve too quickly compared to mathematics, and also because of the mindset that specialized literature is too hard to understand. These disciplines are much more recent, and driven by the currently available technologies; they enjoy great progress every year, with new knowledge and new analysis mechanisms being accumulated. Their novelty does not mean they are unimportant or hard to understand. Works by Nobel Prize winners are incorporated into new textbooks even at the bachelor’s level.
I would like to advise everyone with a background in mathematics to use the skills they gain at the Faculty of Mathematics to keep abreast of other disciplines and areas of knowledge that you are interested in, whatever your desired level of knowledge may be, even if your only objective is being able to engage in online disputes on the subject. For this, you only need to develop the skill of finding solid sources, reading academic articles and critically approaching what you have read. Since we enjoy the privilege of being able to do it, our responsibility is not to become hostages of our propensity to simply validate our views.
Mathematics is so fascinating that I never ask myself whether it will be useful in life. I think we should change the question a little: rather, how exactly can we use it to bring maximum benefit for ourselves, others, and science?
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