‘The Faculty of Mathematics taught us to be extremely transparent and honest’

Elena Kulakova studied mathematics and computational linguistics, worked in a bank, and now teaches algebra and geometry in the Letovo school for giften children. In this interview with Age-Mates, she spoke about her thesis on knot theory, bombshell discriminants, and why authority and money are powerless in mathematics.

Why did you decide to attend HSE University and how did you choose your major?

As a school student, I liked all the subjects. And it wasn’t until I was in the 11th grade that I realised that all my classmates already knew where they wanted to study but that I hadn’t thought about it. As a result, I applied to all the universities with drama programmes, to Moscow State University’s (MSU) faculties of physics, biology, psychology and mechanics & mathematics, as well as to the Faculty of Mathematics and Faculty of Psychology at HSE University. I was accepted everywhere except to the MSU faculties of drama and mechanics & mathematics.

For the first time at the MSU Faculty of Mechanics & Mathematics (FMM), in the year I applied, only the results of the Unified State Examination (U.S.E.) were required. HSE University had additional entrance exams: they gave us a paper with a list of tasks on it. We had to solve them and then explain our answers to the teachers. I liked it; it gave me a chance to meet the teachers, and they also saw the students in person.

The 40 spots for full scholarships to the MSU FMM were almost immediately taken by really great students, winners of Academic Olympics, and enrollment for those spots was closed. Then, some of those students changed their minds and a few slots opened up, and they called me from the waiting list.

Right then, I was submitting my formal application to the MSU Faculty of Psychology. I consulted with my parents and they said something I would often hear later: ‘If you graduate from the Faculty of Mathematics, you can work anywhere’. This is an exaggeration, of course, but I was only 16 and not sure of anything, so I enrolled at the Faculty of Mathematics. The HSE University Faculty of Mathematics turned out to be much better than the MSU FMM. During the four years that I studied there, the HSE Faculty of Mathematics grew famous, the competition for admission increased, and Academic Olympics winners began applying first to HSE and then, just in case, to the MSU FMM.

How were your studies?

The first two years were the same for everyone, and then the electives began. My academic advisor suggested which ones to take. I recall that in my third year I took math courses and decided to take macroeconomics for my general development. But after attending several classes, I changed my mind: they took one formula—actually, a simple, linear one—and built some kind of theory out of it. I switched to studying algebra and Lie groups, which are much more interesting, and never regretted it.

What did you write your thesis on?

It was on knot theory, under the supervision of Sergey Lando. It had a very good, visual theme. For small dimensions, everything could be drawn on a piece of paper, built, and calculated. You take a rope and make a closed loop from it. The question is: can it be unwound back into a circle? My thesis looked at the knot invariant. This is an expression that we attribute to a knot and that should remain constant for all equivalent knots.

My work became part of a scientific article for the European Journal of Combinatorics. We came up with an invariant and proved its invariance—that for all permutations, it remains unchanged. It matched some coefficient in some algebra.

Four people worked on the article. Lando came up with everything. I manually checked the small dimensions (my entire thesis consisted of drawings), a female master’s student created a program that checks large dimensions, and a second teacher contributed ideas. Three months later, using purely algebraic methods, two Canadian mathematicians proved our hypothesis that this invariant matches some coefficient in some algebra.

Why did you choose Computational Linguistics for your master’s degree?

In my forth year, I could take courses at the Yandex School of Data Analysis. I signed up for a C++ programming course and began attending classes. Once, I came on the wrong day and walked into a linguistics class for programmers taught by Boris Iomdin. It impressed me so much that I decided to study the subject for my master’s.

After attending the Faculty of Mathematics, it was very easy for me to study there. Only one female programmer from Tomsk University studied with me, and all the rest were philologists. I remember that I conducted informal seminars on probability theory, explaining our teacher’s lectures to all my classmates who were interested, because it was difficult for them.

But finally, my dream to go on an internship came true. It had been unrealistic to do this at the Faculty of Mathematics because it is very difficult to make up for the six months of mathematical courses you would miss. But the last semester of the master’s programme was fairly relaxed. I took an internship in South Korea, in the city of Daejeon. It was a great experience. I spent a whole semester there. Because I only had to complete a project seminar and submit my thesis for the master’s programme, I could take any courses I wanted at the Korean university. So I signed up for everything I like, even music theory. And I wrote my thesis.

What impressions of HSE University have stayed with you?

When I was a student, the Faculty of Mathematics was separate from everything else; we studied in the building on Vavilov Street. It seemed to me that the HSE University students from the main campus were all ambitious, goal-oriented, vying for ratings, and had big plans for the future. Almost everyone wanted to get an MBA or open their own business. But on the other hand, for all its separateness at that time, the Faculty of Mathematics taught us to be extremely transparent and honest. This is probably peculiar to mathematics.

You can’t just go around saying, ‘I’m a great mathematician, so now 2 + 2 = 5’. A celebrity teacher could visit and a student might correct him, point out a mistake. That was okay. It’s not about disrespecting authority; it’s about not being afraid to speak your mind. This is the free spirit of HSE University.

What was missing from your student experience?

A swimming pool. The only available pool was far from us, near the Electrozavodskaya metro station. Also, the usual student things: I lived in Troitsk and spent three hours commuting to classes. Still, in my first year, I went to the theatre for six months and really liked it. It’s just that almost everything was incompatible with the Faculty of Mathematics. The studies were difficult. One-third of the students had come from School No. 57; they were all friends and they all helped each other. They had studied mathematical analysis in the 10th and 11th grades. But I wasn’t from a math school and for me it was new.

What was your first job?

Tutoring schoolchildren. I went to the office when I was in graduate school. I wrote dialogues for a robot. For example, a person wants to know the weather. The robot must understand the queries: ‘What’s the weather today?’, ‘What is the weather in Arkhangelsk?’, ‘What’s the weather?’, ‘Will it rain today?’ I wrote scripts in Python, which we learned in graduate school.

I also did computational linguistics in my next job. And there, I gradually began working as a translator between programmers and analysts. Analysts made infographics and wrote cool analytical notes, but didn’t understand technical terms very well. And I explained to programmers what analysts wanted from them.

I shared this general story during an interview with Tinkoff Bank. It turned out that they have a whole position for this called ‘business analyst’. I got a job there and realised that work can be completely different. At my previous job, there was a lot of tension; the boss put a lot of pressure on us and shouted. It wasn’t very pleasant. And since I had little experience, I thought it was like this at work for everyone. At Tinkoff, people also argued, but they used logical arguments and not just ‘I’m the boss, I said so’. I felt at home there because they were all graduates of the FMM, the Faculty of Physics, and the Moscow Institute of Physics and Technology, and everyone was about my age. Everyone played the ‘What? Where? When?’ game show and other intellectual games. And everyone worked very hard.

I spent a year and a half there and left because I got burned out—although it was a shame to lose all that. I had a good project, but I did a lot of technical work, the result of which was not immediately visible. They assigned me the Credit for Online Purchases project . In 2017, not everyone understood what that was. Offline credit was clear to everyone and a large team of developers was working on that. But my tasks for programmers were always a low priority due to the small volume of loans. I worked with odd little stores such as a store selling children’s ball pools. Of course, some people bought them on credit, but their initial price of 5,000 rubles, with a loan, turned into 9,000.

I put a lot of energy into trying to merge online and offline work with one and the same client to make a cool product. I spent a year and a half on this. Finally, the time came when the technical work was almost finished and I could do something new, fantasise. It seemed very promising to integrate it with a single social network that had shops, and where it would be possible to make a button reading: ‘Buy on credit at Tinkoff’. But I ran out of steam. Ideally, I would have taken a long vacation, but I decided to leave. I took a creative break.

I handed over all my work to my subordinate. During the pandemic, she wrote to me: ‘The first one million purchases in a month’. Before that, they had only hit one million a month in December, when people buy gifts. Then she wrote: ‘The first 10 million a month’. Then there was the first 100 million, then a billion. As a result, she has her own development team with developers who work exclusively on her tasks. The project is in its heyday now because everyone has gone online. But all this would not have been possible if we hadn’t laid the technical groundwork for it.

After working at a bank, why did you decide to work at a school?

A friend who works at the New School asked me to come oversee a geometry test there. I went and checked out the school. I was very surprised: they had aquariums with fish, a room for playing flute, and there were drums in the hallway. And I really liked overseeing the test and greatly enjoyed talking with the kids: you explain something to them, they get surprised by something, and you discover something new for yourself. I had always wanted to do something good for the world and I didn’t get enough of that at the bank.

It didn’t work out with the New School, so I sent an application to Letovo. I wasn’t a teacher before that, but I had been explaining things to people my whole life. I had worked as a tutor, then as a teaching assistant at HSE University explaining game theory to students at the Faculty of Political Science. When the pandemic started, I got a letter from Letovo inviting me to an interview. It was conducted in what was for me the best possible format: I had to sit and solve 9th-grade problems. I had prepared, but had forgotten a lot of things. The head of the department told me something from which I deduced something else. He said, ‘Don’t worry if you can’t remember something; it’s clear that you are able to learn’. They gave me the 8th and 9th grades and I prepared for the lessons all summer.

At the start of the year, the teaching staff decides what the programme and order of subjects will be. For example, there is a fundamental question of what to give first in the 8th grade—the discriminant or the Vieta theorem. Usually, children are immediately given the discriminant, and this is such a bombshell. They can solve any equation, but it takes a long time for them to do the calculation. But we at Letovo put it off until last and teach alternative ways to solve the equation faster.

Are you planning to switch professions again?

I like school, the kids, my co-workers, and teaching classes. My college classmates were very focused on specific subjects—especially those who, after undergraduate studies, went abroad for a PhD, mainly to America, and then studied mathematics. But I have always had wide-ranging interests, and I feel at ease as a teacher. I teach not only strong students, but also those who struggle with math, who require audio-visual aids to understand. Because with every new math topic, they simply break down in tears—especially the little ones, although the older ones, too, sometimes.

I will definitely stay on to see my students graduate from the 11th grade. I want them all to get good scores on the U.S.E. and get into HSE University. I’m glad that HSE University has long surpassed other institutions as the top preference for college-bound Letovo students. When the kids asked me where I studied, they got excited and said, ‘Cool! We also want to go to HSE University’. It’s nice that this is your alma mater and that they think of it in this way.