‘Studying with Enthusiastic People Around is Fun’

In 2015 eight graduates from the HSE Faculty of Mathematics started PhD programmes at MIT, McGill, Caltech, Pennsylvania State University and other top universities. HSE 4th year student Dmitry Pirozhkov who has got a place at Columbia University talked to the HSE News Service about how to get onto a prestigious PhD programme and about his expectations and academic plans. 

I’m mad about mathematics - it’s partly my mum’s fault (she’s an engineer and we had a lot of science and technology books, journals like ‘Kvant’ - Quantum and Nauka i zhizni - Science and Life at home) and my own curiosity. I went to a regular school in Orenburg, I had a good math teacher but apart from that, I was bored. I read quite a lot and tried to study advanced mathematics by myself. Towards the end of school I got friendly with a kid who was fanatical about computer programming and I kind of got interested in it too, probably because there was someone to talk to about it. Right up until I started my degree, I wasn’t sure whether I’d study math or programming, but in the end, mathematics won the day.

I had to choose between Mechanical Math at Moscow State, Novosibirsk State and HSE. I chose the Math Faculty at HSE because of the reputation and high level of activity of the professors. There wasn’t much information available about the faculty itself four years ago but I had heard of the teachers, Alexey Gorodentsev, Mikhail Verbitsky, Evgeny Smirnov and many others, mainly because they taught at the Independent University of Moscow [a small elite college for future research mathematicians]. 

The first years were hard going. I didn’t want to learn everything that we covered and I had to overcome my lack of desire to study . Later on it got easier because the programme allows you to chose your own topics. I started to read more fiction in my spare time. I particularly like sci-fi. 

Why go abroad to study?

I’m sure there are places in Moscow to study math too, I considered the option of staying but I want to experiment a bit, meet other people and try something new.

It’s usual in Mathematics, at least in the USA, to go straight on to a PhD after you graduate. In Europe it’s less common which is why all my year group have applied for American universities. Sveta Makarova who got a place at MIT was considering going to Tokyo.

Columbia took me (two guys from our Math Faculty are studying there, by the way) although I applied to other places too. It is a very good university, it’s true, for my specialisation - algebraic geometry - and there aren’t that many specialists in it. But, for example Johan de Jong teaches there - the creator of the Stacks Project, a collaborative project of recording  standard assertions from algebraic geometry with proofs.

It’s a big plus for a candidate when he can say, not only which area of the subject he wants to study at the faculty but also knows (not necessarily personally) the actual professor he wants to study with.

I like being in a community of people who are fanatical about their work, who care about what they do

The main difference between post grad and undergrad study is that you need to be more self-reliant and do more research. I think I’m ready for working independently - there are regular seminars at the Math Faculty conducted by students themselves , they get together without a professor and study things they are interested in. My class-mate Grisha Kondyrev for example organised a seminar like that when we were second-years. The seminar was on Fridays and lasted 6 hours from 5 to 11. Grisha invited people who were working on all kinds of different topics. It was the first regular student seminar in the Math Faculty.

Inspiration and complex problems

I’m inspired by the ideas of the French mathematician Alexander Grothendieck. He wrote that one shouldn’t concentrate on complex problems but seek out what can be said about an object, having examined it from all sides. This way he found answers to many complex problems which no one had been able to solve before him. He invented the apparatus of contemporary algebraic geometry. In his famous autobiographical work ‘Harvests and Sowings’ there’s a passage about how people usually try to solve a problem as though it’s a hard object you need to smash with a hammer, when it’s more effective to put it in water and wait until it opens by itself.

How to cope with life if you are very clever

There’s a stereotype that mathematicians are rather unworldly. When I started in the Math Faculty I think I was like that. My parents brought me to university on my first day. Until then, I hadn’t travelled much. But thanks to the many clever and more active students who were equally mad on math, I got better at handling life in the real world. They’ve created an atmosphere here where students can socialise, work together, learn something from each other and not just mathematics. And the teachers here are very approachable. We can ask them anything. Misha Verbitsky, for example is very open with the students, he’ll stop and chat in the corridor with anyone, everyone knows him, we are all on informal terms with him, and he’s always ready to give advice or explain something. He invites us to his seminar, recommends summer schools, gives us support when we need it.

Another thing that really helps with studying and socialising is going to summer schools. I’ve been to the traditional school of the Institute of Theoretical and Experimental Physics twice (once in Sebastopol and then in Dubno). I went to a school on classical and p-adic Hodge theory in France and to a winter school on hyperbolic dynamics in Brazil. There were a lot of Russian speakers there, by the way.  

Why I want to be a Mathematician

I think that academic life is less about money and more about freedom to learn new things, do research, give lectures, help people. There isn’t so much routine work, you can always find something interesting for yourself in mathematics. I don’t think the mathematics profession is an elite, it’s more a community of people who are interested in something that others don’t care about.

I like being in a community of people who are fanatical about their work, who care about what they do. I would think it a success to be in that kind of atmosphere and be happy myself with my work. Of course I worry about the material side of things. I want to be able to live normally, but I think that a teaching post in a good Russian university or abroad would allow that.

Ludmilla Mezentseva, HSE News Service