My mathematical life

Because my boyfriend does not know how to use Google translate, I decided to convert my latest post into English. For the Czech version, see http://mujsvetmojematematika.blogspot.com/2015/07/muj-matematicky-zivot.html

Being too restless to think of new things, I decided to share with the world some of the thoughts I have used elsewhere. For instance, this is a part of my effort to convince young ladies during a mentoring program http://www.zenyaveda.cz/ that doing maths can be nice and interesting.

Disclaimer: in exactly the same way I would support any young guys thinking about pursuing a mathematical career. However, I remember quite well how scared I was of my mathematical life, how convinced I was that there is no real place for women in science and that I will never be good enough as of course, women have a different education, social status, we are simply in a different starting position. But whatever, I do what I do, I enjoy what I do, I don't have to prove anything to anyone. I am as good as how well I work on myself. Some might be more talented, some might be faster learners, but who cares,  I study for myself, not for others. I don't believe anymore that maths is a male-only game, it is all about effort, persistence and strain and that can be found in anyone.

So this is my slightly jovial response to what does it mean to study pure mathematics, what do we do afterwards and how easy it is to start studying math. This account of my studies relies almost exclusively on the experience I have had at Masaryk, Brno.

So what is the difference between pure mathematics and applied? It's mostly different in content and attitude. It certainly is not only for the mathematical geniuses from all the Olympiads, on the contrary, those in particular have to deal with a great shock of suddenly starting to study different maths they might not excel at anymore and actually, some of them burn out completely... About lectures - in Brno the approach is very much definition, theorem, proof, it is difficult from the beginning to get oriented, but you should not be afraid of that, it is enough to be active and if you don't understand, get someone to talk you through it, annoy all the people around you to help you explain things again and again, get them to tell you what to read and what to work on.

Pure mathematics should lead towards the world of research mathematics. Therefore, the concepts are more abstract and it is particularly important to interact with senior mathematicians, be interested in what is happening in the world, the math community, it is not just about what you learn in the lectures. For it to make sense, at some point you will have to step out of the safe zone and become interested in things outside - it might sound scary, but definitely with your thesis you will start studying things outside the standard lectures and you will learn how to ask your own questions and pursue your own answers. It might be frightening, but you will learn how to spend your time on mathematics outside the school. At some point, anyone will find a thing that interests them, some things might be boring, but sooner or later something will capture your attention.

In applied math you learn more practical concepts, but many pure mathematicians leave for commercial sectors anyway and we are well sought for, we might not have as much experience with a specific computational software, but we are used to studying difficult, abstract concepts, solving problems for which you do not know in advance whether they will have any solution at all. I myself am a bit skeptical about applied math: for instance, in statistics, you know what kind of answers you are looking for and try to get them!:)

You will be more than fine with just high school math background, but as anywhere else, you will need some time to get acquainted with the new language, concepts and approach, but this is nothing to worry about. What do they want from us in Brno? Not much. Frankly, if you have some good background from your high school, you don't have to do anything until the exam period and for most of the exams (definitely the bachelor ones) I did not need more than a week to prepare, despite having done very little during the semester and despite being no genius, I do have to work hard to get those things done.

What can  you do with pure maths? The most beautiful option is to stay in research, you can do crypto, where they are really in desperate need for mathematicians, you can learn how to code better and be a programmer, you can do "big data" = "big money", a new and exciting field. But even from applied courses in Brno you can get to Berkeley and I got accepted to Cambridge, so the education we get is good enough for many places. Concerning travelling: to get to summer schools is easy, to get enough funding is... sometimes tricky. But I got to many summer schools this year, two of those were organized by the Institute for Advanced Study that mostly covered my expenses and Brno was generous enough to cover the rest, I got to some that cover some subset of room, board and travel expenses. You can't get everywhere you want but I can pick from (for instance if they cannot offer to give me enough support and it wouldn't make much sense for me to go there then).

And what do we do at such summer schools? You attend lectures, solve problems, meet people, travel. For instance, now I am in Utah for 3 weeks, we have 2 lectures a day, a problem session and we are supposed to write a 3-5 page investigation of some topic I am pursuing on my own here for 3 weeks. But you can attend more advanced lectures, research seminars. However, I chose to do most of my mathematical interactions here by talking to people about interesting things, mathematical as well as current affairs and problems. There are two Fields medalists, which is always inspiring to be around, but also many mathematicians who transformed or modernized their fields... I have been lucky to meet some of these superstars in my life and it always inspired me immensely.

However, I do not know your attitude towards math. For me it is a hobby I do enjoy a lot, I might not be as smart or good, but there are things I want to learn and enjoy. Sometimes it is frustrating, sometimes it is difficult, but you don't have to work 24/7 in Brno as is the case at other universities. But it is very much about your motivation and dedication. But if you are interested, in Brno, at any course, almost everybody will be happy to talk to you and support you in anything you might be into. It is enough to be a bit active - see how well it works for me! I don't work hard, frankly, I devote the very minimum to math. But I like it.

And if you do stay in pure mathematics, you will travel. Be it some research stays, summer schools, conferences or even going abroad for good, mathematics is about meeting people and spreading the ideas and learning new things from new places. And it is always great to see how things are done elsewhere.