Why is the field important? Algebraic topology is romantic and beautiful branch and at the same time it involves many "engeneering ideas" that, what at least my intuition says, necessarily have to appear in the nature of algorithms.
Pros:
- This was actually my first-rate criterion in my last year's choice of the PhD position but now I of course have doubts whether it should be on the first place: I have got a top-class advisor that I can talk to.
- With exaggeration, I was created for this area. It is geometric imagination, where I feel strong in mathematics. This field can be basically researched by two kinds of people: computer scientists - who usually have poor knowledge of algebraic topology - or by mathematicians - who usually don't find algorithmic questions interesting or (at the same time) have only basic knowledge in complexity. I am capable to become an exception.
- Two high quality semesters of algebraic topology taken at VU Amsterdam (probably incomparable to what I could get in Prague) give me a front position in our research team.
- A first "love affair" with (combinatorial) topology dates back already to 2nd year at Matfyz:)
- Although I can still consider myself to work in mathematics that "stands behind computers", it is a bit too "far from earth" (theoretical) to be in harmony with my engineering soul.
- This is a hard-core-mathematical area miles away from the programmers lifes, that programmers cannot be taught. This will split my profession into two disjoint (orthogonal!) parts: teaching and research. Advances in research will not push me forward in teaching and the other way round. (In previous two points I compare my situation with my alternative-universe profession cryptologist)
- I got to a department I have very little common interests with. The last Homonolo in Jizerky was a almost a shock: I was able to find very little passion for things my colleagues do! (Here I can compare with the group of Lex Schrijver at CWI, Amsterdam.)
- I can hardly talk about my work with others. Not with normal people, of course, but, for exmple, not with my almost-computer-science-PhD brother and, in the end, not even my department's colleagues (besides my advisor).
That was a short review of my attitude to my job.
It leaves the question of profession fairly unanswered. I'm almost sure already now that if I
stay in mathematics, I'll do its wonderful and amazing
part that "drives computers".
But what are the alternatives? To pack my stuff and go outside my beloved Republic to do the cryptology? (Amsterdam would not be a bad place, besides that Germany, Switzerland..).
Or quit academia? I feel confident to be able to bring inovations in the field of software developement, but am I able to preserve my mental health while dealing with computers of flesh and blood? (Google in Zurich sounds pretty nice. Just get the job! I should come up with more alternatives if I want to think about it seriously.) Or take the usual trail of mathematics students and work in finances?
Let's stop boring suggestions! Become a cook. Run a bakery. A journalist.
In the end, isn't it way too restrictive to admit only single profession for the only single life we live?
