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I got an opportunity (thanks to my advisor) to attend a real conference in Mathematics - presenting the results of my Bachelor's thesis. Following, just a few random thoughts and remarks of mine:

It took place in Bedlewo, Poland - my first ('serious') visit to Poland. We lived in a castle and a building nearby and were wonderfully cared for.

I used almost all languages I knew (Czech, English, Spanish, French, Russian), except for Dutch and Chinese. Actually, I met a Dutch person and I talked to him, yet I wanted to get information from him, and as he was rather busy, I preferred getting information over practicing the language.

I met mathematicians, whose articles/books I'd had read before (so I consider them as nearly legends - oh come on, how many (little) books and articles has a bachelor read?) - Jonathan Smith, Rudiger Goebel, Anna Romanowska

A conversation:

"Is he good?"
"Yes."
"Extremely good?"
"I don't know, he is not my student."
(To me:) "Unless you are extremely good, don't do universal algebra. It's too isolated... Maybe try combinatorics.

I was asked several times, what Mathematics I want to do in future. A lot of questions makes one think about it thoroughly. What I have thought out so far: I don't like geometric arguments (and am not good at making them). I'm good at abstracting (yes, this part is still rather vague...).
Hmmm, but what does it mean, "geometric arguments", which areas of Mathematics does it encompass?? In what I have met so far in my life - the subjects: (Real and Complex) analysis, Topology, Differential geometry and Analysis on manifolds were full of such, while subjects encompassing Algebra and Logic mostly missed them (but also Functional analysis!!); Lie group theory was a mix. But now - does this say anything about the (mathematical) "real life"???
The Princeton Companion to Mathematics sort of divides mathematicians into geometers, analysts and algebraists. Distinction between algebraists and analysts being (succintly and imprecisely :-P ): "algebraists like equalities and analysts like inequalities". Do I really "prefer equalities", or is that just because of the plentitude of geometric arguments in early Analysis courses (together with the fact, that people in our Algebra department seemed more human-like than those at our Analysis department), that I consider myself to be an algebraist nowadays??

Being clever is not too appreciated (after all, every person doing Mathematics is; usually more then I am). What is appreciated, very appreciated - dedication, being hard working, passion and curiosity. This probably holds (as of my experience so far) in many other areas in life.

I don't want to end up doing research just for the sake of research (i.e. not interesting to anyone else, with almost no prospect of being interesting to anyone else even in future) - just a path too easy to follow in Mathematics (judging from what I saw and - even more - from the opinions of people who can probably be judged as "quality mathematicians"). But on the other hand (judging from what I saw and from the opinions of people who can probably be judged as "quality mathematicians")...there seems to be also so so much of the interesting Mathematics!

Giving talks, making presentations: slogans, pictures, examples...and motivation, if there is any.

"One has to have a lot of examples to develop the intuition."