There is an obvious and explicit change in the nature of Mathematics education from Bachelors to Masters. In Bachelors, somehow, there are lots of books available to read and people enjoy working on problems and what they are doing. But in Masters, things gradually get technical and dry, and the enjoyment gets lost somehow.
Now that I am a Masters student in Mathematics, in particular Probability, I envy the Bachelors students who always seem to have a chapter to study, some exercises to do, so there is something very definite in their lives. On the other hand, I am approaching research, and slowly entering a domain where things are technical, not really what you call enjoyable, and too open...there are big problems people try to solve, using techniques we are not at all familiar with, so it somehow shakes my belief in my abilities.
I am not sure I would enjoy this, and I am considering a PhD in mathematics. I am all for learning techniques and trying to solve problems on my own but the lack of a goal or definite program does not seem very convincing to me. Is research like this? I want to learn mathematics and the tools but am not sure I really want to do a PhD. For some reason, I have always found Math PhD students extremely demotivated and this scares me; one of them even warned me against a PhD in mathematics. My field is Probability Theory though, a relatively new field with lots of work going on. But still, is it worth putting life at the threshold of uncertainty with no definite program in mind for 5 years? Or is it better to be a good teacher and hence maintain a source of income, while studying good mathematics on my own? Scope of getting good teaching position without doing a PhD is difficult, I am aware. But I do not want fame...I just intend to learn. Will learning be too difficult without a PhD?
For some context, I am a good student according to my university transcript and am involved in writing a Masters thesis so I know what happens a bit in research although in my Masters thesis, the problems I am looking at are rather simple as I have only one year at hand. I have the habit of studying books, lecture notes and research papers and this is something I genuinely enjoy. But I am not sure I really like the idea of working on one single thing for 5 years. What if I lose motivation as some stage? Already I see the element of fun/enjoyment is missing in all the serious stuff I am reading now.