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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.

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closed as off-topic by J.-E. Pin, Xander Henderson, Don Thousand, Arnaud D., ArsenBerk Oct 29 '18 at 13:56

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  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – J.-E. Pin, Don Thousand, Arnaud D., ArsenBerk
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  • $\begingroup$ I prefer thinking on known things from different angles rather than rightaway working on an unsolved problem. I don't know how I'll feel about it one or two years from now but this is what I feel currently. $\endgroup$ – Landon Carter Oct 28 '18 at 17:35
  • $\begingroup$ More precisely, I get satisfaction by observing connections among seemingly different things, or where a different method gets utilised to solve a particular problem. Does it have no value at all? Going by the enormous number of publications, it possibly does not... $\endgroup$ – Landon Carter Oct 28 '18 at 17:36
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    $\begingroup$ First of all, deciding to go to PhD, from Masters, means you already know the topic that interests you. If you don't have the topic, you better find it asap otherwise somebody else will do it for you. $\endgroup$ – rtybase Oct 28 '18 at 17:46
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    $\begingroup$ Regarding your first paragraph, my observation has been almost the reverse, but maybe things are different now than 35+ years ago. During undergraduate study in the U.S. (where you appear to be) I recall both myself and others often being caught up with non-mathematical (and even non-science) course requirements and other activities (intramural sports, dorm activities, activities in clubs you belonged to, most students in your math classes not really that interested in math and did only what was required, etc.), whereas in graduate school these issues mostly vanished. $\endgroup$ – Dave L. Renfro Oct 28 '18 at 17:49
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    $\begingroup$ @rtybase: The situation with research and graduate mathematics training (at least during the first 2 to 3 years) is a bit different in the U.S. than in England. Rather than repeat things I've already written elsewhere, see this comment AND this other comment. $\endgroup$ – Dave L. Renfro Oct 29 '18 at 6:27