Balancing Coursework with original research I am a first-year graduate student in a US university pursuing a PhD in mathematics. 
I am a bit frustrated in trying to balance coursework with original research. I saw students who spend most of their time with classes, but only produce one or two mediocre papers by the end of their PhD careers (I am not saying that not publishing a lot is a bad thing, as that depends on the research group in which the student is involved). 
In my opinion, one should learn by reading papers rather than taking courses at the PhD level. If one wants to study spectral theory, for example, one should read the classic papers by Weyl alongside modern treatments, and should talk with his advisor (hopefully he or she is at an institution with strong research group) with a view towards trying to contribute something new to the field. One should also try to keep up with the new contributions to the field (sometimes a graduate program is blessed the resources that enable it to bring people from the US and/or world to give talks on active topics). 
Unfortunately, with teaching 4 times a week and taking 3-4 math courses with long homework assignments, the idealized scenario that I just described is very hard to follow. My life has turned into finishing homework assignments, and I am not really convinced that spending my time in this way is going to help me. Perhaps, there is a reason why some graduate math programs (such as Princeton, for example) do not require the students to take courses and get grades.
In doing research, if one encounters some new concepts he or she is not familiar with (perhaps, due to not taking enough courses), then he or she should develop the skills necessary to efficiently learn that field/ concept to move forward with his or her research; this can come through with having conversations with fellow graduate students well versed in the field or self-study. Unfortunately, a lot of the graduate programs do not stress this enough in the early stages (and one cannot always a read a book or paper(s) front-to-back); however, Harvard's math department does require the student to write a minor thesis ("The minor thesis is complementary to the qualifying exam. In the course of mathematical research, the student will inevitably encounter areas in which s/he is ignorant. The minor thesis is an exercise in confronting gaps of knowledge and learning what is necessary efficiently."), which is crucial. 
Has anyone else felt this frustration? Obviously, complaining about this is not going to do anything, and I want to find some way to cope, work around or come to terms with this frustration. 
 A: You are in a mediocre program to produce mediocre students; don't let it bring you down...learn to play the game even if it is boring so that you do not sacrifice original research in the long run. I am sorry you have to face this bureaucratic BS... if you are PHD student in mathematics, ideally you will be learning by yourself and building relationships with good researchers in your area of research (hopefully in your institution). 
Taking and learning from generic courses like abstract algebra, complex analysis, etc. will not do you much good at any stage of your graduate career (unless you were underprepared as an undergrad). From the very beginning, you ought to see live, breathing mathematics with a beating heart. The rest- if you intensely dedicate yourself to yoru research- will fall into place. If you only want to work 9-5 with small-talk chitchat with your fellow cubicle mates who lack passion...then just go the mediocre route and take a lot of courses, do homework all day and just get a feel for the mathematical literature...
And you will have a a strong publication record by the time you graduate, whereas most graduate students from mediocre (most are...) institutions will maybe write one or two with their name slapped onto the paper with their adivsor. 
