I've recently started a PhD in pure mathematics, and I'm about to finish my first year. One thing that I have become acutely aware of during this time is that my understanding of much of the mathematics that I learnt throughout my undergraduate and masters has fallen out of my immediate understanding or memory. It seems to me that my peers have a much greater all-round knowledge, and I'm concerned that I am considerably below standard in terms of mathematical competency. I've not directly broached this subject with my supervisor, however he assures me that I am on track and my work is going well. As far as he is concerned I'm doing fine, but I have a strong sense that my understanding of things like topology, analysis, number theory and algebra should really be at a higher level.
My question then is this: If you've completed a PhD, or are currently studying for one, have you experienced something similar? Is it common to have feelings of inadequacy in terms of mathematical ability? And finally, do you have any advice for how to overcome these feelings?
An obvious solution would be to brush up, but of course that is easier said than done when I have my research to be getting on with. In any case, I'd be interested to hear other peoples experiences with this sort of thing!
Edit: For anyone wondering I've now achieved my PhD! :) My feelings of inadequacy are much better now that I made it through the intense scrutiny of a viva.