TITLE: Math overdose? Professional advise how to cope with it
QUESTION [13 upvotes]: I'm a PhD student, currently working on my Thesis. Over the years I have many time encountered a problem. Maybe professional mathematicians know what I'm talking about?
When I study a math topic, frequently I reach a stage when I stop understanding anything in this topic anymore. Like when one repeats a word many times over and over it becomes unintelligible and meaningless. I read a book or a series of papers on a topic and everything which I understood before I started actively studying the topic, are now not understandable anymore, even though I understood (or at least I thought I understood) them when I started reading. So I give it up for a while, because continuing this topic is not possible anymore. And then exactly the same thing happens with the next topic. The study is not lost, because when I return to the topic it is much easier and I'm able to progress deeper into it, until I reach a new stage where I have to give it up again.
Has this happened to other professional mathematicians? Or maybe I'm not meant to be a professional mathematician? Any professional advice how to cope with this situation?

REPLY [16 votes]: I can give three bits of advice.  One that has been given by many other people is to take a break.  People think that endlessly hitting the books without a break is the mark of a hard working mathematician, and that to do anything else is lazy.  This is far from true.  Doing so only depletes ones creativity.
The second bit of advice is to form hobbies and interests that may be mathematically related but that give one an opportunity to make connections outside of ones department.  Doing a PhD. in a ruthlessly competitive environment can be draining.  Getting an opportunity to play pool, MTG, chess, to exercise, play video games, go camping, go hiking or something of the sort may restore a PhD. student's confidence, and also restore one's creativity.
The third bit of advice is not to judge one's worth solely based on one's mathematical achievements.  You may say "What else is there to judge oneself by, and why should I stop this judgement if I want to increase my productivity?"  The answer is that this judgement does not increase your productivity, in fact it decreases it.  When you are highly productive this judgement does not truly increase your productivity.  When your productivity is lower, which happens to every mathematician, then this can tank productivity as all elements that further creativity are reduced.  Realize that you have innate worth beyond your work, and this will also help to shorten those times when creativity is lacking.
I hope that this is helpful as your question is certainly worthwhile and I suspect that your experience is universal among mathematicians.