Is concentration an extremely important working habit? I study mathematics and by "working" in the title, I mean researching and serious reading on my field (reading difficult papers, books, etc.) I believe the answer for other fields would be similar.

Am I right in saying that concentration is an extremely important working habit? I definitely feel that my working habit needs improvement: I stop working and check email/facebook, read news/forums, or even play a few blitz chess games from time to time. I believe that it is very distracting and that my efficiency is low. I also listen to music but this is probably less distracting and sometimes may even be helpful. 

Is it right to say that an ideal working habit is that 


  Be completely immersed in working, avoid all possible distractions, refrain from visiting any irrelevant web sites, turn off mobile phone and email notification. Work for a few hours until reaching a planned milestone, or when the body forcing a stop (micturition, hunger, low energy level, etc.)?
As a mathematician, this is a very personal matter. Some people work 9-17; some have very irregular working times. Some have a habit of always going to the office to work, to help mentally separate 'work' and 'time off'; some work from home when they have no teaching or administrative tasks to do. Some people listen to music, some don't. Some check their Facebook at work, some don't. Some work in long streaks, some prefer to have a quick pause every half an hour or so.

Do whatever works for you. At this point in your career, you have been a student for at least 12 years; you should know yourself and be able to evaluate your productivity objectively.

This is even more true for a mathematician: mathematics is mostly a mental endeavour, and it is easy to start thinking about your work in your head when you are engaged in other activities, such as walking, driving or showering.
Sometimes your best ideas will come when you are not actively working/studying. Of course, you can't do everything like this, but the important ideas often strike at improbable times.

If you are a student starting out with maths, the only advice that I can give you is plan ahead, and recognize when you are going to be late if you don't increase your productivity. Many students can't tell when it's the moment to really turn off your Facebook and start studying until it's too late. Poor midterms should be taken as a big warning sign.