I realize many math problems solved by mathematicians require a tremendous perseverance over a period of years. My question is not about endurance over a long period of time, but over several hours.

I can only spend an hour and a half to two hours working through problems or reading textbooks until my mind becomes cloudy and then I need to take a 30 minute to 1 hour break in order for me to make anymore meaningful progress. This was never a problem when I was an undergraduate since exams were at most 2 hours long. But I realize there are qualifying exams and math competitions like the Putnam exam where contestants solve problems in 3 hour chunks.

How does one develop the stamina to concentrate for so long in a single sitting? Should I continue to do math even though my mind is fatigued?

How important is it for a professional mathematician to be able to work on a problem for a long period of time in a single sitting?

  • 1
    $\begingroup$ It's mostly practice. Find a problem you really want to solve and hack away at it for a few hours. Also avoid excessive stimulants such as video games which will naturally decrease your attention span. $\endgroup$ – CaptainCodeman Jul 15 '14 at 8:21
  • $\begingroup$ It is not even slightly important for a professional mathematician to have this skill. Professional mathematics takes place on a time scale much longer than several hours. $\endgroup$ – Qiaochu Yuan Jul 15 '14 at 8:47
  • $\begingroup$ One recommendation would be to improve your physical condition. But I firmly agree with Qiaochu: this has no relevance or importance for professionals. It's all about making meaningful progress. Take whatever rest you need in order to make progress. $\endgroup$ – ShyPerson Jul 18 '14 at 18:57

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