TITLE: How long to do math each day?
QUESTION [37 upvotes]: I have seen some posts math.SE (mkko's answer) indicating that it is the norm for (undergrad?) math majors to study 70-80 hours per week. I'm a little bit shocked by that. For some background on me, I'm not very advanced (only finished calculus 1-3 and taking my first DE class). However, personally if I am trying to solve a tough problem or prove a theorem, I can't work on it for more than an hour at a time without killing my ability to think creatively, which is the most important skill we mathematicians should cultivate, right? After about one or two hours, I can't engage the theorem in deep thought, so trying proving it becomes more of just an unproductive guessing game. If I just come back the next day, I feel like I have digested the problem much better and gained more perspective. When there is new material, I do spend multiple hours just trying to learn the material and become familiar with all the definitions and intricacies. However, I feel that it's most important to focus on problem-solving and proofs.
So my question is, what do these 80 hours a week consist of for typical math students? Is most of that time spent on trying to just learn the material? Is it actually spent on cultivating problem-solving skills but I have just have a really low tolerance for focusing? Is spending no more than 1-2 hours per day on the same problem optimal, but just a luxury that students can't afford once they reach a certain level?

REPLY [2 votes]: In the book Outliers, author Malcolm Gladwell says that it takes roughly ten thousand hours of practice to achieve mastery in a field. 
If you want to (Bachelor + Graduate + PhD) this makes roughly 5/6 hours per day. That's it. I find this estimate quite reasonable. If you want to accomplish the same result before graduation You have to switch to the 10 hours mode.