Just a soft-question that has been bugging me for a long time:
How does one deal with mental fatigue when studying math?
I am interested in Mathematics, but when studying say Galois Theory and Analysis intensely after around one and a half hours, my brain starts to get foggy and my mental condition drops to suboptimal levels.
I would wish to continue studying, but these circumstances force me to take a break. It is truly a case of “the spirit is willing but the brain is weak”?
How do people maintain concentration over longer periods of time? Is this ability trainable or genetic? (Other than taking illegal drugs like Erdős.)
I know this is a really soft question, but I guess asking mathematicians is the best choice since the subject of Mathematics requires the most mental concentration compared to other subjects.
I recently read an article on the 40 hour work week and I think it is somewhat related. The basic idea of it was that in the mid 20th century, they had a 40 hour work week and they had lots of research on it showing that it was optimal in many ways. That is, if you increased your work week from 40 hours to 60 hours, you wouldn’t gain 50% extra productivity. You would gain 20-30% extra productivity. But, this is only over the short run.
Once you work 8 weeks of 60 hour work weeks, you end up breaking even. That is, over that period, you would have gotten the same amount of work done if you had just worked 40 hours every week. If you do 80 hour weeks, it only takes about 2 or 3 weeks for you to break even and start doing less than if you had just worked 40 hour weeks the whole time.
And, the article mentioned that with jobs that take a lot of mental work, e.g., doing complicated mathematics, in fact you had even less than 40 hours of productive work per week.
So, do some mathematics. When you get tired and fatigued mentally, go do something else for a while. Then, come back. Getting enough exercise and sleep, eating healthy, and having fun activities you do is important. That is part of the reason the 40 hour work week is good. Once you start doing too much work, you lose out on all those other important things that help you function normally.