I've experienced this effect numerous times. Sleep is a wonderful thing. One time in high school I was working on an advanced calculus problem for several hours

I've experienced this effect numerous times. Sleep is a wonderful thing. One time in high school I was working on an advanced calculus problem for several hours before going to sleep. I woke up in the middle of the night to use the restroom and realized that suddenly I had the key insight needed to find the solution. The problem was to find the solution to \int_{0}^{\infty} t^{- \frac{1}{2}} e^{-t} dt. If only this worked all the time. Perhaps I should read up on the Riemann Hypothesis and see what happens tonight.