I think it is like with almost every type of mind activity. There are people who work most effectively just after they wake up early morning, but they have to go to sleep when they feel tired in the evening. The other group prefers to learn or to perform other brain activity on evenings - they can sometimes sit long hours after midnight, but between 5 and 9 a.m. they can't think about anything.
Our brain becomes less effective after it starts to feel tired, but it doesn't drop to zero at once. We usually can force it a bit when we have to. It can be sometimes made with help of chemical substances like caffeine (every coffee lover knows that), but doing it all the time may lead to something like sleep and rest debt, which we have to repay later. Sometimes we have to do it (e.g. before an important exam). I have done it many times during my studies - the amount of things to learn was too big to do it just after returning home after my classes, so I had to sit until 3.a.m. and then sleep until 6.a.m. and go to next classes. It was effective enough in the beginning of the week, but the night from Thursday to Friday was a nightmare. On the other occasion I had to read the whole book which I managed to borrow the day before I needed it - so again I've spent the whole night on reading.
No I try to avoid such situations and go to sleep when my body demands it. So... it's 0:18 CET now... Good night :-)