The plus side I've found is there are radically less distractions around at 1am, so I can often get more work done between 11pm and 2am than I can in the whole afternoon. Last night I managed to complete an entire application form for an internship with BP, whereas in the day all I'd managed was half a page of geometry notes.

Possibly even more importantly, mindlessly hitting refresh on facebook is not an acceptable activity at 2am, whereas earlier in the day it is, so if I am awake then, it’s because I'm actually working.