Sleep On It

From the dreams of August Kekulé that led to the conception of a simple structure for benzene and Dmitry Mendeleyev that initiated the creation of the periodic table of elements, to the late-night dreaming of Otto Loewi, which inspired the experimental demonstration of neurochemical transmission, examples of creativity occurring during sleep are not uncommon.

Continuing to describe an experiment, in which participants either did or didn't sleep prior to attempting a series of complex mathematical problems, the authors conclude:

Thus, 'sleeping on the problem' in this case more than doubled the likelihood of solving it.

(Robert Stickgold and Matthew Walker, "To sleep, perchance to gain creative insight?", in Trends in Cognitive Sciences, Vol. 8, Iss. 5, May 2004, pp. 191–192).