As a young mathematician in the 1950s, the late Don Newman taught at the Massachusetts Institute of Technology alongside rising star and Nobel-laureate-to-be John Nash. Newman had been struggling to solve a particular math problem: “I was ... trying to get somewhere with it, and I couldn't and I couldn't and I couldn't,” he recalled.
One night Newman dreamed that he was reflecting on the problem when Nash appeared. The sleeping Newman related the details of the conundrum to Nash and asked if he knew the solution. Nash explained how to solve it. Newman awoke realizing he had the answer! He spent the next several weeks turning the insight into a formal paper, which was then published in a mathematics journal.