I read in the proof-sheets of Hardy on Ramanujan: 'As someone said, each of the positive integers was one of his personal friends.' My reaction was, … - John Edensor Littlewood

I had been struggling for two months to prove a result I was pretty sure was true. When I was walking up a Swiss mountain, fully occupied by the effort, a very odd device emerged - so odd that, though it worked, I could not grasp the resulting proof as a whole. But not only so; I had a sense that my subconscious was saying, 'Are you never going to do it, confound you; try this.'

My research began, naturally, in the Long Vacation of my 3rd year, 1906. My director of studies (and tutor) E. W. Barnes suggested the subject of integral functions of order 0... [After success,] Barnes was now encouraged to suggest a new problem: 'Prove the Riemann Hypothesis'.

It was Mr. Littlewood (I believe) who remarked that "every positive integer was one of his personal friends."