Maybe I missed it in this story, but this anecdote about Poincare himself is apropos:
"The famous French mathematician Henri Poincaré was very interested in mathematical creativity. He describes a period of hard and seemingly fruitless effort to solve a problem, from which he took a break to join a geological expedition. As he was stepping on a bus, he made one of the most important breakthroughs of his life. The solution came to him out of nowhere, and was accompanied by a perfect certainty as to its correctness"
"The famous French mathematician Henri Poincaré was very interested in mathematical creativity. He describes a period of hard and seemingly fruitless effort to solve a problem, from which he took a break to join a geological expedition. As he was stepping on a bus, he made one of the most important breakthroughs of his life. The solution came to him out of nowhere, and was accompanied by a perfect certainty as to its correctness"
(from this blog: https://kjosic.wordpress.com/2012/06/19/creativity-and-waste...)