(for the leaderboards) I thought you might like this quote. It was brought to my attention by the journalist John Rentoul, who posted it online, but it comes from an interview with the composer Alvin Singleton. It might resonate with you, it certainly did with me. Switch music for cryptography and composing for mathematics and it is pretty close to a definition of research:
Later I talked to him about how whenever I try to write music, the first thirty to forty-five seconds comes naturally to me, but then I get stuck. I wondered if, for him, whole songs just spring to mind the way short riffs and vamps spring to my mind. The answer was a steadfast negative. “What you call ‘being stuck, ” he said, a twinkle in his eyes, “I call composing.”
Alvin Singleton, interviewed by Brian Christian, via John Rentoul