I found this fantastic quote by the artist Chuck Close. It was his advice for young artists. However, I think that if you replace artist by researcher,^* the same advice applies. I would certainly pass this advice along to young mathematicians: just start working, the ideas will come. Conversely, if you don’t put in the time, do not expect that “ah-ha” moment.

The advice I like to give young artists, or really anybody who’ll listen to me, is not to wait around for inspiration. Inspiration is for amateurs; the rest of us just show up and get to work. If you wait around for the clouds to part and a bolt of lightning to strike you in the brain, you are not going to make an awful lot of work. All the best ideas come out of the process; they come out of the work itself. Things occur to you. If you’re sitting around trying to dream up a great art idea, you can sit there a long time before anything happens. But if you just get to work, something will occur to you and something else will occur to you and something else that you reject will push you in another direction. Inspiration is absolutely unnecessary and somehow deceptive. You feel like you need this great idea before you can get down to work, and I find that’s almost never the case.

[As far as I can tell, the source for this quote is Close’s interview in the book/DVD Wisdom, by Andrew Zuckerman.]

^*The similarity between artist and mathematician was famously pointed out by G. H. Hardy in A Mathematician’s Apology: “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”