A little from column A, a little from column B. Einstein worked on relativity for a decade, i think. Newton looks to have spent about 8 years sorting out calculus. A professor once said the Fourier transform was worked out over a couple of weeks in a French chateau accompanied by Fourier's lover. I've never found a source other than that prof's story though.

For me, and i suspect most people, when i work on something hard, i have a lot of ideas. most of them suck. some of them are promising but kind of die on the vine. That one sweet answer though, that idea is memorable. i think it's memorable because of the weeks, months, or years spent validating the idea is good enough.

I agree. Learning everything about something without getting too attached to any point of view makes big leaps forward possible.