Subparent that started this. Having had a eureka moment, they definitely exist. That said, it's still 1% inspiration, 99% perspiration. In my case, it's more like 0.00001% inspiration, and all the rest is perspiration.
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.
The majority of technological advancement is done by cautious, slow research not by frenetic leaps and bounds.