Everyone knows the story of Archimedes' "Eureka!" moment. And likewise, everyone knows about Newton and the apple. Because they're cool and interesting stories, even if they are about physics.
Unfortunately, they also give two badly false impressions. The first is that that's the full extent of the story - Newton saw an apple fall, and the notion of gravity (and all that goes with it) popped into his head. That is, science is a matter of inspiration.
The second false impression is that science is, or should be, fundamentally easy - breakthroughs are just a matter of getting into the bath. And so, if you find it hard, you must therefore be terribly stupid, or doing it wrong, or whatever.
But here's the reality: Archimedes and Newton were amongst the finest scientific minds in the world at the time. They had spend days, weeks, years thinking about the specific problem that they solved, on top of further days, weeks, years, decades of dealing with similar or contributory problems.
And the problems they were solving are now things we teach to school-children.
That's the nature of the beast. Science is hard, and requires a great deal of thought and effort. What's more, it's not a matter of inspiration - you don't suddenly have a flash of insight as a lightbulb appears over your head (fortunately, since both Archimedes and Newton predated Edison). Instead, it's a matter of absorbing obscene amounts of knowledge, training your mind to think in particular patterns and particular paths, and then if you're very lucky you get the moment of insight as everything fits together. (More commonly, you spend years finding hundreds of ways not to build a lightbulb before hitting on the right way. And then some assistant drops it.)
I bring this up because twice in the last two days I've startled LC when I've had moments of insight as I solved work-related problems while doing other things. Which I daresay was rather unsettling for her, but in both cases it was a matter of some huge relief to me as the pieces suddenly lined up neatly.