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I'm often frightened by how spontaneously my brain seems to come up with something, because it could just as easily stop doing that and I'd have no idea how to fix it.

I once walked past a math book one of my friends had left open, glanced over, stopped, pointed to a formula, and said, "This is wrong." (Which it was.) I only did it that once, but it's the sort of anecdote you can tell for the rest of your life. And if my brain stopped doing that, I'd be screwed.

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You're lucky! I'll never get the same innate ability for problem solving, but what I'm hoping is that it's actually possible to train my brain towards such spontaneity.

E.g., by spending time to solve a lot of challenging puzzles over a long period of time. It's like when you try to remember a shopping list by visualizing the items. After repeating the items enough times, you don't visualize the list anymore; you just know it.

I remember in fifth grade we were learning to multiply 3 digit by 3 digit numbers. My teacher wrote two 3 digit numbers on the board and I immediately blurted out the answer. He looked down at his notes, and just looked back at me, I had been right.

Like you, I've never had this experience again. It makes this feel true: http://xkcd.com/447/

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