This is a very soft question, and I ask it with some trepidation.
When I begin studying a new topic, I don’t feel I really understand it until I go to bed Friday thinking I’ve found an inconsistency in mathematics, spend Saturday mulling over the problem, and awaken Sunday seeing my mistake.
Do others have the same experience, or is it just me?
I don't mean I literally think there's an inconsistency. But the issue gnaws at me, making it impossible to think about anything else. Whereas if I'm stuck solving a problem or completing a proof, I can let it go.
This experience always occurs in the context of a concrete example. Here's an instance, as best I can recall.
When I first started learning complex analysis, I computed a residue two different ways, getting different answers. Eventually I realized I was unconsciously assuming this "fact": if $\lim_{z\rightarrow a}f(z)=c\neq\infty$, and the residue of $g(z)$ at $a$ is 0, then the residue of $f(z)g(z)$ at $a$ will also be 0. (Hey, it's true if $c\neq0$! And if $c=0$, doesn't that create even more "pressure" on the residue to be 0?) As I said, I didn't realize I was assuming this ($f(x)$ and $g(x)$ were pretty complicated, and just a piece of the whole computation), and once I stated it explicitly I saw my error.
