That's assuming, of course, you never ever try to solve a problem with anyone else before grad school. That seems possible but highly unlikely.

After five or six lines he stopped, scratched his head, looked at the proof, and crossed out the last line he'd written. Then he looked at it some more. After a couple of minutes he looked up, apologised, and said he'd got stuck and that we'd go back over it in the next lecture.

It was a great relief to me that my own struggles were not the result of laziness or stupidity: some things are just hard, and take a while to get right, and it's rare to be able to write down something in its correct form on the first pass.