In college I used to study a class ahead to be ready with questions. A professor said that something couldn’t be done analytically, but I just hours before had learned the proof of the analytical solution so I told them it could be done, he said it couldn’t, I said I can prove it. He gave me the chalk I went to the board and prove the analytical solution. He was like wow, I didn’t knew that. He gave me extra credits on the final for that.