Just because he wrote it doesn't mean he understands. That is left to the student as an exercise.
Walter Rudin and his band of Analysis thugs released their new Hit "Proof left as an Exercise" followed by their debut single "It's Obvious"
This reminds me of a tutorial I had. The professor was about to explain how to do a 3 part question, and this is what he said: "Part 1 is trivial, part 2 is straight forward, part 3 is...." (after thinking for a moment) "...obvious". No Shit, Sherlock! What was the point of these tutorials again?
Granted, the question wasn't difficult. But still, that was one of the more useless things I've heard in a tutorial.
From the Futility Closet:
"One day while teaching a class at Yale, Shizuo Kakutani wrote a lemma on the blackboard and remarked that the proof was obvious. A student timidly raised his hand and said that it wasn’t obvious to him. Kakutani stared at the lemma for some moments and realized that he couldn’t prove it himself. He apologized and said he would report back at the next class meeting.
After class he went straight to his office and worked for some time further on the proof. Still unsuccessful, he skipped lunch, went to the library, and tracked down the original paper. It stated the lemma clearly but left the proof as an “exercise for the reader.”
The author was Shizuo Kakutani."
Yes--sometimes it is obvious, but you have to get into just the right frame of mind to get the perspective where it is elementary. That's when I wish these sort of shortcuts--obvious, trivial, left as exercise--were outlawed. At least in published papers.
Wait, but then the perceived laziness of mathematicians would disintegrate! Think of all the children who look up to mathematicians, and hope that one day, with hard work, they too will be able so lazy!