“One day Shizuo Kakutani was teaching a class at Yale. He wrote down a lemma on the blackboard and announced that the proof was obvious. One student timidly raised his hand and said that it wasn’t obvious to him. Could Kakutani explain?
After several moments’ thought, Kakutani realized that he could not himself prove the lemma. He apologized, and said that he would report back at their next class meeting.
After class, Kakutani, went straight to his office. He labored for quite a time and found that he could not prove the pesky lemma. He skipped lunch and went to the library to track down the lemma. After much work, he finally found the original paper. The lemma was stated clearly and succinctly. For the proof, the author had written, ‘Exercise for the reader.’
The author of this 1941 paper was Kakutani.”
from Mathematical Apocrypha by Steven Krantz
Leong, Ng Boon. “What Is The Most Ridiculous Example Of “The Proof Is Left As An Exercise To The Reader” In A Mathematics Book?” 2021. Quora. https://www.quora.com/What-is-the-most-ridiculous-example-of-the-proof-is-left-as-an-exercise-to-the-reader-in-a-mathematics-book.
[Wolfgang] Pauli was lecturing, and he said “this is obvious”. A student raises his hand and says “sorry professor, I don’t think that is obvious”. Pauli stares at the board, back at the students. He thinks for a bit. He starts pacing in front of the class, thinking. He looks back at the board. Eventually he leaves the room, comes back 20 minutes later and says “I’ve thought about it and yes, it is obvious”.
Trent, Ray. “Is It Possible To Solve A Complex Math Problem Just By Looking At It?”. 2023. Quora. https://qr.ae/py18it.
Mathematical Mysteries 