# Kakutani's Lemma

I read this story a while ago, and I'm wondering whether there's any proof that it is true or whether it's just made up?

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.

• Various versions of this joke are told about various mathematicians. In one version, the lecturer after 10 minutes of thinking finally says: "Yes, it is indeed obvious". Dec 29, 2016 at 12:50
• Wikipedia says K. published his fixed-point theorem in 1941. en.wikipedia.org/wiki/Kakutani_fixed-point_theorem Dec 29, 2016 at 20:14
• @Spencer did you check that paper yourself? It is short and no lemma in it is left as an exercise.
– KCd
Dec 30, 2016 at 14:07
• @KCd behind a paywall? No way. Anyway, if the story is apocryphal there wouldn't be an exercise left for the reader. Dec 30, 2016 at 15:07
• @Spencer there are ways of getting around a paywall (heard of Sci-Hub?).
– KCd
Dec 30, 2016 at 17:32