Mathematician:Shizuo Kakutani

Mathematician
Japanese-American mathematician, best known for his Kakutani Fixed-Point Theorem.

Nationality
Japanese-American

History

 * Born: August 28, 1911 in Ōsaka
 * Died: August 17, 2004 in New Haven, Connecticut

Theorems and Definitions

 * Kakutani Skyscraper


 * Kakutani's Theorem
 * Kakutani Fixed-Point Theorem
 * Markov-Kakutani Fixed-Point Theorem (with )
 * Kakutani's Theorem (Geometry)
 * Kakutani-Rokhlin Lemma (with )
 * Riesz-Markov-Kakutani Representation Theorem (with and )

Critical View

 * 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 by

Also known as
In Japanese: 角谷 静夫

Also rendered Kakutani Shizuo