He gave the first necessary and sufficient condition for positive invariance of closed sets under the flow induced by ordinary differential equations (Nagumo/Bony-Brezis theorem).
[2] Mitio Nagumo graduated from the Department of Mathematics at the Imperial University of Tokyo in March 1928.
In February 1932 he left Japan for an academic visit to Göttingen, where he remained for two years.
In March 1937 Nagumo received a Doctor of Science degree from the Imperial University of Tokyo.
[1] Much of Nagumo's original work was published in Japanese and German,[1] however his research and teaching have influenced numerous mathematicians (especially in Japan) who have since made many of his results available in English.