Mitio (Michio) Nagumo (; May 7, 1905 – February 6, 1995) was a

Japanese Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspor ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, who specialized in the theory of differential equations. He gave the first

necessary and sufficient condition In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...

for positive invariance of

closed set In geometry, topology, and related branches of mathematics, a closed set is a Set (mathematics), set whose complement (set theory), complement is an open set. In a topological space, a closed set can be defined as a set which contains all its lim ...

s under the flow induced by ordinary differential equations ( Nagumo/Bony-Brezis theorem).

Biography

Mitio Nagumo graduated from the Department of Mathematics at the

Imperial University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

in March 1928. In March 1931 he was appointed Lecturer in the Faculty of Technology at the Imperial University of Kyushu. In February 1932 he left

Japan Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...

for an academic visit to

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, where he remained for two years. Upon his return from

in March 1934, he was appointed Lecturer in the Department of Mathematics at the Imperial University of Osaka, and was promoted to Associate Professor in September that year, becoming Professor in the Faculty of Science in March 1936. In March 1937 Nagumo received a

Doctor of Science A Doctor of Science (; most commonly abbreviated DSc or ScD) is a science doctorate awarded in a number of countries throughout the world. Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the s ...

degree from the

. In the 1960s he made a number of academic visits abroad, spending time at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

(where he visited Kurt Friedrichs and other old acquaintances from his time at

) and the

Federal University of Rio Grande do Sul The Federal University of Rio Grande do Sul (, UFRGS) is a Brazilian Public university, public National university, federal research university based in Porto Alegre, Rio Grande do Sul. UFRGS is among the largest and highest-rated universities ...

in 1960, followed by a visit to the

National Tsing Hua University National Tsing Hua University (NTHU) is a public research university in Hsinchu, Taiwan. It was first founded in Beijing. After the Chinese Civil War, president Mei Yiqi and other academics relocated with the retreating Nationalist government to ...

in 1963-64. He retired from

Osaka University The , abbreviated as UOsaka or , is a List of national universities in Japan, national research university in Osaka, Japan. The university traces its roots back to Edo period, Edo-era institutions Tekijuku (1838) and Kaitokudō, Kaitokudo (1724), ...

in December 1966, after which he was granted the title of Honorary Professor. He was subsequently appointed Professor at

Sophia University Sophia University (Japanese language, Japanese: 上智大学, ''Jōchi Daigaku''; Latin: ''Universitas Sedis Sapientiae'') is a private List of Jesuit educational institutions, Jesuit research university in Tokyo, Tokyo, Japan. Founded in 1913 by ...

, from which he retired in March 1976, having reached

mandatory retirement Mandatory retirement also known as forced retirement, enforced retirement or compulsory retirement, is the set age at which people who hold certain jobs or offices are required by industry custom or by law to leave their employment, or retire. A ...

age. Much of Nagumo's original work was published in

and

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

, however his research and teaching have influenced numerous mathematicians (especially in

) who have since made many of his results available in English.

Works

* * * * * * *

Literature

* *

References

{{DEFAULTSORT:Nagumo, Mitio 1905 births 1995 deaths 20th-century Japanese mathematicians University of Tokyo alumni Academic staff of Kyushu University Academic staff of Osaka University Academic staff of Sophia University Scientists from Yamagata Prefecture