# ShiingShen Chern

**Shiing-Shen Chern** (陳省身; pinyin: Chén Xǐngshēn; October 26 1911–December 3 2004) was a Chinese mathematician, who was one of the leading differential geometers of the twentieth century.

His last name is pronounced "Chen", a common Chinese surname; the spelling "Chern" is the transliteration in the old Gwoyeu Romatzyh romanization, with the silent "r" indicating a second-tone syllable in Mandarin, which is a tonal language.

## Contents

## Background

He was born in Kashing, Chekiang Province in China (today known as Jiaxing in Zhejiang province). He moved to Tientsin (today known as Tianjin) in 1922 to be with his father, and from 1926 he was a student at Nankai University in that city, graduating in mathematics in 1930. He was a master student under Dan Sun at Tsing Hua University from 1931 to 1934, working on projective differential geometry.

He died at Nankai University, Tianjin at the age of 93. The asteroid 29552 Chern is named after him.

## His European studies

In 1932 Wilhelm Blaschke from the University of Hamburg visited Tsing Hua and was impressed with Chern. In 1934 Chern went on a scholarship to Hamburg, working on the Cartan-Kähler theory, and finishing his Ph.D. degree in 1936. In 1936–1937 he learned directly from Élie Cartan in Paris, returning to Beijing, China to a professorial position in Tsing Hua (which had evacuated to Kunming after the Japanese attacks).

## In America

In 1943 Chern went to the Institute for Advanced Study (IAS) at Princeton, working there on characteristic classes in differential geometry. Shortly afterwards, he was invited by Solomon Lefschetz to be an editor of *Annals of Mathematics*.

He returned to Shanghai in 1946 to found the Mathematical Institute of Academia Sinica, which was later moved to Nanking. From 1948 he was again at the IAS, becoming a professor at the University of Chicago in 1949.

He moved to the University of California, Berkeley in 1960. The next year he became a naturalized citizen of the United States. At Berkeley, he founded the Mathematical Sciences Research Institute (MSRI) in 1981 and acted as the director until 1984. In 1985 he founded the Nankai Insititute of Mathematics in Tientsin.

## Research

Chern's work spreads over all the classic fields of differential geometry. It includes areas currently fashionable (the Chern-Simons theory arising from a 1974 paper written jointly with Jim Simons), perennial (the Chern-Weil theory linking curvature invariants to characteristic classes from 1944, after the Allendoerfer-Weil paper of 1943 on the Gauss-Bonnet theorem), the quotidian (Chern classes), and some areas such as projective differential geometry and webs that have a lower profile. He published results in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.

He was a true follower of Élie Cartan, working intensely on the 'theory of equivalence' in his time in China from 1937-1943, in relative isolation. In 1954 he published his own treatment of the pseudogroup problem that is in effect the touchstone of Cartan's geometric theory. He used the moving frame method with success only matched by its inventor; he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory. Indeed, one of his books is entitled, "Complex Manifolds without Potential Theory"! In his contribution to the IMU Millennium volume, Chern proposed that Finsler metrics would be important to the mathematics of the twenty-first century.

## Awards

He was awarded a National Medal of Science in 1975; a Wolf Prize in mathematics in 1984; and a Shaw Prize in mathematical sciences in May, 2004.

## Family

His wife, Shih-ning (Cheng) Chern, whom he married in Kunming in 1939, died in 2000. They had a daughter, May Chu, and a son, Paul.

## See also

See also: Chern-Gauss-Bonnet theorem, Chern-Weil homomorphism.