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Shiing-Shen Chern (simplified Chinese: 陈省身; traditional Chinese: 陳省身; pinyin: Chén Xǐngshēn, October 26, 1911 – December 3, 2004) was a Chinese American mathematician, one of the leaders in differential geometry of the twentieth century.

Biography

Chern was born in Jiaxing in Zhejiang province. He moved to Tianjin in 1922 to be with his father, and starting in 1926 he studied there at Nankai University, graduating in mathematics in 1930. He was a graduate student under Dan Sun at Tsinghua University from 1931 to 1934, working on projective differential geometry.

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

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 Chern Institute of Mathematics (part of Nankai University) in Tianjin, where he died in 2004 at the age of 93. Chern was also a director and advisor of the Center of Mathematical Sciences at Zhejiang University in Hangzhou until his death.

Research

Chern's work extends 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 foundational (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 follower of Élie Cartan, working on the 'theory of equivalence' in his time in China from 1937 to 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 the last years of his life, he advocated the study of Finsler geometry, writing several books and articles on the subject.

Honours and awards

* National Medal of Science (1975)[1]
* Leroy P. Steele Prize, 1983;
* Wolf Prize in mathematics, 1984;
* Lobachevsky Medal, 2002;
* Shaw Prize in mathematical sciences, May 2004;
* The asteroid 29552 Chern is named after him.
* The Chern Medal is named in his honour.

Family

His wife, Shih-ning Cheng(Chinese: 郑士宁; pinyin: Zheng Shining), who he married in 1939, died in 2000. He also had a daughter, May Chu (Chinese: 陈璞; pinyin: Chen Pu), wife of the physicist Chu Ching-wu, and a son named Paul (pinyin: Chen Bolong).

Transliteration and pronunciation

Chern's surname is a common Chinese surname which is now usually spelt Chen. The unusual spelling "Chern" is a transliteration in the old Gwoyeu Romatzyh (GR) romanization for Mandarin Chinese used in the early twentieth century China. It uses special spelling rules to indicate different tones of Mandarin, which is a tonal language with four tones. The silent r in "Chern" indicates a second-tone syllable, written "Chén" in pinyin but in practice often written by non-Chinese without the tonal mark. In GR the spelling of his given name "Shiing-Shen" indicates a third tone for Shiing and a first tone for Shen, which are equivalent to the syllables "Xǐngshēn" in pinyin.

In English, Chern pronounced his name "Churn," and this pronunciation is now universally accepted among English-speaking mathematicians and physicists.

References

1. ^ National Science Foundation - The President's National Medal of Science