Shiing-shen Chern (陳省身; Pinyin: Chén Xǐngshēn; born October 26 1911) is a Chinese mathematician, who was one of the leading differential geometers of the twentieth century.
He was born in Kashing (嘉興), Chekiang Province（浙江省） in China. From 1926, he was a student at Nankai University in Tientsin (where he moved to be with his father four years earlier), graduating in mathematics in 1930. He was a research student under Dan Sun at Tsing Hua University from 1931 to 1934, working on projective differential geometry.
In 1934 he went to Hamburg, working on the Cartan-Kähler theory, and finishing a higher degree in 1936. In 1936-1937 he learned directly from Élie Cartan in Paris, returning to China to a professorial position in Tsing Hua (which had evacuated to Kunming after the Japanese attacks).
In 1943 Chern came to the Institute for Advanced Study at Princeton, working there on characteristic classes in differential geometry. He returned to China, to Shanghai in 1947. 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.
Chern's work spreads over all the classic fields of differential geometry. It includes areas currently fashionable (the Chern-Simons theory arising from a joint paper in 1974), 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 In his contribution to the IMU Millennium volume, Chern proposed that Finsler metrics would be important to the mathematics of the twenty-first century.
He was awarded a Wolf Prize in mathematics, in 1984.
Chern is married to Zheng Shining (鄭士寧) with a daughter, Pu Chern (陳璞).