ShiingShen Chern
ShiingShen Chern
ShiingShen Chern  

ShiingShen Chern, 1976


Born  Jiaxing, Zhejiang, China 
October 26, 1911
Died  December 3, 2004 Tianjin, China 
(aged 93)
Nationality  Chinese, American (Multiple Citizenship) 
Fields  Mathematics 
Institutions  Tsinghua University Institute for Advanced Study University of Chicago University of California, Berkeley Nankai University CMS 
Alma mater  Nankai University University of Hamburg 
Doctoral advisor  Wilhelm Blaschke 
Doctoral students  Louis Auslander Thomas Banchoff Manfredo do Carmo Harold Levine Alan Weinstein ShingTung Yau 
Known for  Chern–Simons theory Chern–Weil theory Chern class 
Notable awards 

ShiingShen Chern  
Traditional Chinese  陳省身  

Simplified Chinese  陈省身  

ShiingShen Chern (Mandarin: [tʂʰən.ɕiŋ.ʂən]; October 26, 1911 – December 3, 2004) was a Chineseborn American mathematician. He was regarded as one of the leaders in differential geometry of the twentieth century.^{1}
Contents
Biography
Early years in China
Chern was born in Xiushui County (秀水縣), Jiaxing, in Zhejiang province. The year after his birth, China changed its regime from the Qing Dynasty to the Republic of China. He graduated from Xiushui Middle School (秀水中學) and subsequently moved to Tianjin in 1922 to accompany his father. In 1926 after spending four years, Chern graduated from Fulun High School (扶輪中學) in Tianjin.^{2}
At age 15, Chern entered the Faculty of Sciences of the Nankai University in Tianjin, studied mathematics there, and graduated with BSc in 1930. At Nankai, Chern's mentor was LiFu Chiang (姜立夫), a Harvardtrained geometer who was also from Zhejiang.
At Nankai, Chern was also heavily influenced by physicist Hu Guoding (胡國定) who was also from Zhejiang. Hu now is considered as one of founding fathers of modern Chinese informatics.
Chern went to Beiping (now Beijing) to teach at the Tsinghua University Department of Mathematics as a teaching assistant. At the same time he also registered at Tsinghua Graduate School as a master student. He studied projective differential geometry under Prof. Sun Guangyuan, a Chicagotrained geometer and logician who was also from Zhejiang. Sun was a notable founder of modern Chinese mathematics. In 1932, Chern published his first research article in Tsinghua University Journal. In summer 1934, Chern graduated from Tsinghua with a master's degree, the first ever masters degree in mathematics issued by China.^{2}
C.N. Yang's father — Yang KoChuen, also a Chicagotrained professor at Tsinghua but algebraist, also taught Chern. At the same time, Chern was C.N. Yang's teacher of undergraduate math at Tsinghua.
At Tsinghua, Hua Luogeng, also a mathematician, was Chern's colleague and room mate.
In 1932, Wilhelm Blaschke from the University of Hamburg visited Tsinghua and was impressed by Chern and his research.
In Europe
In 1934, cofunded by Tsinghua and the Chinese Foundation of Culture and Education, Chern went to continue his study in mathematics in Germany with a scholarship. Chern studied at the University of Hamburg and worked under Blaschke's guidance first on the geometry of webs then on the CartanKähler theory. He obtained his Dr. rer.nat. (Doctor of Science, which is equivalent to PhD) degree in February, 1936. Blaschke recommended Chern to study in Paris.
In August 1936, Chern watched summer Olympics in Berlin together with Hua Luogeng who paid Chern a brief visit. During that time, Hua was studying at the University of Cambridge in Britain.
In September 1936, Chern went to Paris and worked with Élie Cartan. Chern spent one year at the Sorbonne in Paris.
In 1937, Chern accepted Tsinghua's invitation and was promoted to professor of mathematics at Tsinghua. However, at the same time the Marco Polo Bridge Incident (near Beijing) happened and the Second SinoJapanese War started, Tsinghua was forced to move away from Beijing to west China. Three universities including Peking University, Tsinghua, and Nankai formed the National Southwestern Associated University (NSAU), and was relocated in Kunming, Yunnan province. Chern never reached Beijing. In the same year, Hua Luogeng was promoted to professor of mathematics at Tsinghua.
Short stay in USA
In July 1943, Chern went to the United States, and worked at the Institute for Advanced Study (IAS) in Princeton on characteristic classes in differential geometry. Shortly afterwards, he was invited by Solomon Lefschetz to be an editor of Annals of Mathematics.
First return to China
Chern returned to Shanghai in 1946 to help found the Institute of Mathematics of the Academia Sinica, which was later moved to Nanking (thencapital of the Republic of China). Chern was the acting president of the institute. Wu Wenjun was Chern's graduate student at the institute.
In 1948, Chern was elected one of the first academicians of the Academia Sinica. He was the youngest academician elected (at age 37).
USA
In 1949, Chern returned to the United States, again worked at the IAS. In 1949, Chern became professor of mathematics at the University of Chicago. Coincidentally, Ernest Preston Lane, former Chair at UChicago Department of Mathematics, was the doctoral advisor of Chern's undergraduate mentor at Tsinghua — Sun Guangyuan.
Chern moved to the University of California, Berkeley, in 1960, where he worked and stayed until his retirement in 1979. In 1961, Chern became a naturalized citizen of the United States. In the same year, he was elected member of the United States National Academy of Sciences.^{3}
In 1964, Chern was a vicepresident of American Mathematical Society (AMS).
Chern retired from Berkeley in 1981. He founded the Mathematical Sciences Research Institute (MSRI) in 1981 and served as the director until 1984. Afterward he became the honorary director of the institute. MSRI now is one of the largest and most prominent mathematical institutes in the world.^{3} ShingTung Yau was one of his PhD students during this period.
Short visits to China
The Shanghai Communiqué was issued by the United States and the People's Republic of China on February 27, 1972. The relationship between these two nations started normalizing, and American citizens were allowed to visit P.R.China. In September 1972, Chern with his wife visited Beijing. During this period of time, Chern visited China for 25 times, with 14 times to his hometown Zhejiang.
Chern founded the Nankai Institute for Mathematics (NKIM) at his alma mater Nankai in Tianjin. The institute was formally established in 1984 and fully opened on October 17, 1985. NKIM was renamed as the Chern Institute of Mathematics in 2004 after Chern's death.
Final years
Based on Chern's advice, a mathematical research center was established in Taipei, Taiwan, whose cooperational partners are National Taiwan University, National Tsing Hua University and the Sinica Academia Institute of Mathematics.^{4}
Chern was also a director and advisor of the Center of Mathematical Sciences at Zhejiang University in Hangzhou, Zhejiang.
From 2000 to his death, Chern lived in Tianjin, China. Chern died of heart failure at his home in Tianjin in 2004 at age 93.
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
Chern received numerous honors and awards in his life, including:
 1970, Chauvenet Prize, of the Mathematical Association of America;
 1975, National Medal of Science^{5}
 1982, Humboldt Prize, Germany;
 1983, Leroy P. Steele Prize, of the American Mathematical Society;
 1984, Wolf Prize in Mathematics, Israel;
 2002, Lobachevsky Medal;
 2004 May, Shaw Prize in mathematical sciences, Hong Kong;^{6}
 1948, Academician, Academia Sinica;
 1950, Honorary Member, Indian Mathematical Society;
 1961, Member, United States National Academy of Sciences;
 1963, Fellow, American Academy of Arts and Sciences;
 1971, Corresponding Member, Brazilian Academy of Sciences;
 1983, Associate Founding Fellow, TWAS;
 1985, Foreign Fellow, Royal Society of London, UK;
 1986, Honorary Fellow, London Mathematical Society, UK;
 1986, Corresponding Member, Academia Peloritana, Messina, Sicily;
 1987, Honorary Life Member, New York Academy of Sciences;
 1989, Foreign Member, Accademia dei Lincei, Italy;
 1989, Foreign Member, Académie des sciences, France;
 1989, Member, American Philosophical Society;
 1994, Foreign Member, Chinese Academy of Sciences.
Chern was given a number of honorary degrees, including from The Chinese University of Hong Kong (LL.D. 1969), University of Chicago (D.Sc. 1969), ETH Zurich (Dr.Math. 1982), SUNY Stony Brook (D.Sc. 1985), TU Berlin (Dr.Math. 1986), his alma mater Hamburg (D.Sc. 1971) and Nankai (honorary doctorate, 1985), etc.
Chern was also granted numerous honorary professorships, including at Peking University (Beijing, 1978), his alma mater Nankai (Tianjin, 1978), Chinese Academy of Sciences Institute of Systems Science (Beijing, 1980), Jinan University (Guangzhou, 1980), Chinese Academy of Sciences Graduate School (1984), Nanjing University (Nanjing, 1985), East China Normal University (Shanghai, 1985), USTC (Hefei, 1985), Beijing Normal University (1985), Zhejiang University (Hangzhou, 1985), Hangzhou University (1986, the university was merged into Zhejiang University in 1998), Fudan University (Shanghai, 1986), Shanghai University of Technology (1986, the university was merged to establish Shanghai University in 1994), Tianjin University (1987), Tohoku University (Sendai, Japan, 1987), etc.
Publication
 Shiing Shen Chern, Topics in Differential Geometry, Princeton 1951
 Shiing Shen Chern Differential Manifolds 1953 University of Chicago
 Shiing Shen Chern, Complex Manifolds University of Chicago, 1956
 Shiing Shen Chern:Complex manifolds without potential theory
 Shiing Shen Chern, Minimal Sumanifolds in a Riemannian Manifold University of Kansas 1968
 Bao, David DaiWai; Chern, ShiingShen; Shen, Zhongmin Finsler Geometry
 Zhongmin Shen, Shiingshen Chern, Riemann Finsler Geometry
 Shiing Shen Chern, Selected Papers, Vol IIV, Springer
Namesake
 The asteroid 29552 Chern is named after him;
 The Chern Medal, of the International Mathematical Union (IMU);^{7}
 The ShiingShen Chern Prize (陳省身獎), of the Association of Chinese Mathematicians;
 The Chern Institute of Mathematics at Nankai University, Tianjin, China;
 The Chern Lectures, and the ShiingShen Chern Chair in Mathematics, both at the Department of Mathematics, UC Berkeley.^{8}
Family
His wife, Shihning Cheng(Chinese: 鄭士寧; pinyin: Zheng Shining), whom he married in 1939, died in 2000. He also had a daughter, May Chu (Chinese: 陳璞; pinyin: Chen Pu), wife of the physicist Chu Chingwu, 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 secondtone syllable, written "Chén" in pinyin but in practice often written by nonChinese without the tonal mark. In GR the spelling of his given name "ShiingShen" 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 Englishspeaking mathematicians and physicists.
See also
 Chern classes
 Chern–Gauss–Bonnet theorem
 Chern–Simons theory
 Chern–Simons form
 Chern–Weil theory
 Chern–Weil homomorphism
References
 ^ ^{a} ^{b} Nigel Hitchin (2014). "ShiingShen Chern 26 October 1911 — 3 December 2004". Biographical Memoirs of Fellows of the Royal Society. doi:10.1098/rsbm.2014.0018.
 ^ ^{a} ^{b} "ShiingShen Chern" (in Chinese). Jiaxing Culture. Retrieved Aug 22, 2010.
 ^ ^{a} ^{b} Robert Sanders, Media Relations (December 6, 2004). "Renowned mathematician ShiingShen Chern, who revitalized the study of geometry, has died at 93 in Tianjin, China" (shtml). UC, Berkeley. Retrieved Aug 22, 2010.
 ^ "陳省身 (ShiingShen Chern)" (in Chinese). mathland.idv.tw. Retrieved Aug 22, 2010.
 ^ National Science Foundation – The President's National Medal of Science
 ^ Bryant, Robert; Freed, Dan (January 2006). "Obituary: ShiingShen Chern". Physics Today 59 (1): 70–72. doi:10.1063/1.2180187.
 ^ "The IMU Prizes". International Mathematical Union (IMU). Retrieved Aug 22, 2010.
 ^ "The Chern Lectures". UC Berkeley Department of Mathematics. Retrieved Aug 22, 2010.
External links
 UC Berkeley obituary
 1998 interview in Notices of the American Mathematical Society
 ShiingShen Chern at the Mathematics Genealogy Project
 O'Connor, John J.; Robertson, Edmund F., "ShiingShen Chern", MacTutor History of Mathematics archive, University of St Andrews.
 Chern's Work in Geometry by ShingTung Yau
 Shiingshen Chern: 1911–2004 by H. Wu, biography and overview of mathematical work.
 ShiingShen Chern (1911–2004) (PDF), Notices of the American Mathematical Society (Providence, Rhode Island: American Mathematical Society) 58 (9), October 2011: 1226–1249



 1911 births
 2004 deaths
 20thcentury American mathematicians
 21stcentury American mathematicians
 American science writers
 Chinese emigrants to the United States
 Differential geometers
 Educators from Jiaxing
 Foreign Members of the Royal Society
 Institute for Advanced Study faculty
 Members of the French Academy of Sciences
 National Medal of Science laureates
 Members of Academia Sinica
 Nankai University alumni
 People from Jiaxing
 Princeton University faculty
 Recipients of the National Order of Scientific Merit (Brazil)
 Tsinghua University alumni
 University of California, Berkeley faculty
 University of Chicago faculty
 University of Hamburg alumni
 Wolf Prize in Mathematics laureates
 Writers from Jiaxing
 Zhejiang University faculty
 Members of the United States National Academy of Sciences
 Guggenheim Fellows
 Members of the American Philosophical Society