Shiing-Shen Chern

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Shiing-Shen Chern
Shiing-Shen Chern.jpg
Shiing-Shen Chern, 1976
Born (1911-10-26)October 26, 1911
Jiaxing, Zhejiang, China
Died December 3, 2004(2004-12-03) (aged 93)
Tianjin, China
Nationality Chinese, American
(Multiple Citizenship)
Fields Mathematics
Institutions Tsinghua University
Institute for Advanced Study
University of Chicago
University of California, Berkeley
Nankai University
Alma mater Nankai University
University of Hamburg
Doctoral advisor Wilhelm Blaschke
Doctoral students Louis Auslander
Thomas Banchoff
Manfredo do Carmo
Harold Levine
Alan Weinstein
Shing-Tung Yau
Known for Chern–Simons theory
Chern–Weil theory
Chern class
Notable awards
Shiing-Shen Chern
Traditional Chinese 陳省身
Simplified Chinese 陈省身

Shiing-Shen Chern (Mandarin: [tʂʰən.ɕiŋ.ʂən]; October 26, 1911 – December 3, 2004) was a Chinese-born American mathematician. He was regarded as one of the leaders in differential geometry of the twentieth century.[1]


Early years in China[edit]

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 Li-Fu Chiang (姜立夫), a Harvard-trained 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 Chicago-trained 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 Ko-Chuen, also a Chicago-trained 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[edit]

In 1934, co-funded 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 Cartan-Kähler 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 Sino-Japanese 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[edit]

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[edit]

Chern returned to Shanghai in 1946 to help found the Institute of Mathematics of the Academia Sinica, which was later moved to Nanking (then-capital 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).


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 vice-president 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] Shing-Tung Yau was one of his PhD students during this period.

Short visits to China[edit]

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[edit]

Based on Chern's advice, a mathematical research center was established in Taipei, Taiwan, whose co-operational 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.


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 AllendoerferWeil 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[edit]

Chern received numerous honors and awards in his life, including:

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.


  • 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 Dai-Wai; Chern, Shiing-Shen; Shen, Zhongmin Finsler Geometry
  • Zhongmin Shen, Shiing-shen Chern, Riemann Finsler Geometry
  • Shiing Shen Chern, Selected Papers, Vol I-IV, Springer



His wife, Shih-ning 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 Ching-wu, and a son named Paul (pinyin: Chen Bolong).

Transliteration and pronunciation[edit]

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.

See also[edit]


  1. ^ a b Nigel Hitchin (2014). "Shiing-Shen Chern 26 October 1911 — 3 December 2004". Biographical Memoirs of Fellows of the Royal Society. doi:10.1098/rsbm.2014.0018. 
  2. ^ a b "Shiing-Shen Chern" (in Chinese). Jiaxing Culture. Retrieved Aug 22, 2010. 
  3. ^ a b Robert Sanders, Media Relations (December 6, 2004). "Renowned mathematician Shiing-Shen Chern, who revitalized the study of geometry, has died at 93 in Tianjin, China" (shtml). UC, Berkeley. Retrieved Aug 22, 2010. 
  4. ^ "陳省身 (Shiing-Shen Chern)" (in Chinese). Retrieved Aug 22, 2010. 
  5. ^ National Science Foundation – The President's National Medal of Science
  6. ^ Bryant, Robert; Freed, Dan (January 2006). "Obituary: Shiing-Shen Chern". Physics Today 59 (1): 70–72. doi:10.1063/1.2180187. 
  7. ^ "The IMU Prizes". International Mathematical Union (IMU). Retrieved Aug 22, 2010. 
  8. ^ "The Chern Lectures". UC Berkeley Department of Mathematics. Retrieved Aug 22, 2010. 

External links[edit]