# Shiing-Shen Chern

**Shiing-Shen Chern** (/tʃɜːrn/; Chinese: 陳省身; pinyin: *Chén Xǐngshēn*, Mandarin: [tʂʰən.ɕiŋ.ʂən]; October 26, 1911 – December 3, 2004) was a Chinese-American mathematician who made fundamental contributions to differential geometry and topology. He was widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}

Shiing-Shen Chern spent nearly a decade at the University of Chicago before moving to University of California, Berkeley, where he co-founded the world-renowned Mathematical Sciences Research Institute in 1982 and was the institute's founding director.^{[7]} In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics".^{[8]}

## Contents

## Biography[edit]

### 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 in Tianjin, Chern graduated from Fulun High School (扶輪中學).^{[9]}

At age 15, Chern entered the Faculty of Sciences of the Nankai University in Tianjin, but had problems at the laboratory, so he studied mathematics, instead.^{[10]} Chern graduated with a Bachelor of Science degree in 1930.^{[10]} At Nankai, Chern's mentor was mathematician Jiang Lifu, and Chern was also heavily influenced by the physicist Rao Yutai, considered to be one of the founding fathers of modern Chinese informatics.

Chern went to Beiping (now Beijing) to work at the Tsinghua University Department of Mathematics as a teaching assistant. At the same time he also registered at Tsinghua Graduate School as a student. He studied projective differential geometry under Sun Guangyuan, a University of Chicago-trained geometer and logician who was also from Zhejiang. Sun is another mentor of Chern who is considered a founder of modern Chinese mathematics. In 1932, Chern published his first research article in the Tsing Hua University Journal. In the summer of 1934, Chern graduated from Tsinghua with a master's degree, the first ever master's degree in mathematics issued in China.^{[9]}

Yang Chen-Ning's father—Yang Ko-Chuen, another Chicago-trained professor at Tsinghua, but specialising in algebra, also taught Chern. At the same time, Chern was Chen-Ning Yang's teacher of undergraduate maths at Tsinghua. At Tsinghua, Hua Luogeng, also a mathematician, was Chern's colleague and roommate.

In 1932, Wilhelm Blaschke from the University of Hamburg visited Tsinghua and was impressed by Chern and his research.^{[11]}

### In Europe[edit]

In 1934, Chern received a scholarship to study in the United States, but he wanted to study under well-known geometer Wilhelm Blaschke.^{[10]} Co-funded by Tsing Hua and the Chinese Foundation of Culture and Education, Chern went to continue his study in mathematics in Germany with a scholarship.^{[10]} 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.^{[10]} Blaschke recommended Chern to study in Paris.

It was at this time that he had to choose between the career of algebra in Germany under Emil Artin, and the career of geometry in France under Élie-Joseph Cartan. Chern was tempted by what he called the "organizational beauty" of Emil Artin's algebra, but in the end, he decided to go to France in September 1936.^{[12]} He spent one year at the Sorbonne in Paris.

In August 1936, Chern watched the 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 the summer of 1937, Chern accepted the invitation of Tsing Hua's University and returned to China.^{[12]} He was promoted to professor of mathematics at Tsing Hua. However, in August, the Marco Polo Bridge Incident (near Beijing) happened and the Second Sino-Japanese War started, Tsing Hua was forced to move away from Beijing to west China.^{[13]} Three universities including Peking University, Tsing Hua, and Nankai formed the National Southwestern Associated University (NSAU), and relocated to Kunming, Yunnan province. Chern never reached Beijing. In the same year, Hua Luogeng was promoted to professor of mathematics at Tsinghua.

In 1939, Chern married Shih-Ning Cheng, and the couple had two children by the names of Paul and May.^{[13]}

### Short stay in the United States[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*.^{[13]}

### First return to China[edit]

Chern returned to Shanghai in 1945 to help found the Institute of Mathematics of the Academia Sinica, which was later moved to Nanking^{[13]} (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).

### The United States[edit]

By the end of 1948, Chern returned to the United States because of the Chinese Civil War.^{[13]} He then returned to the IAS.^{[13]} In 1949, Chern became professor of mathematics at the University of Chicago.^{[13]} 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.^{[13]} He worked and stayed there until he became an emeritus professor in 1979.^{[14]} 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.^{[15]}

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.^{[15]} 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 to normalise, and American citizens were allowed to visit P.R.China. In September 1972, Chern visited Beijing with his wife. During this period of time, Chern visited China 25 times, of which 14 were to his home province 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 in October 17, 1985. NKIM was renamed the Chern Institute of Mathematics in 2004 after Chern's death.

### Final years and death[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.^{[16]}

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.His former residence, Ningyuan (宁园), is still in campus of Nankai University, kept in the way when he was living there. Every year at Dec. 3rd, Ningyuan is open for visitors for memorial of him.

## Research[edit]

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.

## Honors and awards[edit]

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

- 1970, Chauvenet Prize, of the Mathematical Association of America;
- 1975, National Medal of Science
^{[17]} - 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;
^{[18]} - 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[edit]

- 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

### Namesake[edit]

- The asteroid 29552 Chern is named after him;
- The Chern Medal, of the International Mathematical Union (IMU);
^{[19]} - The Shiing-Shen 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
*Shiing-Shen Chern Chair in Mathematics*, both at the Department of Mathematics, UC Berkeley.^{[20]}

## Family[edit]

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" (/tʃɜːrn/), and this pronunciation is now universally accepted among English-speaking mathematicians and physicists.

## See also[edit]

- Chern classes
- Chern–Gauss–Bonnet theorem
- Chern–Simons theory
- Chern–Simons form
- Chern–Weil theory
- Chern–Weil homomorphism

## References[edit]

- ^
^{a}^{b}Nigel Hitchin (2014). "Shiing-Shen Chern 28 October 1911 — 3 December 2004".*Biographical Memoirs of Fellows of the Royal Society*. doi:10.1098/rsbm.2014.0018. **^**"Chern biography".*www-history.mcs.st-and.ac.uk*. Retrieved 2017-01-16.**^**"12.06.2004 - Renowned mathematician Shiing-Shen Chern, who revitalized the study of geometry, has died at 93 in Tianjin, China".*www.berkeley.edu*. Retrieved 2017-01-16.**^**Chang, Kenneth (2004-12-07). "Shiing-Shen Chern, 93, Innovator in New Geometry, Dies".*The New York Times*. ISSN 0362-4331. Retrieved 2017-01-16.**^**"Interview with Shiing Shen Chern" (PDF).**^**"Shiing-Shen Chern's Centenary".**^**MSRI. "MSRI".*www.msri.org*. Retrieved 2017-01-16.**^**the_technician. "International Mathematical Union (IMU): Details".*www.mathunion.org*. Archived from the original on August 25, 2010. Retrieved January 16, 2017.- ^
^{a}^{b}"Shiing-Shen Chern" (in Chinese). Jiaxing Culture. Archived from the original on July 25, 2011. Retrieved August 22, 2010. - ^
^{a}^{b}^{c}^{d}^{e}Bruno, Leonard C. (2003) [1999].*Math and mathematicians : the history of math discoveries around the world*. Baker, Lawrence W. Detroit, Mich.: U X L. p. 72. ISBN 0787638137. OCLC 41497065. **^**Chern, S. S.; Tian, G.; Li, Peter, eds. (1996).*A mathematician and his mathematical work: selected papers of S. S. Chern*. pp. 48–49.- ^
^{a}^{b}Bruno, Leonard C. (2003) [1999].*Math and mathematicians : the history of math discoveries around the world*. Baker, Lawrence W. Detroit, Mich.: U X L. p. 73. ISBN 0787638137. OCLC 41497065. - ^
^{a}^{b}^{c}^{d}^{e}^{f}^{g}^{h}Bruno, Leonard C. (2003) [1999].*Math and mathematicians : the history of math discoveries around the world*. Baker, Lawrence W. Detroit, Mich.: U X L. p. 74. ISBN 0787638137. OCLC 41497065. **^**Bruno, Leonard C. (2003) [1999].*Math and mathematicians : the history of math discoveries around the world*. Baker, Lawrence W. Detroit, Mich.: U X L. ISBN 0787638137. OCLC 41497065.- ^
^{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. **^**"陳省身 (Shiing-Shen 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: Shiing-Shen Chern".*Physics Today*.**59**(1): 70–72. doi:10.1063/1.2180187.**^**"The IMU Prizes". International Mathematical Union (IMU). Archived from the original on August 18, 2010. Retrieved August 22, 2010.**^**"The Chern Lectures". UC Berkeley Department of Mathematics. Archived from the original on June 7, 2011. Retrieved August 22, 2010.

## External links[edit]

Wikimedia Commons has media related to .Shiing-Shen Chern |

Wikiquote has quotations related to: Shiing-Shen Chern |

- UC Berkeley obituary
- 1998 interview in
*Notices of the American Mathematical Society* - Shiing-Shen Chern at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Shiing-Shen Chern",
*MacTutor History of Mathematics archive*, University of St Andrews. - Shiing-shen Chern: 1911–2004 by H. Wu, biography and overview of mathematical work.
- "Shiing-Shen Chern (1911–2004)" (PDF),
*Notices of the American Mathematical Society*, Providence, Rhode Island: American Mathematical Society,**58**(9): 1226–1249, October 2011 - Chern's Work in Geometry, by Shing-Tung Yau

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