Shiing-Shen Chern

Chern's surname (traditional: 陳, simplified: 陈, pinyin: Chén) is a common Chinese surname which is now usually romanized as Chen. The unusual spelling "Chern" is from the Gwoyeu Romatzyh (GR) romanization system. In English, Chern pronounced his own name with the "r" (). == Biography ==

Early years in China Chern was born in Xiushui, Jiaxing, China in 1911. He graduated from Xiushui Middle School () and subsequently moved to Tianjin in 1922 to accompany his father. In 1926, after spending four years in Tianjin, Chern graduated from . At age 15, Chern entered the Faculty of Sciences of the Nankai University in Tianjin and was interested in physics, but not so much the laboratory, so he studied mathematics instead. Chern graduated with a Bachelor of Science degree in 1930. 1934–1937 in Europe In 1934, Chern received a scholarship to study in the United States at Princeton and Harvard, but at the time he wanted to study geometry and Europe was the center for the maths and sciences. For his third year, Blaschke recommended Chern to study at the University of Paris. He spent one year at the Sorbonne in Paris. There he met Cartan once a fortnight. Chern said: Three universities including Peking University, Tsinghua, and Nankai formed the temporary National Southwestern Associated University (NSAU), and relocated to Kunming, Yunnan province. Chern never reached Beijing. In 1939, Chern married Shih-Ning Cheng, and the couple had two children, Paul and May.... we seemed to share a common attitude towards such subjects, or towards mathematics in general; we were both striving to strike at the root of each question while freeing our minds from preconceived notions about what others might have regarded as the right or the wrong way of dealing with it.It was at the IAS that his work culminated in his publication of the generalization of the famous Gauss–Bonnet theorem to higher dimensional manifolds, now known today as the Chern theorem. It is widely considered to be his magnum opus. In 1961, Chern naturalized as U.S. citizen of the United States. My election to the US National Academy of Sciences was a prime factor for my US citizenship. In 1960 I was tipped about the possibility of an academy membership. Realizing that a citizenship was necessary, I applied for it. The process was slowed because of my association to Oppenheimer. As a consequence I became a US citizen about a month before my election to academy membership.In 1964, Chern was a vice president of American Mathematical Society (AMS). Chern retired from UC Berkeley in 1979 although he still taught Special Topic classes until at least 1983. In 1981, together with colleagues Calvin C. Moore and Isadore Singer, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley, serving 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.Chern and I and many others felt that we have the responsibility to try to create more understanding between the American people and the Chinese people, and... all of us shared the desire to promote more exchanges. Final years and death In 1999, Chern moved from Berkeley back to Tianjin, China permanently until his death. In 2002, he convinced the Chinese government (the PRC) for the first time to host the International Congress of Mathematicians in Beijing.The great Confucius guided China spiritually for over 2,000 years. The main doctrine is “仁” pronounced “ren”, meaning two people, i.e., human relationship. Modern science has been highly competitive. I think an injection of the human element will make our subject more healthy and enjoyable. Let us wish that this congress will open a new era in the future development of math. Chern was also a director and advisor of the Center of Mathematical Sciences at Zhejiang University in Hangzhou, Zhejiang. Chern died of heart failure at Tianjin Medical University General Hospital in 2004 at age 93. In 2010 George Csicsery featured him in the documentary short Taking the Long View: The Life of Shiing-shen Chern. His former residence, Ningyuan (), is still on the campus of Nankai University, maintained as when he was living there. Every year on December 3, Ningyuan is open for visitors in memory of Chern. ==Research==

Physics Nobel Prize winner (and former student) C. N. Yang has said that Chern is on par with Euclid, Gauss, Riemann, Cartan. Two of Chern's most important contributions that have reshaped the fields of geometry and topology include • Chern–Gauss–Bonnet theorem, the generalization of the famous Gauss–Bonnet theorem (100 years earlier) to higher dimensional manifolds. Chern considers this his greatest work. • Chern–Simons theory arising from a 1974 paper written jointly with Jim Simons; and also gauge theory, Chern–Simons form, Chern-Simons field theory. CS theory now has great importance in knot theory and modern string theory and condensed matter physics research, including Topological phases of matter and Topological quantum field theory. • Chern–Weil theory linking curvature invariants to characteristic classes from 1944 • class theory for Hermitian manifolds • Chern-Bott theory, including the Chern-Bott theorem, a famous result on complex geometrizations of complex value distribution functions • value distribution theory of holomorphic functions • Chern-Lashof theory on tight immersions, compiled in a monograph over 30 years with Richard Lashof at Chicago • Chern-Lashof theorem: a proof was announced in 1989 by Sharpe • projective differential geometry • webs • integral geometry, including the 'moving theorem' (), in collaboration with Yan Zhida • minimal surfaces, minimal submanifolds and harmonic mappings • Exterior Differential Systems and Partial Differential Equations 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". Differential forms Along with Cartan, Chern is one of the mathematicians known for popularizing the use of differential forms in math and physics. In his biography, Richard Palais and Chuu-Lian Terng have written His research on Finsler geometry is continued through Tian Gang, Paul C. Yang, and Sun-Yung Alice Chang of Princeton University. He was known for unifying geometric and topological methods to prove stunning new results. == Honors and awards ==

Chern received numerous honors and awards in his life, including: • 1948, Academician, Academia Sinica; • 1950, Honorary Member, Indian Mathematical Society; • 1950, Honorary Fellow, Tata Institute of Fundamental Research • 1961, Member, United States National Academy of Sciences; • 1963, Fellow, American Academy of Arts and Sciences; • 1970, Chauvenet Prize, of the Mathematical Association of America; • 1971, Corresponding Member, Brazilian Academy of Sciences; • 1975, National Medal of Science; • 1982, Humboldt Prize, Germany; • 1983, Leroy P. Steele Prize, of the American Mathematical Society; • 1983, Associate Founding Fellow, TWAS; • 1984, Wolf Prize in Mathematics, Israel; • 1985, Foreign Fellow, Royal Society of London, UK; • 1986, Honorary Fellow, London Mathematical Society, UK; • 1986, Corresponding Member, Accademia 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. • 2002, Wilhelm Blaschke Medal • 2002, Lobachevsky Medal; • 2004 May, Shaw Prize in mathematical sciences, Hong Kong; 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), Stony Brook University (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. ==Publications==

• Shiing Shen Chern, Topics in Differential Geometry, The Institute for Advanced Study, Princeton 1951 • Shiing Shen Chern, Differential Manifolds, University of Chicago 1953 • Shiing Shen Chern, Complex Manifolds, University of Chicago, 1956 • Shiing Shen Chern: Complex manifolds Without Potential Theory, Springer-Verlag, New York 1979 • Shiing Shen Chern, Minimal Submanifolds in a Riemannian Manifold, University of Kansas 1968 • Bao, David Dai-Wai; Chern, Shiing-Shen; Shen, Zhongmin, Editors, Finsler Geometry American Mathematical Society 1996 • Shiing-Shen Chern, Zhongmin Shen, Riemann Finsler Geometry, World Scientific 2005 • Shiing Shen Chern, Selected Papers, Vol I-IV, Springer • Shiing-Shen Chern, A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds, Annals of Mathematics, 1944 • Shiing-Shen Chern, Characteristic Classes of Hermitian Manifolds, Annals of Mathematics, 1946 • Shiing Shen Chern, Geometrical Interpretation of the sinh-Gordon Equation • Shiing Shen Chern, Geometry of a Quadratic Differential Form, Journal of the Society for Industrial and Applied Mathematics 1962 • Shiing Shen Chern, On the Euclidean Connections in a Finsler Space, Proceedings of the National Academy of Sciences 1943 • Shiing Shen Chern, General Relativity and differential geometry • Shiing Shen Chern, Geometry and physics • Shiing Shen Chern, Web geometry • Shiing Shen Chern, Deformation of surfaces preserving principle curvatures • Shiing Shen Chern, Differential Geometry and Integral Geometry • Shiing Shen Chern, Geometry of G-structures • • • Shiing-Shen Chern, Wei-Huan Chen, K. S. Lam, Lectures on Differential Geometry, World Scientific, 1999 • David Dai-Wai Bao, Shiing-Shen Chern, Zhongmin Shen, An Introduction to Riemann-Finsler Geometry, GTM 200, Springer 2000 • David Bao, Robert L. Bryant, Shiing-Shen Chern, Zhongmin Shen, Editors, A Sampler of Riemann-Finsler Geometry, MSRI Publications 50, Cambridge University Press 2004 ==Namesake and persona==

is located • The asteroid 29552 Chern is named after him; • The Chern Medal, of the International Mathematical Union (IMU); • The Shiing-Shen Chern Prize (), of the Association of Chinese Mathematicians; • The Chern Institute of Mathematics at Nankai University, Tianjin, renamed in 2005 in honor of Chern; • The Chern Lectures, and the Shiing-Shen Chern Chair in Mathematics, both at the Department of Mathematics, UC Berkeley. Chern liked to play contract bridge, Go, read Wuxia-literature of Jin Yong and had an interest in Chinese philosophy and history. Biographies on Chern and other memorabilia Abraham Pais wrote about Chern in his book Subtle is the Lord. To paraphrase one passage: the outstanding mathematician Chern has two things to say, 1) I feel very mysterious that in the fields I'm working on (general relativity and differential geometry) there is so much more that can be explored; and 2) when talking with Albert Einstein (his colleague at the IAS) about his problem of a Grand Unified Theory, I realized the difference between mathematics and physics is at the heart of the journey towards a theory of everything. Manfredo Do Carmo dedicated his book on Riemannian Geometry to Chern, his PhD advisor. In Yau's autobiography, he talks a lot about his advisor Chern. In 1982, while on sabbatical at the New York University Courant Institute, he visited Stony Brook to see his friends and former students CN Yang and Simons. In 2011 ZALA films published a documentary titled Taking the Long View: the Life of Shiing-shen Chern (). In 2013 it was broadcast on US public television.Thirty-six years together Through times of happiness And times of worry too. Time’s passage has no mercy. We fly the Skies and cross the Oceans To fulfill my destiny; Raising the children fell Entirely on your shoulders. How fortunate I am To have my works to look back upon, I feel regrets you still have chores. Growing old together in El Cerrito is a blessing. Time passes by, And we hardly notice. == Students ==

Chern has 43 students, including Fields medalist Shing-Tung Yau, Nobel Prize winner Chen-Ning Yang; and over 1000 descendants. His student James Harris Simons at Stony Brook (co-author of the Chern–Simons theory) later founded the hedge fund Renaissance Technologies and became a billionaire. Simons talks about Chern in his TED talk. Two of his students Manfredo do Carmo and Katsumi Nomizu have written influential textbooks in geometry. Former director of the IAS Phillip Griffiths wrote[Chern] took great pleasure in getting to know and working with and helping to guide young mathematicians. I was one of them. ==Family==

His wife, Shih-ning Cheng (), whom he married in 1939, died in 2000. He also had a daughter, May Chu (), wife of the physicist Chu Ching-wu, and a son named Paul (). On his wife he writes (also see Selected Papers):''I would not conclude this account without mentioning my wife's role in my life and work. Through war and peace and through bad and good times we have shared a life for forty years, which is both simple and rich. If there is credit for my mathematical works, it will be hers as well as mine.''May Chu described her father as an easygoing parent. Paul added that he often saw what was best for you before you realized it. == See also ==