Shiing-Shen Chern (/tʃɜːrn/;Chinese:陳省身;pinyin:Chén Xǐngshēn; October 26, 1911[1] – December 3, 2004) was a Chinese Americanmathematician and poet. He made fundamental contributions todifferential geometry andtopology. He has been called the "father of modern differential geometry" and is widely regarded as a leader ingeometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including theWolf Prize and the inauguralShaw Prize.[1][2][3][4][5][6][7] In memory of Shiing-Shen Chern, theInternational Mathematical Union established theChern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics."[8]
Chern worked at theInstitute for Advanced Study (1943–45), spent about a decade at theUniversity of Chicago (1949-1960), and then moved toUniversity of California, Berkeley, where he cofounded theMathematical Sciences Research Institute in 1982 and was the institute's founding director.[9][10] Renowned coauthors with Chern includeJim Simons, an American mathematician and billionaire hedge fund manager.[11] Chern's work, most notably theChern–Gauss–Bonnet theorem,Chern–Simons theory, andChern classes, are still highly influential in current research in mathematics, including geometry, topology, andknot theory, as well as many branches ofphysics, includingstring theory,condensed matter physics,general relativity, andquantum field theory.[12]
Chern's surname (traditional: 陳, simplified: 陈, pinyin: Chén) is a common Chinese surname which is now usually romanized asChen. The unusual spelling "Chern" is from theGwoyeu Romatzyh (GR)romanization system. In English, Chern pronounced his own name with the "r" (/tʃɜːrn/)[citation needed].
Chern was born in Xiushui, Jiaxing, China in 1911. He graduated from Xiushui Middle School (秀水中學) and subsequently moved toTianjin in 1922 to accompany his father. In 1926, after spending four years in Tianjin, Chern graduated fromFulun High School [zh].[13]
At age 15, Chern entered the Faculty of Sciences of theNankai University in Tianjin and was interested in physics, but not so much the laboratory, so he studied mathematics instead.[5][14] Chern graduated with a Bachelor of Science degree in 1930.[14] At Nankai, Chern's mentor was mathematicianJiang Lifu, and Chern was also heavily influenced by Chinese physicistRao Yutai, considered to be one of the founding fathers of modern Chineseinformatics.
Chern went toBeijing to work at theTsinghua University Department of Mathematics as a teaching assistant. At the same time he also registered at Tsinghua Graduate School as a student. He studiedprojective differential geometry underSun Guangyuan, aUniversity of Chicago-trained geometer andlogician 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 Tsinghua 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.[13]
Yang Chen-Ning's father,Yang Ko-Chuen [zh], another Chicago-trained professor at Tsinghua, but specializing inalgebra, 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.[15]
In 1934, Chern received a scholarship to study in the United States atPrinceton andHarvard, but at the time he wanted to study geometry and Europe was the center for the maths and sciences.[5]
He studied with the well-known Austrian geometerWilhelm Blaschke.[14] 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.[14]
Chern studied at theUniversity of Hamburg and worked under Blaschke's guidance first on the geometry ofwebs then on theCartan-Kähler theory andinvariant theory. He would often eat lunch and chat in German with fellow colleagueErich Kähler.[5]
He had a three-year scholarship but finished his degree very quickly in two years.[5] He obtained hisDr. rer.nat. (Doctor of Science, which is equivalent to PhD) degree in February, 1936.[14] He wrote his thesis in German, and it was titledEine Invariantentheorie der Dreigewebe aus-dimensionalen Mannigfaltigkeiten im (English:Aninvariant theory of 3-webs of-dimensional manifolds in).[16]
For his third year, Blaschke recommended Chern to study at theUniversity of Paris.[5]
It was at this time that he had to choose between the career of algebra in Germany underEmil Artin and the career of geometry in France underÉlie-Joseph Cartan. Chern was tempted by what he called the "organizational beauty" of Artin's algebra, but in the end, he decided to go to France in September 1936.[17]
He spent one year at theSorbonne in Paris. There he met Cartan once a fortnight. Chern said:[5]
Usually the day after [meeting with Cartan] I would get a letter from him. He would say, “After you left, I thought more about your questions...”—he had some results, and some more questions, and so on. He knew all these papers on simpleLie groups,Lie algebras, all by heart. When you saw him on the street, when a certain issue would come up, he would pull out some old envelope and write something and give you the answer. And sometimes it took me hours or even days to get the same answer... I had to work very hard.
In August 1936, Chern watched theSummer Olympics in Berlin together with Chinese mathematicianHua Luogeng who paid Chern a brief visit. During that time, Hua was studying at theUniversity of Cambridge in Britain.
In the summer of 1937, Chern accepted the invitation ofTsinghua University and returned to China.[17] He was promoted to professor of mathematics at Tsinghua.
In late 1937, however, the start ofWorld War 2 forced Tsinghua and other academic institutions to move away from Beijing to west China.[18] Three universities including Peking University, Tsinghua, and Nankai formed the temporaryNational Southwestern Associated University (NSAU), and relocated toKunming,Yunnan province. Chern never reached Beijing.
In 1939, Chern married Shih-Ning Cheng, and the couple had two children, Paul and May.[18]
The war prevented Chern from having regular contacts with the outside mathematical community. He wrote to Cartan about his situation, to which Cartan sent him a box of his reprints. Chern spent a considerable amount of time pondering over Cartan's papers and published despite relative isolation. In 1943, his papers gained international recognition, andOswald Veblen invited him to the IAS. Because of the war, it took him a week to reach Princeton via US military aircraft.[5]
In July 1943, Chern went to the United States, and worked at theInstitute for Advanced Study (IAS) inPrinceton oncharacteristic classes in differential geometry. There he worked withAndré Weil on theChern–Weil homomorphism and theory ofcharacteristic classes, later to be foundational to theAtiyah–Singer index theorem. Shortly afterwards, he was invited bySolomon Lefschetz to be an editor ofAnnals of Mathematics.[18]
Between 1943 and 1964 he was invited back to the IAS on several occasions.[12] On Chern, Weil wrote:[19]
... 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 famousGauss–Bonnet theorem to higher dimensionalmanifolds, now known today as theChern theorem. It is widely considered to be hismagnum opus.[12][5][2] This period at the IAS was a turning point in his career, having a major impact on mathematics, while fundamentally altering the course of differential geometry andalgebraic geometry.[3][12] In a letter to the then directorFrank Aydelotte, Chern wrote:[12]
“The years 1943–45 will undoubtedly be decisive in my career, and I have profited not only in the mathematical side. I am inclined to think that among the people who have stayed at the Institute, I was one who has profited the most, but the other people may think the same way.”
Chern returned to Shanghai in 1945 to help found the Institute of Mathematics of theAcademia Sinica.[18] 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 1948, he accepted an invitation by Weyl and Veblen to return toPrinceton as a professor.[2][18]
By the end of 1948, Chern returned to the United States and IAS.[18] He brought his family with him.[2] In 1949, he was invited by Weil to become professor of mathematics at theUniversity of Chicago and accepted the position as chair of geometry.[18][2] Coincidentally,Ernest Preston Lane, former Chair at UChicago Department of Mathematics, was the doctoral advisor of Chern's undergraduate mentor at Tsinghua—Sun Guangyuan.
In 1950 he was invited by theInternational Congress of Mathematicians inCambridge, Massachusetts. He delivered his address on theDifferential Geometry of Fiber Bundles. According toHans Samelson, in the lecture Chern introduced the notion of aconnection on aprincipal fiber bundle, a generalization of theLevi-Civita connection.[2]
In 1960 Chern moved to theUniversity of California, Berkeley.[18] He worked and stayed there until he became an emeritus professor in 1979.[20] In 1961, Chern became a naturalized citizen of the United States.[2] In the same year, he was elected member of theUnited States National Academy of Sciences.[21]
My election to the US National Academy of Sciences was a prime factor for my US citizenship. In 1960I 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 toOppenheimer. As a consequence I became a US citizen about a month before my election to academy membership.
In 1964, Chern was a vice president ofAmerican Mathematical Society (AMS).
Chern retired from UC Berkeley in 1979.[22][23] In 1981, together with colleaguesCalvin C. Moore andIsadore Singer, he founded theMathematical 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.[21]Shing-Tung Yau was one of his PhD students during this period, and he later won theFields Medal in 1982.
During WW2, the US did not have much of a scene in geometry (which is why he chose to study in Germany). Chern was largely responsible in making the US a leading research hub in the field, but he remained modest about his achievements, preferring to say that he is a man of 'small problems' rather than 'big views.'[5]
TheShanghai 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 normalize, and American citizens were allowed to visit 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.
He was admired and respected by Chinese leadersMao Zedong,Deng Xiaoping, andJiang Zemin. Because of foreign prestigious scientific support, Chern was able to revive mathematical research in China, producing a generation of influential Chinese mathematicians.[7][5]
Chern founded the Nankai Institute for Mathematics (NKIM) at his alma mater Nankai in Tianjin. After his retirement he spent every summer in Houston, Texas where his daughter lived. He gave seminars at Rice University and the University of Houston and donated the proceeds to the mathematics department at Nankai. The institute was formally established in 1984 and fully opened on October 17, 1985. NKIM was renamed theChern Institute of Mathematics in 2004 after Chern's death. He was treated as a rock star and cultural icon in China.[7] Regarding his influence in China and help raising a generation of new mathematicians, ZALA films says:[7]
Several world-renowned figures, such asGang Tian andShing-Tung Yau, consider Chern the mentor who helped them study in western countries following the bleak years of the Cultural Revolution, when Chinese universities were closed and academic pursuits suppressed. By the time Chern started returning to China regularly during the 1980s, he had become a celebrity; every school child knew his name, and TV cameras documented his every move whenever he ventured forth from the institute he established at Nankai University.[7]
He has said that back then the main barrier to the growth of math in China was the low pay, which was important considering that after the cultural revolution many families were impoverished. But he has said that given China's size, it naturally has a large talent pool of budding mathematicians.[5]Nobel Prize winner and former studentCN Yang has said[24]
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.
In 1999, Chern moved from Berkeley back to Tianjin, China permanently until his death.[7]
Based on Chern's advice, a mathematical research center was established inTaipei, Taiwan, whose co-operational partners areNational Taiwan University,National Tsing Hua University and the Academia Sinica Institute of Mathematics.[25]
In 2002, he convinced the Chinese government (the PRC) for the first time to host theInternational Congress of Mathematicians in Beijing.[24] In the speech at the opening ceremony he said:[26]
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 theCenter of Mathematical Sciences at Zhejiang University inHangzhou, Zhejiang.
Chern died of heart failure atTianjin Medical University General Hospital in 2004 at age 93.[27]
In 2010George Csicsery featured him in the documentary shortTaking the Long View: The Life ofShiing-shen Chern.[28]
His former residence, Ningyuan (寧園), 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.
Physics Nobel Prize winner (and former student)C. N. Yang has said that Chern is on par withEuclid,Gauss,Riemann,Cartan. Two of Chern's most important contributions that have reshaped the fields of geometry and topology include
In 2007, Chern's disciple and IAS directorPhillip Griffiths editedInspired by S. S. Chern: A Memorial Volume in Honor of A Great Mathematician (World Scientific Press). Griffiths wrote:[12]
“More than any other mathematician, Shiing-Shen Chern defined the subject ofglobal differential geometry, a central area in contemporary mathematics. In work that spanned almost seven decades, he helped to shape large areas of modern mathematics... I think that he, more than anyone, was the founder of one of the central areas of modern mathematics.”
His work extended over all the classic fields ofdifferential geometry as well as more modern ones includinggeneral relativity,invariant theory,characteristic classes,cohomology theory,Morse theory,Fiber bundles,Sheaf theory, Cartan's theory ofdifferential forms, etc. His work included areas currently-fashionable, perennial, foundational, and nascent:[2][29]
He was a follower ofÉlie 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 thepseudogroup problem that is in effect the touchstone of Cartan's geometric theory. He used themoving frame method with success only matched by its inventor; he preferred incomplex manifold theory to stay with the geometry, rather than follow thepotential theory. Indeed, one of his books is entitled "Complex Manifolds without Potential Theory".
Along with Cartan, Chern is one of the mathematicians known for popularizing the use ofdifferential forms in math and physics. In his biography, Richard Palais and Chuu-Lian Terng have written[29]
... we would like to point out a unifying theme that runs through all of it: his absolute mastery of the techniques of differential forms and his artful application of these techniques in solving geometric problems. This was a magic mantle, handed down to him by his great teacher, Élie Cartan. It permitted him to explore in depth new mathematical territory where others could not enter. What makes differential forms such an ideal tool for studying local and global geometric properties (and for relating them to each other)is their two complementary aspects. They admit, on the one hand, the local operation of exterior differentiation, and on the other the global operation of integration over cochains, and these are related viaStokes's Theorem.
While at the IAS, there were two competing methods of geometry: thetensor calculus and the newerdifferential forms. Chern wrote:[5]
I usually like to say that vector fields is like a man, and differential forms is like a woman. Society must have two sexes. If you only have one, it’s not enough.
In the last years of his life, he advocated the study ofFinsler geometry, writing several books and articles on the subject.[34] His research on Finsler geometry is continued throughTian Gang,Paul C. Yang, andSun-Yung Alice Chang ofPrinceton University.
He was known for unifying geometric and topological methods to prove stunning new results.
Chern received numerous honors and awards in his life, including:
Chern was given a number of honorary degrees, including from TheChinese 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 materHamburg (D.Sc. 1971) andNankai (honorary doctorate, 1985), etc.
Chern was also granted numeroushonorary professorships, including atPeking 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 establishShanghai University in 1994),Tianjin University (1987),Tohoku University (Sendai, Japan, 1987), etc.
Chern liked to playcontract bridge,Go (game), readWuxia-literature ofJin Yong and had an interest inChinese philosophy and history.[24]
In 1975,Chen Ning Yang and Chern found out that their research in non-abelian gauge theory andFiber bundle describe the same theoretical structure, which showed a surprising connection between physics and mathematics. Therefore, Chern asked Fan Zeng to finish a Chinese painting named Shiing-Shen Chern and Chen Ning Yang for that. The painting was later donated to Nankai University.
Apolyglot, he spoke German, French, English,Wu and Mandarin Chinese.
“Whenever we had to go to the chancellor to make some special request, we always took Chern along, and it always worked,” says Berkeley mathematician Rob Kirby. “Somehow he had a presence, a gravitas. There was something about him that people just listened to him, and usually did things his way.”[7]
In 1979 a Chern Symposium offered him a honorary song in tribute:[2]
Hail to Chern! Mathematics Greatest!
He made Gauss-Bonnet a household word,
Intrinsic proofs he found,
Throughout the World his truths abound,
Chern classes he gave us,
and Secondary Invariants,
Fibre Bundles andSheaves,
Distributions and Foliated Leaves!
All Hail All Hail to CHERN.
It's called theChern song.[2]
Allyn Jackson writes[5]
S. S. Chern is the recipient of many international honors, including six honorary doctorates, the U.S. National Medal of Science, Israel’s Wolf Prize, and membership in learned academies around the world. He has also received a more homegrown honor, the dream-turned-reality of an appreciative student of 30 years ago, who grew up in the Bay Area.
When Robert Uomini would buy his 10 tickets for the California State Lottery, he had an unusual “what if I win?” fantasy: He wanted to endow a professorship to honor S. S. Chern. While an undergraduate at U.C. Berkeley in the 1960s, Uomini was greatly inspired by a differential geometry course he took from Chern. With Chern’s support and encouragement, Uomini entered graduate school at Berkeley and received his Ph.D. in mathematics in 1976. Twenty years later, while working as a consultant to Sun Microsystems in Palo Alto, Uomini won $22 million in the state lottery. He could then realize his dream of expressing his gratitude in a concrete way.
Uomini and his wife set up theRobert G. Uomini and Louise B. Bidwell Foundation to support an extended visit of an outstanding mathematician to the U.C. Berkeley campus. There have been threeChern Visiting Professors so far: SirMichael Atiyah of theUniversity of Cambridge (1996),Richard Stanley of theMassachusetts Institute of Technology (1997), andFriedrich Hirzebruch of theMax Planck Institute for Mathematics in Bonn (1998).Jean-Pierre Serre of the Collège de France was the Chern Visiting Professor for 1999. [sic]
The foundation also helps to support theChern Symposium, a yearly one-day event held in Berkeley during the period when the Chern Visiting Professor is in residence. The March 1998 Symposium was co-sponsored by the Mathematical Sciences Research Institute and was expanded to run for three days, featuring a dozen speakers.
The MSRI also set up a Chern Professorship, funded by Chern's children May and Paul as well asJames Simons.[43]
Abraham Pais wrote about Chern in his bookSubtle 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 anddifferential geometry) there is so much more that can be explored; and 2) when talking withAlbert Einstein (his colleague at the IAS) about his problem of aGrand Unified Theory, I realized the difference between mathematics and physics is at the heart of the journey towards atheory of everything.
Manfredo Do Carmo dedicated his book onRiemannian Geometry to Chern, his PhD advisor.
In Yau's autobiography, he talks a lot about his advisor Chern. In 1982, while on sabbatical at theNew York UniversityCourant Institute, he visited Stony Brook to see his friends and former students CN Yang and Simons.[44]
In 2011 ZALA films published a documentary titledTaking the Long View: the Life of Shiing-shen Chern (山長水遠). In 2013 it was broadcast on US public television.[7] It was compiled with the help of his friends includingAlan Weinstein,Chuu-Lian Terng,Calvin C. Moore,Marty Shen,Robert Bryant,Robert Uomini,Robert Osserman,Hung-Hsi Wu, Rob Kirby,CN Yang, Paul Chu,Udo Simon,Phillip Griffiths, etc.[24]
Dozens of other biographies have been written on Chern. See the citations for more info.
Chern was an expressive poet as well. On his 60th birthday he wrote a love letter re-affirming his gratitude towards his wife and celebrating their 'beautiful, long, happy, marriage':[45]
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.
Chern has 43 students, including Fields medalistShing-Tung Yau, Nobel Prize winnerChen-Ning Yang; and over 1000 descendants.[46]
His studentJames Harris Simons atStony Brook (co-author of theChern–Simons theory) later founded the hedge fundRenaissance Technologies and became a billionaire. Simons talks about Chern in his TED talk.[47]
Two of his studentsManfredo do Carmo andKatsumi Nomizu have written influential textbooks in geometry.
Former director of the IASPhillip Griffiths wrote[12]
[Chern] took great pleasure in getting to know and working with and helping to guide young mathematicians. I was one of them.
His wife, Shih-ning Cheng (Chinese:鄭士寧;pinyin:Zhèng Shìníng), whom he married in 1939, died in 2000. He also had a daughter, May Chu (陳璞;Chén Pú), wife of the physicistChu Ching-wu, and a son named Paul (陳伯龍;Chén Bólóng). On his wife he writes (also seeSelected Papers):[2]
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.[24]
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