Shiing-Shen Chern (; ; October 26, 1911 – December 3, 2004) was a Chinese-born American mathematician. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is 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. 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."
Chern worked at the Institute for Advanced Study (1943–45), spent about a decade at the University of Chicago (1949-1960), and then moved to University of California, Berkeley, where he cofounded the Mathematical Sciences Research Institute in 1982 and was the institute's founding director. Renowned coauthors with Chern include Jim Simons, an American mathematician and billionaire hedge fund manager. Chern's work, most notably the Chern–Gauss–Bonnet theorem, Chern–Simons theory, and Chern classes, are still highly influential in current research in mathematics, including geometry, topology, and knot theory, as well as many branches of physics, including string theory, condensed matter physics, general relativity, and quantum field theory.
Name spelling 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. At Nankai, Chern's mentor was mathematician Jiang Lifu, and Chern was also heavily influenced by Chinese physicist Rao Yutai, considered to be one of the founding fathers of modern Chinese informatics.
Chern went to 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 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.
Yang Chen-Ning's father, , another Chicago-trained professor at Tsinghua, but specializing 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.
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.
He studied with the well-known Austrian geometer Wilhelm Blaschke. 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 and invariant theory. He would often eat lunch and chat in German with fellow colleague Erich Kähler.
He had a three-year scholarship but finished his degree very quickly in two years. He obtained his Dr. rer.nat. (Doctor of Science, which is equivalent to PhD) degree in February, 1936. He wrote his thesis in German, and it was titled Eine Invariantentheorie der Dreigewebe aus -dimensionalen Mannigfaltigkeiten im (English: An invariant theory of 3-webs of -dimensional manifolds in ).
For his third year, Blaschke recommended Chern to study at the University of 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 Artin's algebra, but in the end, he decided to go to France in September 1936.
He spent one year at the Sorbonne in Paris. There he met Cartan once a fortnight. Chern said: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 simple Lie 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 the Summer Olympics in Berlin together with Chinese mathematician Hua Luogeng who paid Chern a brief visit. During that time, Hua was studying at the University of Cambridge in Britain.
1937–1943: World War II In the summer of 1937, Chern accepted the invitation of Tsinghua University and returned to China. He was promoted to professor of mathematics at Tsinghua.
In late 1937, however, the start of World War 2 forced Tsinghua and other academic institutions to move away from Beijing to west China. 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.
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, and Oswald Veblen invited him to the IAS. Because of the war, it took him a week to reach Princeton via US military aircraft.
1943–1945: visit to the IAS, the Chern theorem 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. There he worked with André Weil on the Chern–Weil homomorphism and theory of characteristic classes, later to be foundational to the Atiyah–Singer index theorem. Shortly afterwards, he was invited by Solomon Lefschetz to be an editor of Annals of Mathematics.
Between 1943 and 1964 he was invited back to the IAS on several occasions. On Chern, Weil wrote:... 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. 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 and algebraic geometry. In a letter to the then director Frank Aydelotte, Chern wrote:“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.”
1945–1948: first return to China Chern returned to Shanghai in 1945 to help found the Institute of Mathematics of the Academia Sinica. 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 to Princeton as a professor.
1948–1960: return to USA, University of Chicago By the end of 1948, Chern returned to the United States and IAS. He brought his family with him. In 1949, he was invited by Weil to become professor of mathematics at the University of Chicago and accepted the position as chair of geometry. 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 the International Congress of Mathematicians in Cambridge, Massachusetts. He delivered his address on the Differential Geometry of Fiber Bundles. According to Hans Samelson, in the lecture Chern introduced the notion of a connection on a principal fiber bundle, a generalization of the Levi-Civita connection.
Berkeley and MSRI In 1960 Chern moved to the University of California, Berkeley. He worked and stayed there until he became an emeritus professor in 1979. In 1961, Chern naturalized as U.S. citizen of the United States. In the same year, he was elected member of the United States National Academy of Sciences. 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. Shing-Tung Yau was one of his PhD students during this period, and he later won the Fields 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.'
Visits to China and bridging East and West 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 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.