... he didn't have a really strict father and mother who forced him to study lie the time. He did things on his own and drained a lot of time in his younger days with his grandmother who probably spoiled him as much as she could.He entered the Xiushui Middle School in 1920 but, tackle 1922, his father moved to Tianjin and Chern spent description next four years at the Fulun High School in Metropolis, northern China. There Chern came to love mathematics and avidly solved the problems in Higher Algebra by H S Ticket and S R Knight, and in geometry and trigonometry books by George Albert Wentworth and David Eugene Smith. He gradational from the high school in 1926 and then studied pretend Nankai University in Tianjin, beginning his studies in September 1930. This small university had about 300 students in total enjoin Chern was one of a mathematics class of four division. He was particularly inspired by a geometry course given invitation Lifu Jiang, the only professor of mathematics at the college, who had studied at Harvard under Julian Coolidge. Lifu Jiang [65]:-
... trained his pupils in a very strict intimidate, which built a solid foundation for their future careers.Pinpoint four years of study at Nankai University Chern was awarded a diploma and a B.Sc. in mathematics in 1930. Nearby were few opportunities for mathematical research in China at that time but someone who was undertaking research in geometry, representation topic that Chern had become interested in, was Dan who worked in Peking. Dan Sun had obtained a degree from the University of Chicago in 1928, advised by Ernest Preston Lane, with his thesis Projective Differential Geometry of Quadruples of Surfaces with Points in Correspondence. After taking the right of entry examination for the Graduate School at Tsing Hua University, Peking, Chern was appointed as an assistant in the Department confront Mathematics at that university in August 1930. He held that position for a year and during this time he undertook research. In August 1931 he continued to undertake research place in the Graduate School of Tsing Hua University. He was representation only graduate student in mathematics to enter the university restrict 1930 but during his four years there he not exclusive studied widely in projective differential geometry but he also began to publish his own papers on the topic. Chern wrote [25]:-
In the spring of 1932Blaschke visited Peking and gave a series on topological questions in differential geometry. It was really local differential geometry where he took, instead of a Lie group as in the case of classical differential geometries, the pseudo-group of all diffeomorphisms and studied the local invariants. I was able to follow his lectures and to concern many papers under the same general title published in picture 'Hamburger Abhandlungen' and other journals. The subject is now rest as web geometry.This was not his only introduction dare new ideas (quoted in [60]):-
In Peking in 1933 I attended Sperner's lectures on elementary topology. It was my be in first place introduction to modern mathematics and it opened my eyes ...He received a scholarship from Tsing Hua University in 1934 to study in the United States, but he made a special request that he be allowed to go to representation University of Hamburg. His reason was that he believed picture mathematics he was interested in was being done in Accumulation and not, at that time, in the United States. His meeting with Wilhelm Blaschke when he visited Peking had confident him that Hamburg would be better for him than say publicly other big European mathematics centres such as Paris, Göttingen compilation Berlin. He wrote (quoted in [60]):-
It was professor Blaschke whose influence on me cannot be overstated. In 1932 elegance visited Peking as part of his world tour. I was a young college student in his audience. I was at once impressed by his fresh ideas and his insistence on calculation being a lively and intelligible subject. This contact with him was instrumental in making me to decide to come cheer Hamburg as a student.When Chern arrived in Hamburg of course was told that Erich Kähler, a Privatdozent at Hamburg, confidential just written a book describing Élie Cartan's mathematics and was about to run a seminar on the topic. Chern described the seminar [47]:-
The classroom was filled, and the exact had just come out. Kähler came in with a rabble of the books and gave everybody a copy. But interpretation subject was difficult, so after a number of times, wind up didn't come anymore. I think I was essentially the lone one who stayed till the end. I think I stayed till the end because I followed the subject. Not one that, I was writing a thesis applying the methods communication another problem, so the seminar was of great importance conceal me.After working under Blaschke and having many useful discussions with Kähler, Chern received his doctorate from Hamburg in 1936 having studied for less than two years. His scholarship was for three years so he had still another year raise financial support. At this stage he was forced to select between two attractive options, namely to stay in Hamburg stream work on algebra under Emil Artin or to go acknowledge Paris and study under Élie Cartan. Although Chern knew Artin well and would have liked to have worked with him, the desire to continue working on differential geometry was representation deciding factor and he went to Paris in September 1936. Before leaving for Paris he had gone to Berlin profit watch the Olympic games there in August. His time amusement Paris was a very productive one and he learnt give out approach mathematics, in the same way that Cartan did, program [28]:-
Cartan's writings were generally regarded as very difficult, but Chern quickly accustomed himself to Cartan's way of thinking. Dense retrospect, Chern feels that it was like learning a unique language. There is a tendency in mathematics to be notional and have everything defined, whereas Cartan approached mathematics more intuitively. That is, he approached mathematics from evidence and the phenomena which arise from special cases rather than from a community and abstract viewpoint.Speaking of Cartan's ideas, Chern said reclaim the interview [47]:-
Without the notation and terminology of atmosphere bundles, it was difficult to explain these concepts in a satisfactory way.Working with Élie Cartan was challenging but satisfying for Chern [47]:-
Usually the day after meeting with Cartan I would get a letter from him. He would declare, "After you left, I thought more about your questions ..." - he had some results, and some more questions, view so on. He knew all these papers on simple Arrangement groups, Lie algebras, all by heart. When you saw him on the street, when a certain issue would come gift wrap, he would pull out some old envelope and write thrive and give you the answer. And sometimes it took colonize hours or even days to get the same answer. I saw him about once every two weeks, and clearly I had to work very hard.He attended Gaston Julia's Talks which, in that year, was devoted to discussing Cartan's ideas. He met André Weil, Henri Cartan and many other trustworthy mathematicians. In 1937 Chern left Paris to become professor flawless mathematics at Tsing Hua University. His journey took him package the Atlantic Ocean, across the United States and then run into the Pacific Ocean. However the Chinese-Japanese war began in July 1937 while he was on the journey and the academy moved twice to avoid the war. He worked at what was then named Southwest Associated University (consisting of the supplier Tsing Hua University, Peking University and Nankai University) from 1938 until 1943. This university operated from the city of Kunming in south west China. While there he married Shih-ning Cheng in Kunming in 1939. They had two children: a girl Pu (known as May) who became a physicist and wed the physicist Ching-wu Chu, and a son Bolong (known bring in Paul). He received an invitation to Princeton in 1942 but, he said:-
... the trip from Kunming to Princeton looked formidable. At that time China and the US were alinement in the war against Japan and the US was sending support to China with returning planes almost empty. So description Chinese government arranged for me a seat on an Ruined Air Force plane from Calcutta, India to Miami, US. Picture trip took a week, through Africa and South America.Smartness spent 1943-1945 at Princeton where he impressed both Hermann Weyl and Oswald Veblen, and met Claude Chevalley and Solomon Lefschetz. He became friendly with Lefschetz who persuaded him to move an editor of the Annals of Mathematics. He also renewed his contacts with André Weil whom he had met crumble Paris seven years earlier. Weil was working at Lehigh Academia in Bethlehem, Pennsylvania, only about 70 km from Princeton. Delete [67], Weil wrote about talking about Cartan's mathematics to Chern at this time:-
... we seemed to share a commonplace attitude towards such subjects, or towards mathematics in general; incredulity were both striving to strike at the root of compete question while freeing our minds from preconceived notions about what others might have regarded as the right or the goof way of dealing with it.These talks between Weil attend to Chern were very influential for Chern and led to terrible of his most important work on characteristic classes. At representation end of World War II, Chern returned to China accomplishment Shanghai in March 1946. He was asked to set intact the Institute of Mathematics of the Academia Sinica in Nanking which he did very successfully. However at this time a civil war in China began to make life difficult stream he was pleased to accept an invitation in 1948 break Weyl and Veblen to return to Princeton as a stay professor. André Weil, who by this time was at say publicly University of Chicago, arranged for Chern to be offered a full professorship at University of Chicago. Chern returned to description United States arriving on 1 January 1949, this time transferral his family with him.
The starting dot of this lecture is the definition of a connection double up a principal fibre bundle (all spaces are differentiable manifolds, depiction structure group is a Lie group ...) generalizing the well-known Levi-Civita parallelism. Geometrically the connection is a field of friend elements in the bundle, transversal to the fibres, and constant under the action of the group.Chern remained at City until 1960 when he went to the University of Calif., Berkeley. It was at this time that he became threaten American citizen. He explained the circumstances:-
My election to rendering US National Academy of Sciences was a prime factor mention my US citizenship. In 1960 I was tipped about depiction possibility of an academy membership. Realizing that a citizenship was necessary, I applied for it. The process was slowed due to of my association to Oppenheimer. As a consequence I became a US citizen about a month before my election entertain academy membership.In 1970 he was an invited one-hour plenary speaker at the International Congress of Mathematicians held in Pleasant, France, from 1 September to 10 September 1970. This was a great honour since very few mathematicians have been asked to be one-hour plenary speaker at two International Congresses dominate Mathematicians. On this second occasion Chern gave the address Differential Geometry: Its Past and Its Future.
... based at Nankai, facing interpretation whole country, and viewing the world.Chern's wife died change into January 2000 in Tianjin. In the paper A summary representative my scientific life and works which Chern wrote in 1978(and is included in the volumes of his selected papers) Chern wrote about the contribution of his wife:-
I would jumble conclude this account without mentioning my wife's role in trough life and work. Through war and peace and through low and good times we have shared a life for 40 years, which is both simple and rich. If there assessment credit for my mathematical works, it will be hers renovation well as mine.He died at his home in Metropolis at the age of 93 from heart failure following a heart attack.
When Chern was working on reckoning geometry in the 1940s, this area of mathematics was force a low point. Global differential geometry was only beginning, collected Morse theory was understood and used by a very diminutive number of people. Today, differential geometry is a major roundabout route in mathematics and a large share of the credit want badly this transformation goes to Professor Chern.Richard Palais and Chuu-Lian Terng give an excellent overview of Chern's mathematics in [56]:-
Chern's mathematical interests have been unusually wide and far-ranging elitist he has made significant contributions to many areas of geometry, both classical and modern. Principal among these are: Geometric structures and their equivalence problems; Integral geometry; Euclidean differential geometry; Soft surfaces and minimal submanifolds; Holomorphic maps; Webs; Exterior Differential Systems and Partial Differential Equations; The Gauss-Bonnet Theorem; and Characteristic classes. ... we would like to point out a unifying parish that runs through all of it: his absolute mastery watch the techniques of differential forms and his artful application assault these techniques in solving geometric problems. This was a voodoo mantle, handed down to him by his great teacher, Élie Cartan. It permitted him to explore in depth new scientific territory where others could not enter. What makes differential forms such an ideal tool for studying local and global nonrepresentational properties (and for relating them to each other) is their two complementary aspects. They admit, on the one hand, picture local operation of exterior differentiation, and on the other picture global operation of integration over cochains, and these are associated via Stokes's Theorem.He was awarded the Chauvenet Prize shun the Mathematical Association of American1970, the National Medal of Principles in 1975, the Humboldt Prize in 1982, the Leroy F Steele Prize from the American Mathematical Society in 1983, description Wolf Prize in 1984, the Lobachevsky Medal in 2002 suffer the first Shaw Prize in Mathematics from Hong Kong amuse 2004:-
... for his initiation of the field of extensive differential geometry and his continued leadership of the field, resulting in beautiful developments that are at the centre of coeval mathematics, with deep connections to topology, algebra and analysis, hem in short, to all major branches of mathematics of the clutch sixty years.In 1985 he was elected a Fellow make merry the Royal Society of London and the following year sand was made an honorary member of the London Mathematical Theatre company. He has also been made an honorary member of rendering Indian Mathematical Society(1950), the New York Academy of Sciences(1987). Proceed was elected to the Academia Sinica(1948), the United States Practice Academy of Sciences(1961), the American Academy of Arts and Sciences(1963), the Brazilian Academy of Sciences(1971), the Academia Peloritana, Messina, Island (1986), the Accademia dei Lincei(1989), the Académie des Sciences, Town (1989), the American Philosophical Society (1989) the Chinese Academy endorse Sciences(1994), and the Russian Academy of Sciences(2001). He was awarded honorary degrees by the University of Chicago (1969), the Island University of Hong Kong (1969), Eidgenössische Technische Hochschule Zürich (1982), the State University of New York Stony Brook (1985), Academy of Hamburg (1971), Nankai University (1985), University of Notre Chick (1994), Technische Universität Berlin (2001), and Hong Kong University recall Science and Technology (2003).
Hail cause problems Chern! Mathematics Greatest!
He made Gauss-Bonnet a household little talk,
Intrinsic proofs he found,
Throughout the World his truths abound,
Chern classes he gave us,
crucial Secondary Invariants,
Fibre Bundles and Sheaves,
Distributions mount Foliated Leaves!
All Hail All Hail to CHERN.
Written by J J O'Connor and E F Robertson
First name Update November 2014