Ch'en Hsing-shen 陳省身 S. S. Chern Shüng-shen Chern Ch'en Hsing-shen (26 October 1911-), known as S. S. Chern, prominent mathematician, specialized in differential geometry and topology. He worked at the Institute of Advanced Study at Princeton (1943-46) and directed the institute of mathematics of the Academia Sinica (1945-48). In 1949 he returned to the United States, where he became a professor at the University of Chicago and later at the University of California at Berkeley.

Chiahsing (Kashing) hsien in Chekiang province was the birthplace of S. S. Chern. His father, Ch'en Pao-chen, was a government official who, in accordance with the practice of the time, served outside his native province. The home was supervised by a grandmother who kept young Chern at home, where he began his education under tutors. His father, on one of his visits home, taught him the Arabic numerals and simple arithmetic. There was a copy of an arithmetic manual at home, and the boy began to work the problems, which he solved with ease.

His proficiency in mathematics enabled S. S. Chern to gain admission to the missionary sponsored Kashing High School in 1920. In the autumn of 1922, the family moved to Tientsin, where Chern's father had been appointed to the local court. There Chern entered the Fulun Middle School, which was operated, principally for the children of railway workers, by the ministry of communications. He was graduated from the school in 1926. A friend of Ch'en Pao-chen, Ch'ien Pao-tsung, was then a professor at Nankai University and a noted scholar who specialized in the history of Chinese mathematics. Chern decided to enter Nankai, which he did in the autumn of 1926.

Chern at first considered the study of physics and chemistry. But a few lessons in chemistry, particularly the laboratory experiments, revealed that he had no aptitude for the subject. Mathematics seemed to be the best alternative. Chern later stated that his field seemed to have been decided for him from the start—because he was not proficient in foreign languages or laboratory experiments. The chairman of the mathematics department at Nankai University was Chiang Li-fu. He and Hu Tah (T. Mingfu) were the only Chinese at that time who had obtained the doctorate in mathematics from Harvard. Chiang Li-fu was on leave the year Chern entered Nankai, and he therefore studied differential and integral calculus with Chien Pao-tsung, his father's friend, who also taught him mechanics. When Chiang returned to Nankai, he was impressed by Chern and he introduced new courses which were at the time still unfamiliar in China, including linear algebra, the theory of functions of a complex variable, and differential geometry. Chern also studied German and French under Tuan Mou-lan and learned enough to read mathematical works in those languages. Chern was graduated from Nankai with a B.S. degree in 1930, when he was 19. Tsinghua University had begun to establish a graduate program, and Chern began graduate study in mathematics at Tsinghua. One of Chern's objectives was to study under Sun Tang, who had specialized in projective differential geometry and who had obtained his doctorate from the University of Chicago. Sun was at the time the only Chinese mathematician who wrote post-doctoral papers and published them in Western professional journals. While at Tsinghua, Chern published his first professional paper, "Pairs of Plane Curves with Points in One-to-one Correspondence," in Tsinghua University Science Reports (1932).

Because S. S. Chern was the only student seeking advanced instruction in mathematics, the university decided to postpone the inauguration of a graduate department of mathematics. During his first year at Tsinghua, Chern served as an assistant. He did not begin graduate studies until 1931, by which time there were other students in the department. In addition to Sun Tang, the professors included Hiong King-lai (Hsiung Ching-lai), Yang Wu-chih, and Cheng Tung-sun, whose daughter Chern later married. It was in 1931 that Hua Lo-keng (q.v.) first came to Tsinghua to serve as librarian in the department of mathematics. In 1932 Hu Kun-sheng, who had obtained his doctorate at the University of Chicago, came to Tsinghua as a lecturer. A number of distinguished Western professors, including George Birkhoff of Harvard University and Wilhelm Blaschke of the University of Hamburg, also visited China at that time. Impressed by a series of lectures on differential geometry given by Blaschke, Chern resolved to go to Hamburg for advanced work in mathematics.

Chern was at Tsinghua for four years, from 1930 to 1934. Mathematical studies were then developing rapidly in China, and Chinese work was beginning to gain international recognition. Chinese students were returning after study abroad, and a number of Chinese universities, notably Peking University, Chekiang University, Wuhan University, and Sun Yat-sen University at Canton, were making important strides forward in mathematics. The China Mathematical Society was formed in 1935, and the first issue of its journal appeared in 1936. While at Tsinghua, S. S. Chern selected differential geometry as his field of specialization. The application of differential and integral calculus to geometry had long been studied, and after Einstein's enunciation of his theory of relativity, many geometers had attempted to discover in geometry the prototypes of physics. After receiving his M.S. degree from Tsinghua in the summer of 1934, Chern received a fellowship for two years of study abroad. While the Tsinghua fellowships normally provided for study in the United States, Chern, because of his specialized interests, received permission to go to Germany. Still Only in his early twenties, he had two papers dealing with problems of linear congruences accepted for publication in the Japanese Tohoku Mathematical Journal; they appeared in 1935.

Although created after the First World War, the mathematics faculty at Hamburg had rapidly gained a world reputation. In addition to Wilhelm Blaschke, there were two other distinguished professors, Emil Artin and Erich Hecke. Artin, who had gained a full professorship while in his twenties, was regarded as one of the creators of modern abstract algebra, though his interests covered virtually all fields of mathematics. On arrival at Hamburg, Chern first attracted attention by discovering a loophole in a recent paper of Blaschke's. Blaschke was pleased and told Chern to correct the error, which he did. Since Blaschke was frequently away from the university, Chern had more contact with Dr. E. Kaehler. Kaehler was then an assistant to Blaschke and had just completed the important paper dealing with Kaehler space. He had also written a book expounding the theories of the French mathematician Elie Cartan on differential equations, and discussiohs of this book at Hamburg led Chern to recognize the genius of Cartan. Indeed, his own doctoral dissertation dealt with "The Application of the Cartan Method to Differential Geometry." He completed the thesis in the autumn of 1935 but did not receive his D.Sc. degree until early 1936, when Blaschke returned to Germany. Although Chern was invited to return to China to teach in 1936, he delayed his return for one year to work with Professor Cartan at Paris, aided by a fellowship from the China Foundation. The year at Paris was a critical one in the development of Chern's mathematical thinking, for Cartan was both an excellent teacher and an amiable counselor. Chern then prepared to return to Tsinghua in the summer of 1937. Before he left Paris, however, the Sino- Japanese war broke out. He revised his travel plans and went to Changsha and later to Kunming, where he became professor of mathematics at Southwest Associated University and held that position for six years.

In 1943 Chern received an invitation to go to the United States to work at the Institute for Advanced Study at Princeton. It was one of the major decisions of his life, since travel conditions were hazardous and his future was indefinite. Chern decided to accept the invitation and made the long journey by American military aircraft in July 1943, taking seven days to fly from Kunming to Miami, Florida, by way of India, Africa, and South America. Chern spent the remaining war years at Princeton. His work, which immediately attracted attention, was a new proof and generalization of the famous Gauss-Bonnet theorem. During the next few years he published a series of significant papers on differential geometry.

Earlier, in 1941, the Academia Sinica, China's principal center of advanced scholarly research, had decided to establish an institute of mathematics. Chiang Li-fu was named to undertake preliminary preparations. After the Japanese surrender in 1945, the institute was given temporary housing at Shanghai, and in the spring of 1946, S. S. Chern returned from the United States to take over its directorship. In July 1947 the institute of mathematics was formally established at Nanking. In March 1948 Chern was elected to membership in the Academia Sinica, one of 81 prominent Chinese scientists and scholars then so honored. The newly elected members held their first meeting at Nanking in September 1948 and appointed 32 men, including S. S. Chern, to the council of Academia Sinica, the executive group responsible for formulating national research policies and planning advanced research. In the following year, the deterioration of the military situation on the mainland led to a complete split in the work of the Academia Sinica. Only two of its constituent units, the institute of mathematics and the institute of history and philology (see Li Chi) were able to transport their equipment and libraries to Taiwan when the National Government moved to that island.

In the years between 1937 and 1948, S. S. Chern's work at the Southwest Associated University and at the institute of mathematics of the Academia Sinica had begun to leave its mark on the younger generation of Chinese mathematicians. With the advent of Communist control on the mainland, S. S. Chern made the difficult decision to leave China for the United States. In July 1949 he became professor of mathematics at the University of Chicago. Chern held that position for over a decade, during which time he consolidated his reputation as a leading figure in the field of pure mathematics. While a member of the faculty at Chicago, Chern lectured in the United States, Canada, Europe, and Latin America. During the academic year 1959-60 he was in Europe, where he spent most of his time in Paris. In July 1960 he became professor of mathematics at the University of California at Berkeley. Chern's research in mathematics covered many fields: differential geometry, topology, algebraic geometry, and functions of several complex variables. He published notable articles in the Journal of the Chinese Mathematical Society in 1940 and in the Proceedings of the National Academy of Science in the United States in 1943 extending the application of Cartan's methods. Thanks primarily to Chern's leadership, the methods of Cartan came to be widely used in differential geometry. There are certain so-called characteristic classes which have been a dominant theme in many recent investigations in differential geometry and topology. These classes are called the Chern characteristic classes. They were first discovered by Chern for the case of a complex analytic manifold in his 1946 paper in the Annals of Mathematics . The integral formula which he obtained in that paper is regarded as a milestone in differential geometry. The distinguished mathematician Heinz Hopf, commenting on Chern's contributions there, stated that they had created a new era in the field of geometry. Chern's unusual geometric insight was later demonstrated in important published papers that generalized, extended, and reformulated key topological concepts. Chern's world reputation was indicated by the fact that he was twice invited to speak to the International Congress of Mathematicians (1950 and 1958). In 1960 he became the first Chinese to deliver the annual American Mathematical Society Colloquium Lectures. In April 1961, immediately after his naturalization as a United States citizen, he was elected to membership in the National Academy of Sciences. At various times he has served as editor of the Proceedings of the American Mathematical Society (1956), the Transactions of the American Mathematical Society (1957-59), the Illinois Journal of Mathematics (I960-), and as associate editor of the Annals of Mathematics, the American Journal of Mathematics, the Journal of Mathematics and Mechanics, and the Duke Mathematical Journal. He was elected to membership in the American Academy of Arts and Sciences in 1963 and served as a vice president of the American Mathematical Society in 1963-64. A full bibliography of S. S. Chern's professional papers through the year 1960 is to be found in the Bibliography of Chinese Mathematics, 1918-1960, prepared by Yuan T'ung-li (q.v.) and published in 1963.

While in Kunming during the war, Chern married Cheng Shih-ning on 28 July 1 939. They had two children, a son and a daughter, whose English names were Paul and May.