# Kuo Tsai Chen

### Born: 15 July 1923 in Chekiang (now Zhejiang), China

Died: August 1987 in Urbana, USA

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**Kuo-Tsai Chen**studied at the Southwest Associated University. In 1938 war had broken out between China and Japan and Beijing University, Qinghua University, and Nankai University moved to Kungming to form the State Southwest Associated University. Chen graduated with a Bachelor of Science degree in 1946. This was the year that, following the end of the war, Southwest Associated University was split into the three universities which returned to Beijing, Qinghua, and Nankai. Chen moved to Shanghai where he was employed as an assistant at the Mathematics institute of the Academia Sinica.

After working at the Academia Sinica for one year, Chen was advised to go to the United States to gain a doctorate. He went there in 1947, working under the supervision of Samuel Eilenberg at Indiana University. However Eilenberg had accepted an appointment at Columbia University in New York so Chen followed his supervisor there. Chen supported himself by taking two appointments while in New York, the first appointment was as a mathematics instructor at the National Bible Institute which he held from 1948 to 1950. In the second of these two years he also worked as an assistant at Columbia University. Let us note in passing that the National Bible Institute of New York changed its name to Shelton College, then left New York in 1953. Chen submitted his doctoral dissertation

*Integration in Free Groups*in 1950 to Columbia University and was awarded a Ph.D.

After the award of his doctorate, Chen was appointed as an Instructor at Princeton University. After spending the year 1950-51 at Princeton he was appointed as a Research Associate at the University of Illinois where he again spent a year. In 1952 he was appointed as a Lecturer at the University of Hong Kong where he worked until 1958. His early work, following on from his doctoral dissertation, was on group theory and the theory of links. He published

*Integration in free groups*(1951),

*Commutator calculus and link invariants*(1952),

*Isotopy invariants of links*(1952), and

*A group ring method for finitely generated groups*(1954).

The authors of [2] write:-

After leaving Hong Kong in 1958, Chen went to Brazil where he was appointed as an Associate Professor at the Instituto Tecnologico de Aeronautica in São Jose dos Campos. He was promoted to Professor in 1959 then, following two visits to the Institute for Advanced Study at Princeton (in the winter of 1960-61 and the spring of 1962), he was appointed Associate Professor at Rutgers University in 1962. After being promoted to full Professor at Rutgers in 1963, he left two years later to take up a position at the State University of New York in Buffalo. After two years in Buffalo he returned to the University of Illinois as Professor. He remained in this post for 20 years until his death in 1987.His parents were then living in Taipeh, Taiwan. In the first course he gave in Hong Kong, Chester Chen, as he had become known, met a charming sophomore, Julia Tse-Yee Fong, who became his bride in1953. His very strict sense of duty did not allow him to give his preferred student special help, which occasionally made her very mad at him. Their happy marriage brought forth three children: Matthew in1955, who earned a Doctorate in mathematics at the University of California at Berkeley and who is currently[1990]an electrical engineer with AT&T; Lydia in1956, who graduated from Sarah Lawrence College, and is now a painter and editor; Lucia in1960, who graduated from MIT and is now a graduate student in material science at the University of Illinois.

In Chen's Collected Papers [1] his work is summarised as follows:-

Chen was advisor to six doctoral students at the University of Illinois and these graduated between 1970 and 1980. Richard Hain, who was Chen's last doctoral student graduating in 1980 with his thesisKuo-Tsai Chen is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. His work is intimately related to the theory of minimal models as developed by Dennis Sullivan, whose own work was in part inspired by the research of Chen. An outstanding and original mathematician, Chen's work falls naturally into three periods: his early work on group theory and links in the three sphere; his subsequent work on formal differential equations, which gradually developed into his most powerful and important work; and his work on iterated integrals and homotopy theory, which occupied him for the last twenty years of his life. The goal of Chen's iterated integrals program, which is a de Rham theory for path spaces, was to study the interaction of topology and analysis through path integration.

*Iterated Integrals, Minimal Models and Rational Homotopy Theory*, is the coauthor of the articles [2], and [3]. The authors of [3] note that Chen's death:-

... followed a long illness. He was a devout Christian throughout his life.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (3 books/articles)

**Mathematicians born in the same country**

**Other Web sites**