# Hsien Chung Wang

### Quick Info

Peking (now Beijing), China

New York, USA

**Hsien Chung Wang**was a Chinese-born American mathematician who worked in differential geometry, Lie groups and algebraic topology.

### Biography

**Hsien Chung Wang**studied at Nankai High School in Tientsin. He began his university studies at Tsing Hua University in Peking in 1936. His original intention was to take a degree in physics so he began his studies taking courses which would lead to this degree.

On 7 July 1937 Japanese and Chinese troops clashed near Peking. In late July further fighting broke out and the Japanese quickly captured Peking and Tientsin. Tsing Hua University was moved to Southwest China where it was amalgamated with Nankai and Peking universities. Wang had to journey to the new site of his university and begin his studies again. Perhaps the political events had a positive effect as far as mathematics was concerned since Wang changed his studies to mathematics when he took them up again at the re-established university.

Wang graduated in 1941 and began to study under S S Chern. He was awarded a master's degree in 1944 and began teaching in a school. However, after one year, he was awarded a British Council Scholarship to continue his studies in England. After a while at Sheffield he studied under Newman at Manchester and received a Ph.D. in 1948.

On his return to China, Wang took up a research post at the Chinese National Academy of Sciences. However political events were again to play a major part in Wang's career. Between early November 1948 and early January 1949 the Communists and Nationalists fought for control. The National Government re-established itself on Taiwan where it had withdrawn early in 1949. The Chinese National Academy of Sciences was set up on Taiwan and Wang followed the Academy there.

From 1949 Wang lived in the United States. This was not an easy time to obtain a mathematics post in the United States and Wang, although he had an impressive reputation as a mathematician by this time, could only manage a succession of temporary posts. First he taught at Louisiana State, then for two years at Baton Rouge before he spent his first year at Princeton in 1951-52. Again he held temporary posts, this time for two years at Alabama Polytechnic, then 1954-55 at Princeton again, 1955-57 at the University of Washington in Seattle followed by a time at Columbia in New York. Wang married during his time in Seattle.

The year 1957 saw Wang receive an offer of a permanent post for the first time. This was at Northwestern University where he remained, having further spells at Princeton during this time, until 1966 when he was appointed to Cornell.

Wang worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group.

Wang's most important work was on discrete subgroups of Lie groups, a topic on which he continued to work. He published

*Two-point homogeneous spaces*in 1952 which dealt with a homogeneous space of a compact Lie group. In 1960 he studied transformation groups of $n$-spheres and wrote the highly original paper

*Compact transformation groups of $S^{n}$ with an $(n-1)$-dimensional orbit*.

The latter part of Wang's life is described in [1] as follows:-

Wang's last paper was published in 1973, after which his research was much curtailed because of anxiety for his wife, who had developed cancer. His teaching and other mathematical and administrative activities continued unabated, however, and he played an important role in the department at Cornell. He was very much liked there, as everywhere, for his modesty, generosity, kindness and curtsey. He was a fine teacher and lecturer. ... He enjoyed excellent health until he was suddenly stricken with leukaemia in June 1978. He succumbed within weeks, to be survived for only a few months by his wife.

### References (show)

- W M Boothby, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - W M Boothby, S S Chern and S P Wang, The mathematical work of H C Wang,
*Bull. Inst. Math. Acad. Sinica***8**(2-3, pt 1) (1980), xiii-xxiv. - Hsien Chung Wang,
*Bull. Institute of Mathematics, Academia Sinicia***8**(1980). - S T Hu, Hsien Chung Wang 1918-1978,
*Bull. Inst. Math. Acad. Sinica***8**(2-3, pt 1) (1980), i-xii. - Z D Yan, Deep mourning for the late Hsien Chung Wang (Chinese),
*Adv. in Math. (Beijing)***10**(1) (1981), 77-78.

### Additional Resources (show)

Other websites about Hsien C Wang:

Written by J J O'Connor and E F Robertson

Last Update December 1996

Last Update December 1996