Hao Wang (academic)
20 May 1921|
Qihe, Shandong, China
|Died||13 May 1995
New York City, New York, USA
|Fields||Mathematics, philosophy, computer science|
|Institutions||Harvard University, Oxford University, Rockefeller University|
|Alma mater||National Southwestern Associated University, Tsinghua University, Harvard University|
|Doctoral advisor||Willard Quine|
|Doctoral students||Stephen Cook, Shimon Even, Joyce Friedman|
|Known for||Wang tiles|
Born in Jinan, Shandong, in the Republic of China (today in the People's Republic of China), Wang received his early education in China. After obtaining a B.Sc. degree in mathematics from the National Southwestern Associated University in 1943 and an M.A. in Philosophy from Tsinghua University in 1945, he moved to the United States for further graduate studies. He studied logic at Harvard University, culminating in a Ph.D. in 1948. He was appointed to an assistant professorship at Harvard the same year.
During the early 1950s, Wang studied with Paul Bernays in Zurich. In 1956, he was appointed Reader in the Philosophy of Mathematics at Oxford University. In 1959, Wang wrote on an IBM704 computer a program that in only 9 minutes mechanically proved several hundred mathematical logic theorems in Whitehead and Russell's Principia Mathematica. In 1961, he was appointed Gordon Mckay Professor of Mathematical Logic and Applied Mathematics at Harvard. From 1967 until 1991, he headed the logic research group at Rockefeller University in New York City, where he was professor of logic. In 1972, Wang joined in a group of Chinese American scientists led by Chih-Kung Jen as the first such delegation from the U.S. to the People's Republic of China.
One of the most important contributions of Wang was the invention of Wang tiles. He showed that any Turing machine can be turned into a set of Wang tiles. The first noted example of aperiodic tiling is a set of Wang tiles, whose nonexistence Wang had once conjectured, discovered by his student Robert Berger in 1966. He also chronicled Kurt Gödel's philosophical ideas and authored several books on the subject.
In 1983 he was presented with the first Milestone Prize for Automated Theorem-Proving, sponsored by the International Joint Conference on Artificial Intelligence.
- A Survey of Mathematical Logic, Science Press, Peking, 1962, (also North-Holland Publishing Company, Amsterdam).
- From Mathematics to Philosophy, Routledge & Kegan Paul, London, 1974.
- Popular Lectures on Mathematical Logic, Van Nostrand, NY, 1981, ISBN 0-486-67632-3.
- Beyond Analytic Philosophy: Doing Justice to what we know, MIT Press, Cambridge, Mass, 1985, ISBN 0-262-23124-7.
- Reflections on Kurt Gödel, MIT Press, Cambridge, Mass, 1990, ISBN 0-262-73087-1.
- Computation, Logic, Philosophy. A Collection of Essays, Science Press, Beijing, 1990, ISBN 7-03000211-3.
- A Logical Journey: From Gödel to Philosophy, MIT Press, Cambridge, Mass, 1996, ISBN 0-262-23189-1.
- Detailed bibliography of Hao Wang's writings from Philosophia Mathematica, broken link.
- Hao Wang at the Mathematics Genealogy Project
- Wang, Hao (January 1960). "Toward Mechanical Mathematics". IBM Journal of Research and Development 4 (1): 2–22. doi:10.1147/rd.41.0002.
- Wang, Hao (1960), "Toward Mechanical Mathematics", IBM Journal of Research and Development 4 (1): 2–22, doi:10.1147/rd.41.0002
- Loveland, Donald W.; Bledsoe, W. W. (1984). Automated theorem proving: after 25 years. Providence, Rhode Island: American Mathematical Society. ISBN 0-8218-5027-X., page 47