Wang Hao
Encyclopedia
Wang Hao, also Hao Wang was a Chinese American
logician, philosopher and mathematician
.
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 MacKay 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 tile
s. 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
.
Chinese American
Chinese Americans represent Americans of Chinese descent. Chinese Americans constitute one group of overseas Chinese and also a subgroup of East Asian Americans, which is further a subgroup of Asian Americans...
logician, philosopher and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Born in Jinan
Jinan
Jinan is the capital of Shandong province in Eastern China. The area of present-day Jinan has played an important role in the history of the region from the earliest beginnings of civilisation and has evolved into a major national administrative, economic, and transportation hub...
, Shandong, in the Republic of China
Republic of China
The Republic of China , commonly known as Taiwan , is a unitary sovereign state located in East Asia. Originally based in mainland China, the Republic of China currently governs the island of Taiwan , which forms over 99% of its current territory, as well as Penghu, Kinmen, Matsu and other minor...
(today in the People's Republic of China
People's Republic of China
China , officially the People's Republic of China , is the most populous country in the world, with over 1.3 billion citizens. Located in East Asia, the country covers approximately 9.6 million square kilometres...
), Wang received his early education in China. After obtaining a B.Sc. degree in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from the National Southwestern Associated University
National Southwestern Associated University
When the Second Sino-Japanese War broke out between China and Japan in 1937, Peking University, Tsinghua University and Nankai University, merged to form Changsha Temporary University in Changsha, and later National Southwestern Associated University in Kunming...
in 1943 and an M.A. in Philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
from Tsinghua University
Tsinghua University
Tsinghua University , colloquially known in Chinese as Qinghua, is a university in Beijing, China. The school is one of the nine universities of the C9 League. It was established in 1911 under the name "Tsinghua Xuetang" or "Tsinghua College" and was renamed the "Tsinghua School" one year later...
in 1945, he moved to the United States for further graduate studies. He studied logic at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, 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
Paul Bernays
Paul Isaac Bernays was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant to, and close collaborator of, David Hilbert.-Biography:Bernays spent his childhood in Berlin. Bernays attended the...
in Zurich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake 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
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
theorems in Whitehead and Russell's Principia Mathematica
Principia Mathematica
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913...
. In 1961, he was appointed Gordon MacKay Professor of Mathematical Logic and Applied Mathematics at Harvard. From 1967 until 1991, he headed the logic research group at Rockefeller University
Rockefeller University
The Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, where he was professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
of logic. In 1972, Wang joined in a group of Chinese American scientists led by Chih-Kung Jen
Chih-Kung Jen
Chih-Kung Jen was a Chinese physicist who emigrated to the U.S. and participated in some of the 20th century's major scientific, political and social developments in both the United States and China....
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 tile
Wang tile
Wang tiles , first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems...
s. He showed that any Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
can be turned into a set of Wang tiles. The first noted example of aperiodic tiling
Aperiodic tiling
An aperiodic tiling is a tiling obtained from an aperiodic set of tiles. Properly speaking, aperiodicity is a property of particular sets of tiles; any given finite tiling is either periodic or non-periodic...
is a set of Wang tiles, whose nonexistence Wang had once conjectured, discovered by his student Robert Berger
Robert Berger (mathematician)
Robert Berger is known for inventing the first aperiodic tiling using a set of 20,426 distinct tile shapes.The unexpected existence of aperiodic tilings, although not Berger's explicit construction of them, follows from another result proved by Berger: that the so-called domino problem is...
in 1966. He also chronicled Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
'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
International Joint Conference on Artificial Intelligence
The International Joint Conference on Artificial Intelligence is a meeting of researchers from the different areas of artificial intelligence . It is organized by the IJCAI, Inc., and has been held every other year since 1969. Originally, the other years saw the meetings of the ECAI, AAAI, and a...
.
Books
- 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 0486676323
- Beyond Analytic Philosophy: Doing Justice to what we know, MIT Press, Cambridge, Mass, 1987.
- Reflections on Kurt Gödel, MIT Press, Cambridge, Mass, 1990, ISBN 0262730871
- Computation, Logic, Philosophy. A Collection of Essays, Science Press, Beijing, 1990.
- A Logical Journey: From Gödel to Philosophy, MIT Press, Cambridge, Mass, 1996, ISBN 0262231891
External links
- Detailed bibliography of Hao Wang's writings from Philosophia Mathematica