Hao Wang (; 20 May 1921 – 13 May 1995) was a Chinese-American

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arg ...

, philosopher, mathematician, and commentator on

Kurt Gödel Kurt Friedrich Gödel ( ; ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly ...

Biography

Born in

Jinan Jinan is the capital of the province of Shandong in East China. With a population of 9.2 million, it is one of the largest cities in Shandong in terms of population. The area of present-day Jinan has played an important role in the history of ...

, Shandong, in the

Republic of China Taiwan, officially the Republic of China (ROC), is a country in East Asia. The main geography of Taiwan, island of Taiwan, also known as ''Formosa'', lies between the East China Sea, East and South China Seas in the northwestern Pacific Ocea ...

(today in the People's Republic of China), Wang received his early education in China. He obtained a BSc degree in mathematics from the

National Southwestern Associated University The National Southwestern Associated University was a national public university from 1938 to 1946 based in Kunming, Yunnan, China. It was formed by the wartime incorporation of National Peking University, National Tsinghua University, and Nat ...

in 1943 and an M.A. in philosophy from

Tsinghua University Tsinghua University (THU) is a public university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of China. The university is part of Project 211, Project 985, and the Double First-Class Constructio ...

in 1945, where his teachers included

Feng Youlan Feng Youlan (; 4 December 1895 – 26 November 1990) was a Chinese philosopher, historian, and writer who was instrumental for reintroducing the study of Chinese philosophy in the modern era. The name he published under in English was 'Fung ...

and Jin Yuelin, after which he moved to the United States for further graduate studies. He studied logic under

W. V. O. Quine W. may refer to: * SoHo (Australian TV channel) (previously W.), an Australian pay television channel * ''W.'' (film), a 2008 American biographical drama film based on the life of George W. Bush * "W.", the fifth track from Codeine's 1992 EP ''Bar ...

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

, 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 Isaac Bernays ( ; ; 17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator ...

Zürich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

. In 1956, he was appointed Reader in the Philosophy of Mathematics at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

. In 1959, Wang wrote on an

IBM 704 The IBM 704 is the model name of a large digital computer, digital mainframe computer introduced by IBM in 1954. Designed by John Backus and Gene Amdahl, it was the first mass-produced computer with hardware for floating-point arithmetic. The I ...

computer a program that in only 9 minutes mechanically proved several hundred

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

theorems in Whitehead and Russell's ''

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1 ...

''. In 1961, he was appointed

Gordon McKay Gordon McKay (1821–1903) was an American businessman and philanthropist. An important figure in the mechanization of the shoe industry, his most lucrative idea was to lease his "McKay machines" rather than selling them outright, collecting a ...

Professor of Mathematical Logic and Applied Mathematics at Harvard. From 1967 until 1991, he headed the logic research group at

Rockefeller University The Rockefeller University is a Private university, private Medical research, biomedical Research university, research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and pro ...

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 Chih-Kung Jen (; August 15 or October 2, 1906 – November 19, 1995) 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 ...

as the first such delegation from the U.S. to the People's Republic of China. One of Wang's most important contributions was the

Wang tile Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, is a class of formal systems. They are modeled visually by square tiles with a color on each side. A set of such tiles is selected, and ...

. He showed that any

Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...

can be turned into a set of Wang tiles. The domino problem is to find an algorithm that uses a set of Wang tiles to tile the plane. The first noted example of

aperiodic tiling An aperiodic tiling is a non-periodic Tessellation, tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic set of prototiles, aperiodic if copie ...

is a set of Wang tiles, whose nonexistence Wang had once conjectured, discovered by his student Robert Berger in 1966. Wang also had a significant influence on theory of computational complexity. A philosopher in his own right, Wang also developed a penetrating interpretation of

Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Witt ...

's later philosophy of mathematics, which he called "anthropologism." Later he broadened this reading in the foundations of mathematics. He chronicled

's philosophical ideas and authored several books on the subject, thereby providing contemporary scholars many insights elucidating Gödel's later philosophical thought. He saw his own philosophy of "substantial factualism" as a middle ground that includes both abstract theoretical formulations and the ordinary language of everyday discourse. In 1983 he was presented with the first Milestone Prize for Automated Theorem-Proving, sponsored by the

International Joint Conference on Artificial Intelligence The International Joint Conference on Artificial Intelligence (IJCAI) is a conference in the field of artificial intelligence. The conference series has been organized by the nonprofit IJCAI Organization since 1969.Jointly sponsored by the IJCAI O ...

. On 13 May 1995, Wang died at

New York Hospital Weill Cornell Medical Center (; previously known as New York Hospital, Old New York Hospital, and City Hospital) is a research hospital in New York City. It is the teaching hospital for Cornell University's medical school and is part of NewYork-P ...

one week from his 74th birthday. According to his wife Hanne Tierney, Wang's cause of death was from

lymphoma Lymphoma is a group of blood and lymph tumors that develop from lymphocytes (a type of white blood cell). The name typically refers to just the cancerous versions rather than all such tumours. Signs and symptoms may include enlarged lymph node ...

. In addition to Tierney, Wang was survived by a daughter and two sons.

Books

*''Les Systèmes axiomatiques de la Théorie des Ensembles'', Gauthier-Villars; Paris, 1953. ang 1953a, with Robert McNaughton *''A Survey of Mathematical Logic''. Peking: Science Press; Amsterdam: North-Holland, 1962. ang 1962a *''From Mathematics to Philosophy''. London: Routledge & Kegan Paul, 1974. ang 1974a *''Popular Lectures on Mathematical Logic''. New York: Van Nostrand, 1981. ang 1981a . Dover reprint 2014. *''Beyond Analytic Philosophy: Doing Justice to What We Know''. Cambridge, Massachusetts: MIT Press, 1985. ang 1985a . *''Reflections on Kurt Gödel''. Cambridge, Massachusetts: MIT Press, 1987. ang 1987a . *''Computation, Logic, Philosophy. A Collection of Essays''. Beijing: Science Press; Dordrecht: Kluwer Academic, 1990. ang 1990a . *''A Logical Journey: From Gödel to Philosophy''. Cambridge, Massachusetts: MIT Press, 1996. ang 1996a .Rodríguez-Consuegra, Francisco
"Philosophy in Hao Wang's Conversations with Gödel: Review of Hao Wang, A Logical Journey. From Gödel to Philosophy."
Modern Logic 8, no. 3–4 (2001): 137–152.

References

External links

*
Video interview with Hao Wang
and

Robin Gandy Robin Oliver Gandy (22 September 1919 – 20 November 1995) was a British mathematician and logician. He was a friend, student, and associate of Alan Turing, having been supervised by Turing during his PhD at the University of Cambridge, where ...

(and portrait of Wang) ;Detailed bibliography
"A Bibliography of Hao Wang"
from ''Philosophia Mathematica.'' References in square brackets are to this source. {{DEFAULTSORT:Wang, Hao 1921 births 1995 deaths 20th-century American mathematicians Philosophers of mathematics Chinese emigrants to the United States Chinese logicians American logicians Harvard Graduate School of Arts and Sciences alumni Harvard University Department of Philosophy faculty Tsinghua University alumni American writers of Chinese descent Writers from Dezhou Educators from Shandong Scientists from Shandong Philosophers from Shandong Corresponding fellows of the British Academy National Southwestern Associated University alumni