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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, 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 had an imme ...

Biography

Born in

Jinan Jinan (), Postal Map Romanization, alternately romanization of Chinese, romanized as Tsinan, is the Capital (political), capital of Shandong province in East China, Eastern China. With a population of 9.2 million, it is the second-largest city i ...

Shandong Shandong ( , ; ; alternately romanized as Shantung) is a coastal province of the People's Republic of China and is part of the East China region. Shandong has played a major role in Chinese history since the beginning of Chinese civilizati ...

, in the

Republic of China Taiwan, officially the Republic of China (ROC), is a country in East Asia, at the junction of the East and South China Seas in the northwestern Pacific Ocean, with the People's Republic of China (PRC) to the northwest, Japan to the northeast ...

(today in the

People's Republic of China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

), Wang received his early education in China. He obtained a BSc degree in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

from the

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 Universi ...

in 1943 and an M.A. in

Philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

from

Tsinghua University Tsinghua University (; abbreviation, abbr. THU) is a National university, national Public university, public research university in Beijing, China. The university is funded by the Ministry of Education of the People's Republic of China, Minis ...

in 1945, where his teachers included Feng Youlan and Jin Yuelin, after which he moved to the United States for further graduate studies. He studied logic under W.V. Quine at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, 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 of ...

Zürich Zürich () is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 43 ...

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

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

. In 1959, Wang wrote on an

IBM 704 The IBM 704 is a large digital mainframe computer introduced by IBM in 1954. It was the first mass-produced computer with hardware for floating-point arithmetic. The IBM 704 ''Manual of operation'' states: The type 704 Electronic Data-Pro ...

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

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

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 mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

''. In 1961, he was appointed

Gordon McKay Gordon McKay (1821–1903) was an American businessman and philanthropist. Biography He was born in Pittsfield, Massachusetts. He was trained as an engineer, worked on a railroad, and then on the Erie Canal before he purchased a machine shop. ...

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 biomedical research and graduate-only university in New York City, New York. It focuses primarily on the biological and medical sciences and provides doctoral and postdoctoral education. It is classif ...

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

, where he was

professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...

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 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, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, an ...

. 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 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 if copies of these tiles can form only non- period ...

is a set of Wang tiles, whose nonexistence Wang had once conjectured, discovered by his student Robert Berger in 1966. 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-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...

'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. His interpretations of Gödel are taken to be authoritative. 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 the leading conference in the field of Artificial Intelligence. The conference series has been organized by the nonprofit IJCAI Organization since 1969, making it the oldest p ...

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

*

from ''The New York Times.''
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 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