Hao Wang (; 20 May 1921 – 13 May 1995) was a Chinese-American
logician,
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.
Biography
Born in
Jinan,
Shandong
Shandong ( , ; ; Chinese postal romanization, alternately romanized as Shantung) is a coastal Provinces of China, province of the China, People's Republic of China and is part of the East China region.
Shandong has played a major role in His ...
, in the
Republic of China (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 List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slig ...
), 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 Univers ...
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. ...
from
Tsinghua University 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 highe ...
, 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
Zürich
, neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon
, twintowns = Kunming, San Francisco
Z ...
. 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 computer a program that in only 9 minutes mechanically proved several hundred
mathematical logic
Mathematical logic is the study of 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 forma ...
theorems in
Whitehead and
Russell's ''
Principia Mathematica''. 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 in
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 academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...
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. 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 alg ...
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 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 consi ...
's later philosophy of mathematics, which he called "anthropologism." Later he broadened this reading in the foundations of mathematics. He chronicled
Kurt Gödel'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 pr ...
.
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 Wangand
Robin Gandy (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