Hao Wang (mathematician)

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Hao Wang ( Chinese  王 浩 , Pinyin Wáng Hào ; born May 20, 1921 in Jinan , Shandong Province , China ; † May 13, 1995 in New York City ) was a Sino-American logician, mathematician and philosopher . He developed u. a. the Wang tiling named after him .

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Hao Wang studied in China at the National University of the Southwest, where he received his bachelor's degree in 1943. In 1945 he received his master's degree in philosophy from Tsinghua University and then went to the United States, where he studied logic at Harvard University . In 1948 he received his doctorate there under Willard Van Orman Quine ( An Economic Ontology for Classical Arithmetic ) and at the same time became Assistant Professor in Philosophy and 1951 Junior Fellow. In 1950/51 he was with Paul Bernays in Zurich , 1953/54 with the Burroughs Corporation and from 1956 John Locke Lecturer at Oxford University . In 1961 he became Gordon McKay Professor of Mathematical Logic at Harvard and from 1967 to 1991 he was professor and head of the research group for mathematical logic at Rockefeller University in New York. In 1991 he retired, but stayed at the university.

Wang made many contributions to mathematical logic. At IBM in 1960 he developed computer programs for the derivation of propositional and predicate logic sentences, as formulated in the Principia Mathematica by Bertrand Russell and Alfred North Whitehead . In 1961 he invented Wang tiling, which, according to Wang, provides predictability models equivalent to Turing machines. In 1966 they also provided the first examples of aperiodic tiling ( Robert Berger ), the best-known examples of which are known as quasicrystals .

Wang also studied the philosophical work of Kurt Gödel , about which he wrote several articles and books.

In 1952, Wang was elected to the American Academy of Arts and Sciences . Since 1970 he has been a corresponding member of the British Academy . In 1985 he became an honorary professor at Peking University and in 1986 at Qinghua University .

His PhD students include Stephen Cook and Robert Berger.


  • A formal system for logic , Journal of Symbolic Logic, Volume 15, 1950, pp. 25-32
  • The non finitizability of impredicative principles , in: Proceedings of the National Academy of Sciences (USA), Vol. 39 (1950), pp. 479-484
  • The irreducibility of impredicative principles , in: Mathematische Annalen, Vol. 125 (1952), pp. 56-66
  • with Robert McNaughton: Les systèmes axiomatiques de la théorie des ensembles. Gauthier-Villars 1953.
  • On denumerable bases of formal systems , in: Mathematical Interpretations of formal Systems, Amsterdam North Holland 1955
  • A Survey of Mathematical Logic. North Holland 1963, also as Logic, Computers and Sets. Chelsea 1970 (with reprints of some of his articles).
  • Games, Logic and Computer. Scientific American November 1965.
  • From Mathematics to Philosophy. Routledge 1974.
  • Popular Lectures on Mathematical Logic. 1981, Dover 1993.
  • Beyond Analytic Philosophy: Doing Justice to What We Know. MIT Press 1985.
  • Reflections on Kurt Gödel. MIT Press 1987.
  • Computation, Logic, Philosophy - a Collection of Essays. Kluwer 1990.
  • A Logical Journey: from Gödel to Philosophy. MIT Press 1996.
  • Toward Mechanical Mathematics. IBM Journal of Research and Development, Vol. 4, 1962, p. 2.
  • Proving Theorems by Pattern Recognition. Part 1, Journal ACM , Vol. 3, 1960, p. 220, Part 2, Bell System Technical Journal Vol. 40, 1961, p. 1.


  • Charles Parsons: Hao Wang - in memoriam. Bulletin of Symbolic Logic, Vol. 2, 1996, p. 108.

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