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Arend Heyting (; 9 May 1898 – 9 July 1980) was a Dutch
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
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 ...
.
Biography
Heyting was a student of
Luitzen Egbertus Jan Brouwer
Luitzen Egbertus Jan Brouwer (; ; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and compl ...
at the
University of Amsterdam
The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...
, and did much to put
intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...
on a footing where it could become part of
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 ...
. Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics. The inclusion of Brouwer's name in the
Brouwer–Heyting–Kolmogorov interpretation In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogorov. It is also sometimes called the real ...
is largely honorific, as Brouwer was opposed in principle to the formalisation of certain intuitionistic principles (and went as far as calling Heyting's work a "sterile exercise").
In 1942 he became a member of the
Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...
.
Heyting was born in
Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population ...
,
Netherlands
)
, anthem = ( en, "William of Nassau")
, image_map =
, map_caption =
, subdivision_type = Sovereign state
, subdivision_name = Kingdom of the Netherlands
, established_title = Before independence
, established_date = Spanish Netherl ...
, and died in
Lugano
Lugano (, , ; lmo, label=Ticinese dialect, Ticinese, Lugan ) is a city and municipality in Switzerland, part of the Lugano District in the canton of Ticino. It is the largest city of both Ticino and the Italian-speaking southern Switzerland. Luga ...
,
Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
.
Selected publications
*Heyting, A. (1930) Die formalen Regeln der intuitionistischen Logik. (German) 3 parts, In: Sitzungsberichte der preußischen Akademie der Wissenschaften. phys.-math. Klasse, 1930, 42–56, 57-71, 158-169.
*Heyting, A. (1934) Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie. Springer, Berlin.
*Heyting, A. (1941) Untersuchungen der intuitionistische Algebra. (German) Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect. 1. 18. no. 2, 36 pp.
*Heyting, A. (1956) Intuitionism. An introduction. North-Holland Publishing Co., Amsterdam.
*Heyting, A. (1959) Axioms for intuitionistic plane affine geometry. The axiomatic method. With special reference to geometry and physics. Proceedings of an International Symposium held at the Univ. of Calif., Berkeley, Dec. 26, 1957–Jan 4, 1958 (edited by L. Henkin, P. Suppes and A. Tarski) pp. 160–173 Studies in Logic and the Foundations of Mathematics North-Holland Publishing Co., Amsterdam.
*Heyting, A. (1962) After thirty years. 1962 Logic, Methodology and Philosophy of Science (Proc. 1960 Internat. Congr.) pp. 194–197 Stanford Univ. Press, Stanford, Calif.
*Heyting, A. (1963) Axiomatic projective geometry. Bibliotheca Mathematica, Vol. V. Interscience Publishers John Wiley & Sons, Inc., New York; P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam.
*Heyting, A. (1966) Intuitionism: An introduction. Second revised edition North-Holland Publishing Co., Amsterdam.
*Heyting, A. (1973) Address to Professor A. Robinson. At the occasion of the Brouwer memorial lecture given by Prof. A.Robinson on the 26th April 1973. Nieuw Arch. Wisk. (3) 21, pp. 134–137.
*Heyting, A. (1974) Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie. (German) Reprint. Springer-Verlag, Berlin–New York.
*Heyting, A. (1980) Axiomatic projective geometry. Second edition. Bibliotheca Mathematica
athematics Library V. Wolters-Noordhoff Scientific Publications, Ltd., Groningen; North-Holland Publishing Co., Amsterdam–New York.
References
External links
*
1898 births
1980 deaths
Dutch mathematicians
Dutch logicians
Members of the Royal Netherlands Academy of Arts and Sciences
University of Amsterdam alumni
University of Amsterdam faculty
Scientists from Amsterdam
Intuitionism
{{Europe-mathematician-stub