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Nicolaas Govert (Dick) de Bruijn (; 9 July 1918 – 17 February 2012) was a Dutch mathematician, noted for his many contributions in the fields of
analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...
, number theory, combinatorics and logic.Nicolaas Govert de Bruijn's obituary
2012


Biography

De Bruijn was born in The Hague where he attended elementary school between 1924 and 1930 and secondary school until 1934. He started studies in mathematics at
Leiden University Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of L ...
in 1936 but his studies were interrupted by the outbreak of World War II in 1939. He became a full-time Assistant in the Department of Mathematics of the Technological University of Delft in September 1939 while continuing his studies. MacTutor History of Mathematics archive: Nicolaas Govert de Bruijn. He completed his undergraduate studies at the University of Leiden in 1941. He received his PhD in 1943 from the '' Vrije Universiteit Amsterdam'' with a thesis entitled "''Over modulaire vormen van meer veranderlijken''" advised by
Jurjen Ferdinand Koksma Jurjen Ferdinand Koksma (21 April 1904, Schoterland – 17 December 1964, Amsterdam) was a Dutch mathematician who specialized in analytic number theory. Koksma received his Ph.D. degree (''cum laude'') in 1930 at the University of Gronin ...
. From June 1944 he was a Scientific Associate working in Philips Research Laboratories in Eindhoven. He married Elizabeth de Groot on 30 August 1944. The couple had four children: Jorina Aleida (born 19 January 1947), Frans Willem (born 13 April 1948), Elisabeth (born 24 November 1950), and Judith Elizabeth (born 31 March 1963). De Bruijn started his academic career at the University of Amsterdam, where he was Professor of Mathematics from 1952 to 1960. In 1960 he moved to the Technical University Eindhoven where he was Professor of Mathematics until his retirement in 1984. Among his graduate students were Johannes Runnenburg (1960), Antonius Levelt (1961), S. Ackermans (1964), Jozef Beenakker (1966), W. van der Meiden (1967), Matheus Hautus (1970), Robert Nederpelt Lazarom (1973), Lambert van Benthem Jutting (1977), A. Janssen (1979), Diederik van Daalen (1980), and Harmannus Balsters (1986). In 1957 he was appointed member of the Royal Netherlands Academy of Arts and Sciences. He was Knighted with the
Order of the Netherlands Lion The Order of the Netherlands Lion, also known as the Order of the Lion of the Netherlands ( nl, De Orde van de Nederlandse Leeuw, french: L'Ordre du Lion Néerlandais) is a Dutch order of chivalry founded by King William I of the Netherlands on ...
.


Work

De Bruijn covered many areas of mathematics. He is especially noted for: * the discovery of the
De Bruijn sequence In combinatorial mathematics, a de Bruijn sequence of order ''n'' on a size-''k'' alphabet ''A'' is a cyclic sequence in which every possible length-''n'' string on ''A'' occurs exactly once as a substring (i.e., as a ''contiguous'' subseque ...
, * discovering an
algebraic theory Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Sentential logic is the subset ...
of the Penrose tiling and, more generally, discovering the "projection" and "multigrid" methods for constructing quasi-periodic tilings, * the De Bruijn–Newman constant, * the ''De Bruijn–Erdős theorem'', in
graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
, * a different theorem of the same name: the ''De Bruijn–Erdős theorem'', in incidence geometry, * the BEST theorem in graph theory, and * De Bruijn indices. He wrote one of the standard books in advanced
asymptotic analysis In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as beco ...
(De Bruijn, 1958). In the late sixties, he designed the
Automath Automath ("automating mathematics") is a formal language, devised by Nicolaas Govert de Bruijn starting in 1967, for expressing complete mathematical theories in such a way that an included automated proof checker can verify their correctness. Ov ...
language for representing mathematical proofs, so that they could be verified automatically (see automated theorem checking). Shortly before his death, he had been working on models for the human brain.


Publications

Books, a selection: * 1943. ''Over modulaire vormen van meer veranderlijken'' * 1958. ''Asymptotic Methods in Analysis,'' North-Holland, Amsterdam. Articles, a selection: * de Bruijn, Nicolaas Govert. "A combinatorial problem", 1946. In Proceedings of the Section of Sciences, Vol. 49, No. 7, pp. 758–764. Koninklijke Nederlandse Akademie v. Wetenschappen. * de Bruijn, Nicolaas Govert.
The mathematical language AUTOMATH, its usage, and some of its extensions
" Symposium on automatic demonstration. Springer Berlin Heidelberg, 1970. * de Bruijn, Nicolaas Govert.
Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem
" Indagationes Mathematicae (Proceedings). Vol. 75. No. 5. North-Holland, 1972.


References


External links


Nicolaas Govert de Bruijn's obituary

Bruijn N.G. de
at win.tue.nl (in Dutch) {{DEFAULTSORT:Bruijn, Nicolaas Govert de 1918 births 2012 deaths 20th-century Dutch mathematicians Graph theorists Leiden University alumni Vrije Universiteit Amsterdam alumni University of Amsterdam faculty Eindhoven University of Technology faculty Scientists from The Hague Knights of the Order of the Netherlands Lion Members of the Royal Netherlands Academy of Arts and Sciences