Nicolaas Govert (Dick) de Bruijn (; 9 July 1918 – 17 February 2012) 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 ...

, 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 (38 ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

and

logic 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 ...

.Nicolaas Govert de Bruijn's obituary
2012

Biography

De Bruijn was born in

The Hague The Hague ( ; nl, Den Haag or ) is a city and municipality of the Netherlands, situated on the west coast facing the North Sea. The Hague is the country's administrative centre and its seat of government, and while the official capital of ...

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 university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...

in 1936 but his studies were interrupted by the outbreak of

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

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 The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathemati ...

: 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 The Vrije Universiteit Amsterdam (abbreviated as ''VU Amsterdam'' or simply ''VU'' when in context) is a public research university in Amsterdam, Netherlands, being founded in 1880. The VU Amsterdam is one of two large, publicly funded research ...

'' 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 Groning ...

. From June 1944 he was a Scientific Associate working in

Philips Koninklijke Philips N.V. (), commonly shortened to Philips, is a Dutch multinational conglomerate corporation that was founded in Eindhoven in 1891. Since 1997, it has been mostly headquartered in Amsterdam, though the Benelux headquarters i ...

Research Laboratories in

Eindhoven Eindhoven () is a city and municipality in the Netherlands, located in the southern province of North Brabant of which it is its largest. With a population of 238,326 on 1 January 2022, De Bruijn started his academic career 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 ...

, where he was Professor of Mathematics from 1952 to 1960. In 1960 he moved to the

Technical University Eindhoven The Eindhoven University of Technology ( nl, Technische Universiteit Eindhoven), abbr. TU/e, is a public technical university in the Netherlands, located in the city of Eindhoven. In 2020–21, around 14,000 students were enrolled in its BSc a ...

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 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 ...

. 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'' subseq ...

, * 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 o ...

of the

Penrose tiling A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of the plane by non-overlapping polygons or other shapes, and ''aperiodic'' means that shifting any tiling with these shapes by any finite distance, without r ...

and, more generally, discovering the "projection" and "multigrid" methods for constructing quasi-periodic tilings, * the

De Bruijn–Newman constant The de Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zero of a function, zeros of a certain function (mathematics), function ''H''(''λ'', ...

, * 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 conne ...

, * a different theorem of the same name: the ''De Bruijn–Erdős theorem'', in

incidence geometry In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that involves concepts such as length, angles, continuity, betweenness, and incidence. An ''incidenc ...

, * the

BEST theorem In graph theory, a part of discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of the names of people who discovered it: de Bruijn, van Aarden ...

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. Ove ...

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 The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the ...

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