Albert Nijenhuis (November 21, 1926 – February 13, 2015) was a Dutch-American
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 ...
who specialized in
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
and the theory of
deformations in algebra and geometry, and later worked in
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 ...
.
His high school studies at the gymnasium in Arnhem were interrupted by the evacuation of Arnhem by the Nazis after the failure of
Operation Market Garden
Operation Market Garden was an Allies of World War II, Allied military operation during the World War II, Second World War fought in the Netherlands from 17 to 27 September 1944. Its objective was to create a Salient (military), salient into G ...
by the Allies. He continued his high school mathematical studies by himself on his grandparents’ farm, and then took state exams in 1945.
His university studies were carried out 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 received the degree of Candidaat (equivalent to a Bachelor of Science) in 1947, and a Doctorandus (equivalent to a Masters in Science) in 1950, cum laude. He was a Medewerker (associate) at the Mathematisch Centrum (now the
Centrum Wiskunde & Informatica
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Cou ...
) in Amsterdam 1951–1952. He obtained a
Ph.D.
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
in mathematics in 1952, cum laude (Theory of the geometric object). His thesis advisor was
Jan Arnoldus Schouten
Jan Arnoldus Schouten (28 August 1883 – 20 January 1971) was a Dutch mathematician and Professor at the Delft University of Technology. He was an important contributor to the development of tensor calculus and Ricci calculus, and was one of the ...
.
He came to the United States in 1952 as a
Fulbright
The Fulbright Program, including the Fulbright–Hays Program, is one of several United States Cultural Exchange Programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the people of ...
fellow (1952–1953) at
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
. He then studied at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in Princeton, New Jersey 1953–1955, after which he spent a year as an Instructor in mathematics at the
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
. He then moved to the
University of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington.
Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...
in Seattle, first as an Assistant Professor and then a Professor of Mathematics, departing in 1963 for the
University of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
, where he was a Professor of Mathematics until his retirement in 1987. He was a Fulbright Professor at the University of Amsterdam in 1963–1964, and a visiting professor at the
University of Geneva
The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centu ...
in 1967–1968, and at
Dartmouth College
Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native A ...
in 1977–1978. following his retirement, he was a Professor Emeritus of the University of Pennsylvania and an Affiliate Professor at the University of Washington.
In 1958 he was an invited speaker at the
International Mathematical Congress in Edinburgh. He was a J.S.
Guggenheim Fellow
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
in 1961–1962, again studying at the Institute for Advanced Study. In 1966 he became a correspondent 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 ...
, and in 2012 he became a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
Career
His early work was in the area of
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
. He developed the
Nijenhuis tensor
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not compl ...
in 1951, during his Ph.D studies at the University of Amsterdam. It was also during this time that he explored the properties of the
Schouten-Nijenhuis bracket, although his work was not published until 1955. In a lecture at the American Mathematical Society Summer Institute in Differential Geometry (1956) in Seattle he was the first to mention
deformation
Deformation can refer to:
* Deformation (engineering), changes in an object's shape or form due to the application of a force or forces.
** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies.
* Defor ...
s of complex structures and their exact relationship to
cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...
.
[“Operations on vector-valued differential forms,” unpublished lecture notes, on file with the Archives of American Mathematics http://www.cah.utexas.edu/collections/math.php]
With Alfred Frölicher, he developed the
Frölicher-Nijenhuis bracket (1955). Further work in this area with Roger Richardson yielded the
Nijenhuis–Richardson bracket In mathematics, the algebraic bracket or Nijenhuis–Richardson bracket is a graded Lie algebra structure on the space of alternating multilinear forms of a vector space to itself, introduced by A. Nijenhuis and R. W. Richardson, Jr (1966, 196 ...
(1964).
Soon thereafter his interests shifted to combinatorics. Much of his work was done with
Herbert S. Wilf
Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylv ...
, with whom he published a book in 1975.
After retiring, his interest in differential geometry was rekindled. His last conference presentation and paper were presented when he was nearly 70.
Personal life
Albert Nijenhuis became a U.S. citizen in 1959. He was married since 1955 and had four children. He died at the age of 88 after several months of failing health.
Selected publications
*
*
*
*
*
References
External links
*
University of Washington page
{{DEFAULTSORT:Nijenhuis, Albert
1926 births
2015 deaths
People from Eindhoven
Dutch mathematicians
University of Pennsylvania faculty
University of Washington faculty
Fellows of the American Mathematical Society
Members of the Royal Netherlands Academy of Arts and Sciences