Wilhelmus Luxemburg
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Wilhelmus Anthonius Josephus Luxemburg (11 April 1929 – 2 October 2018) was a Dutch American mathematician who was a professor of
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
at the
California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...
. He received his B.A. from the
University of Leiden Leiden University (abbreviated as ''LEI''; ) is a public research university in Leiden, Netherlands. Established in 1575 by William, Prince of Orange as a Protestant institution, it holds the distinction of being the oldest university in the Neth ...
in 1950; his M.A., in 1953; his Ph.D., from the Delft Institute of Technology, in 1955. He was an assistant professor at Caltech from 1958-60; an associate professor from 1960–62; a professor from 1962–2000; and a professor Emeritus, from 2000. He was the Executive Officer for Mathematics during 1970–85. 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, ...
. Luxemburg became a corresponding member of the
Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...
in 1974. Luxemburg contributed to the development of
non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definitio ...
by popularizing the construction of
hyperreal number In mathematics, hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite if, and only if, , x, for some integer n
s in the 1960s. Though Edwin Hewitt had shown the construction in 1948, the formalization of non-standard analysis is generally associated with
Abraham Robinson Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorp ...
. Other notable work he did was in the theory of
Riesz space In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper ''S ...
s ( partially ordered
vector space In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called sc ...
s where the order structure is a lattice).


Selected publications

* 1955: ''Banach function spaces''. Thesis, Technische Hogeschool te Delft, 1955. * 1969: "A general theory of monads", in ''Applications of Model Theory to Algebra, Analysis, and Probability'' (Internat. Sympos., Pasadena, Calif., 1967) pp. 18–86
Holt, Rinehart and Winston Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in high schools. The Holt name is derived from that of U.S. publisher Henry Holt (1840–1926), co-founder of ...
* 1971: (with Zaanen, A. C.) ''Riesz Spaces''. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York. * 1976: (with Stroyan, K. D.) ''Introduction to the Theory of Infinitesimals''. Pure and Applied Mathematics, No. 72.
Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...
* 1978: (with Schep, A. R.) "A Radon-Nikodym type theorem for positive operators and a dual", Nederl. Akad. Wetensch. Indag. Math. 40, no. 3, 357–375. * 1979: ''Some Aspects of the Theory of Riesz Spaces'', University of Arkansas Lecture Notes in Mathematics, 4.
University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a Public university, public Land-grant university, land-grant research university in Fayetteville, Arkansas, United States. It is the Flagship campus, flagship campus of the University of Arkan ...
, Fayetteville, Ark.


References


External links

*


See also

* Influence of non-standard analysis {{DEFAULTSORT:Luxemburg, Wilhelmus 20th-century Dutch mathematicians 21st-century Dutch mathematicians American people of Dutch descent 20th-century American mathematicians 21st-century American mathematicians California Institute of Technology faculty Delft University of Technology alumni Fellows of the American Mathematical Society Members of the Royal Netherlands Academy of Arts and Sciences People from Delft 1929 births 2018 deaths Functional analysts