Richard Allen Askey (4 June 1933 – 9 October 2019)
was an 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, mathematical structure, structure, space, Mathematica ...
, known for his expertise in the area of
special function
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications.
The term is defin ...
s. The
Askey–Wilson polynomials (introduced by him in 1984 together with
James A. Wilson
James Arthur Wilson is a mathematician working on special functions and orthogonal polynomials who introduced Wilson polynomials, Askey–Wilson polynomials In mathematics, the Askey–Wilson polynomials (or ''q''-Wilson polynomials) are a family ...
) are on the top level of the (
-)
Askey scheme
In mathematics, the Askey scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in , the Askey scheme was first drawn by and by , ...
, which organizes
orthogonal polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
The most widely used orthogonal polynomials are the cl ...
of (
-)hypergeometric type into a hierarchy. The
Askey–Gasper inequality for
Jacobi polynomials is essential in
de Brange's famous proof of the
Bieberbach conjecture In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was ...
.
Askey earned a B.A. at
Washington University
Washington University in St. Louis (WashU or WUSTL) is a private research university with its main campus in St. Louis County, and Clayton, Missouri. Founded in 1853, the university is named after George Washington. Washington University is ...
in 1955, an M.A. at
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...
in 1956, and a Ph.D. at
Princeton University
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...
in 1961.
After working as an instructor at Washington University (1958–1961) and
University of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
(1961–1963), he joined the faculty of the
University of Wisconsin–Madison
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...
in 1963 as an Assistant Professor of Mathematics. He became a full professor at Wisconsin in 1968, and since 2003 was a professor emeritus.
Askey was a
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 ...
, 1969–1970, which academic year he spent at the ''
Mathematisch Centrum'' in Amsterdam.
In 1983, he gave an
invited lecture at the International Congress of Mathematicians (ICM)
in
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is official ...
.
He was elected a Fellow of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...
in 1993.
In 1999, he was elected to the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...
.
In 2009, he became a fellow of the
Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...
(SIAM).
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 ...
.
In December 2012, he received an honorary doctorate
from
SASTRA University in
Kumbakonam, India.
Askey explained why
hypergeometric functions appear so frequently in mathematical applications: "
Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first r ...
showed that the requirement that a differential equation have regular singular points at three given points and every other complex point is a regular point is so strong a restriction that
(Riemann's) differential equation is the
hypergeometric equation with the three singularities moved to the three given points. Differential equations with four or more singular points only infrequently have a solution which can be given explicitly as a series whose coefficients are known, or have an explicit integral representation. This partly explains why the classical hypergeometric function arises in many settings that seem to have nothing to do with each other. The differential equation they satisfy is the most general one of its kind that has solutions with many nice properties".
Askey was also very much involved with commenting and writing on mathematical education at American schools. A well-known article by him on this topic is ''Good Intentions are not Enough''.
Works
* .
*
* .
See also
*
Askey–Bateman project
The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthu ...
References
External links
Obituary for Richard Allen "Dick" Askey*
ttp://staff.science.uva.nl/~thk/pictures/Askey80.html Photo gallery on the occasion of Dick Askey's 80th.search on author Richard Askeyfrom
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes p ...
*
{{DEFAULTSORT:Askey, Richard
1933 births
2019 deaths
Writers from St. Louis
Members of the United States National Academy of Sciences
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
Mathematical analysts
Princeton University alumni
University of Wisconsin–Madison faculty
Washington University in St. Louis alumni
Washington University in St. Louis mathematicians
Mathematicians from Missouri
Scientists from Missouri
Scientists from St. Louis
Baltimore City College alumni
Fellows of the Society for Industrial and Applied Mathematics
Fellows of the American Academy of Arts and Sciences
Fellows of the American Mathematical Society
Washington University in St. Louis faculty