Richard Askey

Richard Askey
Name	Richard Askey
Birth date	March 4, 1933
Birth place	St. Louis, Missouri
Death date	March 9, 2019
Death place	Madison, Wisconsin
Citizenship	United States
Fields	Mathematics
Alma mater	Harvard University, Washington University in St. Louis
Doctoral advisor	Salomon Bochner
Known for	Theory of orthogonal polynomials, Askey scheme

Richard Askey was an American mathematician known for foundational work on special functions and orthogonal polynomials. He contributed to the classification of hypergeometric orthogonal polynomials and influenced analysis through collaborations and mentorship at major research institutions. His work connected classical analysis with representation theory and mathematical physics, earning recognition from several scientific societies and award committees.

Early life and education

Askey was born in St. Louis, Missouri and attended University of Chicago-area schools before matriculating at Washington University in St. Louis and later Harvard University. At Harvard University he studied under Salomon Bochner and completed a doctorate that situated him in the lineage of analysts including Norbert Wiener, Andrey Kolmogorov, Paul Erdős, and John von Neumann. During his formative years he engaged with seminars influenced by figures such as Gábor Szegő, George Pólya, Paul Erdős collaborators, and contemporaries from Princeton University and Massachusetts Institute of Technology.

Academic career

Askey held appointments at institutions including University of Chicago (visiting), Michigan State University, University of Wisconsin–Madison, and visiting positions at Institute for Advanced Study, University of Cambridge, University of Oxford, and ETH Zurich. He collaborated with mathematicians affiliated with National Academy of Sciences members and contributed to programs at Mathematical Sciences Research Institute, Clay Mathematics Institute, and Institut des Hautes Études Scientifiques. He supervised doctoral students who later held positions at Stanford University, University of California, Berkeley, Yale University, and Princeton University, linking him to networks involving Roger Howe, Israel Gelfand, Harish-Chandra, and Richard Feynman-era mathematical physicists.

Research and contributions

Askey's research centered on hypergeometric functions and orthogonal polynomials, synthesizing results related to the Gauss hypergeometric function, Jacobi polynomials, Hermite polynomials, Laguerre polynomials, and Gegenbauer polynomials. He helped develop the Askey scheme, organizing families such as the Wilson polynomials, Racah polynomials, Hahn polynomials, Meixner polynomials, and Krawtchouk polynomials into a coherent classification that connects with the theory of q-analogues and basic hypergeometric series. His work linked classical analysis to representation-theoretic structures like Lie algebras, SU(2), SO(n), and constructions in quantum groups associated with Vladimir Drinfeld and Michio Jimbo. Askey also studied limit transitions, orthogonality relations, generating functions, and moment problems related to the Hamburger moment problem and Stieltjes moment problem, connecting to probabilists influenced by William Feller and Andrey Kolmogorov. His expositions clarified relationships among results by Gasper and Rahman, Richard Askey-Wilson, George Gasper, Mizan Rahman, and others, facilitating applications in mathematical physics such as in the contexts of the Ising model, Bethe ansatz, and integrable systems.

Awards and honors

Askey received recognition including election to the National Academy of Sciences and honors from American Mathematical Society, Society for Industrial and Applied Mathematics, and American Association for the Advancement of Science. He was awarded prizes and fellowships tied to institutions such as the National Science Foundation, Guggenheim Fellowship, and invited lectureships at International Congress of Mathematicians, Joint Mathematics Meetings, and plenary addresses at conferences organized by European Mathematical Society and Royal Society. His students and collaborators also received fellowships from Simons Foundation and grants from the Army Research Office and Office of Naval Research.

Selected publications

- "Some basic hypergeometric orthogonal polynomials" in proceedings edited by George Andrews and Rogers–Ramanujan identities-related volumes; collaborations with James Wilson and Richard Askey-Wilson on orthogonal polynomials. - Survey articles in journals associated with American Mathematical Society and Proceedings of the National Academy of Sciences summarizing the Askey scheme and extensions to q-series developed by Gasper and Rahman. - Expository works and lecture notes prepared for summer schools at Mathematical Sciences Research Institute and European Mathematical Society meetings, used widely in courses at University of Cambridge, University of Oxford, and Harvard University.

Personal life and legacy

Askey's influence extends through mentorship connecting to mathematicians at University of California, Los Angeles, Columbia University, Duke University, Brown University, Cornell University, Rutgers University, University of Michigan, Pennsylvania State University, and international centers such as Tokyo University, Seoul National University, University of Hong Kong, and University of Toronto. His expository clarity inspired monographs used at Princeton University Press and Cambridge University Press and continues to shape research in areas touched by collaborators from Mathematical Reviews, Zentralblatt MATH, and editorial boards of journals like Transactions of the American Mathematical Society and Journal of Approximation Theory. Askey's passing in Madison, Wisconsin was noted by institutions including University of Wisconsin–Madison and National Academy of Sciences, and his legacy endures through the Askey scheme's central role in ongoing work on special functions, q-series, and connections to mathematical physics and modern representation theory.

Category:American mathematicians