SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #12   ------------   OP-SF NET 5.5  -----------  September 15, 1998
From: Tom H. Koornwinder (
Subject: Rota's "Ten Math problems I will never solve"

(From opsftalk)

The 2/98 issue of the journal "Mitteilungen der Deutschen
Mathematiker-Vereinigung"  has a "Sonderbeilage zum ICM'98 in Berlin"
called "Zukunft der Mathematik". One of the contributors (in English) is
Gian-Carlo Rota with the title "Ten Mathematics Problems I will never
solve"  (Invited address at the joint meeting of the American Mathematical
Society and the Mexican Mathematical Society, December 6, 1997).  His
fourth Problem is "A unified theory of special functions", his eighth
Problem is "Confluent symmetric functions".

Concerning Problem 4 he has a funny comment:
Lately, q-analogs have come into high fashion. They have been ennobled by
the name "quantum groups", even though they are neither quantum nor
groups.  Thirty years ago, those half dozen of us who worked on q-analogs
were looked at with deep suspicion. More than sixty years ago, the
Reverend F.H.  Jackson, who was at that time probably the only person
working on q-analogs, stormed out of the lecture room when someone in the
audience made an unpleasant comment on q-analogs, and he never finished
delivering his lecture on the q-analog of the gamma function.

Tom Koornwinder

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