Reliable Computing 8: 313–320, 2002.
2002 Kluwer Academic Publishers. Printed in the Netherlands.
Grand Challenges and Scientiﬁc Standards in
ur Mathematik, Universit
at Wien, Strudlhofgasse 4, A-1090 Wien, Austria,
e-mail: Arnold.Neumaier@univie.ac.at, WWW: http://www.mat.univie.ac.at/˜neum/
(Received: 21 April 2002)
Abstract. This paper contains a list of “grand challenge” problems in interval analysis, together
with some remarks on improved interaction with mainstream mathematics and on raising scientiﬁc
standards in interval analysis.
Following a question by Jim Demmel on the Reliable Computing Mailing List,
I presented on April 17, 2002 a list of “grand challenge” problems in interval
analysis, together with some remarks on improved interaction with mainstream
mathematics. In the weeks before, there were discussions on the Mailing List
about scientiﬁc standards in interval analysis which complement these remarks.
The following is an edited version of my contributions to the Mailing List on these
topics, revised in the light of the ensuing discussions. It is a heavily value-driven
essay, giving my personal perspective on the issues involved.
I know that a careful posing of the grand challenges would require signiﬁcantly
more detail and references to previous work that would be the basis of correspond-
ing research projects. Only for the ﬁrst challenge, where an international project
is already underway, such a description is available. Unfortunately, due to other
commitments, I have no time in the near future to prepare such a detailed version;
I give only references immediate at hand, and apologize for work not mentioned.
However, upon request by Vladik Kreinovich and Slava Nesterov, I prepared the
current paper for publication in the journal Reliable Computing.
Signiﬁcant progress in mathematics has always been application driven, although
not necessarily by applications outside mathematics. “Grand challenges” describe
problems that may change the way interval analysis is understood by their advocates
and perceived from the outside, and whose purpose is to focus research on a few hot
places. “Grand challenges” are problems where one hopes for a breakthrough in the