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REVIEW:
What is the intellectual merit of the proposed activity?
This is an outstanding proposal by a leader in the field.
Zeilberger has been doing pioneering work on how the computer is used
in mathematics. His work with Wilf on automated identity proving,
called WZ theory, earned him a Steele Prize a few years ago. Zeilberger
proposes to extend WZ theory to quantum groups and algebras. Exploring
quantum versions of combinatorial identities is an important new
direction in combinatorics and in various other fields. Another
interesting area of enumerative combinatorics that Zeilberger proposes
to automate is the area of pattern avoidance.
This proposal is distinguished by its clarity, originality, breadth
and substance, and by the track record of Zeilberger who has settled
many major conjectures in combinatorics.
What are the broader impacts of the proposed activity?
Zeilberger's proposed work on experimental combinatorics could
eventually impact all of mathematics. It contains inovative ideas on
the way to do math in the modern age. His work has been implemented in
major symbolic computation software. He has had many Ph.D. students and
postdocs at Temple and Drexel. Now that he is at Rutgers he has the
opportunity to direct first rate students and postdocs.
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