The successive interchanges on how well the WZ method and Pfaff's
method perform have made an interesting contest. Each successive
discovery has added insight to our knowledge of this branch of of
mathematics. I would hope that one result of this work along with
that of Wilf, Petkovsek and Zeilberger is a refutation of the thesis
advanced by Zeilberger in [17]. Namely, significant amounts of
thought have directed computers in discovering mathematics; nowhere in
all this did computers do it on their own.
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