Mathematics is a formal science, not an empirical science. In other words, both Zeilberger and those he criticizes (as he characterizes them) are wrong. Some in

Mathematics is a formal science, not an empirical science. In other words, both Zeilberger and those he criticizes (as he characterizes them) are wrong. Some interesting books on the subject... "An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure" by James Franklin "German Science" by Pierre Duhem