The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics. No philosophy of mathematics can be excused from explaining such occurrences.