On Immediate Solutions of Some Dynamical Problems

Abstract

As a branch of science advances and its principles become more familiar to the mind of the investigator many things which before appeared involved and mysterious become simple and clear, and it is possible to find proofs of theorems so obvious and brief as to merit the name intuitive in a very real sense, though not that in which the term is frequently applied. For to say that a theorem or principle is intuitively perceived is often tantamount to saying that it is not perceived at all. By an intuitive proof of a proposition I mean a proof which is natural and direct, and it may be almost instantaneous in that the restatement of some element of the proof transforms the whole so that the proposition is at once recognised to be true. But the proof must be complete and rigid to be valid, and completeness and rigidity are qualities which have come to be almost denied by calling a proof “intuitive.”