Lectures on the Philosophy of Mathematics (Paperback)

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1918. Not illustrated. Excerpt: ... CHAPTER I MEANING OF THE PHILOSOPHY OF MATHEMATICS When the thinking person of the present day stops to reflect upon the facts of the wireless telegraph and the long-distance telephone, not to mention many other just as important marks of human progress, and remembers in his thinking that the existence of the wireless telegraph is due to deductions of Maxwell by means of theorems that depend upon the square root of minus one, and that the possibility of the long-distance telephone depends upon investigations of Pupin by means of theorems that depend more directly upon the modern theory of expansions in fundamental functions, he appreciates to the full the power of this branch of human learning. When he further learns that the existence of conical refraction was pointed out to the physicist by a mathematician before it was discovered in a laboratory; that the existence of Neptune was pointed out to the astronomer before his telescope had noticed this wanderer in the remote heavens; when he learns that the mathematician by a theory related to the solution of the problem of finding the roots of an algebraic equation is able to say to the mineralogist "you will never find more than thirty-two distinct types of crystals"--when he meets such facts as these, he must invariably ask: "Who is this magician whose wand creates the marvelous and whose penetrating eye searches the hidden corners of the universe?" He may still listen with an amused smile to the curious properties of four-dimensional space, may delight in the escape from the weary wastes of infinite space in a Riemannian finite universe, may be bewildered by the Minkowski imaginary-time axis, may exhaust his imagination in the vain effort to draw the crinkly curves, but he will not look upon all these as vagari...