Monographs on Topics of Modern Mathematics Relevant to the Elementary Field

RECENT work on the first principles of mathematics has been so far-reaching and revolutionary that most, if not all, of those acquainted with the results are anxious to bring them to bear upon general education. For this there are two main reasons: in the first case, it cannot be right to go on pretending to teach a subject in a strictly logical way when all sorts of assumptions, many of them wrong, are being tacitly made; and secondly (this is still more important), the philosophical side of the new theories is bound, sooner or later, to have a profound effect upon educated thought. It is, for instance, a great achievement that mathematicians have now got definite concepts of three distinct “infinite numbers,” as contrasted with the vague “∞” of former times; that they have proved the possibility of three distinct geometries, in two of which the axiom of parallels does not hold good; and that there is some prospect of bringing the theories of electricity and gravitation under one comprehensive hypothesis—it may be by a restatement of the laws of motion, or even by the assumption of a sort of four-dimensional space.Monographs on Topics of Modern Mathematics Relevant to the Elementary Field.Edited by J. W. A. Young. Pp. viii + 416. (London: Longmans, Green and Co., 1911.) Price 10s. 6d. net.