Theory of Numbers

Abstract

THE book under review is a great contrast in many ways to the “Théorie des Nombres” of M. Edouard Lucas, the first volume of which has recently appeared under the ægis of Messrs. Gauthier-Villars. The latter, reminding the reader much of the same author's “Récréations Mathématiques,” exhales human interest from well-nigh every page. The former is on severe philosophical lines, and may be greeted as the first work of the kind in the English language. That this should be a fact is somewhat remarkable. When the late Prof. H. J. S. Smith died prematurely many years ago he left his fellow-countrymen a very valuable legacy. Fortunately he had been commissioned by the British Association to frame a report on the then present state of the Theory of Numbers, a subject with which he was pre-eminently familiar, and in which his own original researches had won for him a great and world-wide renown. The pages of the reports for the years 1864-66 inclusive yield as a consequence a delightful account of modern research in this recondite subject. It is, however, much more than a recital of victories achieved by many able men in many special fields. Prof. Smith's fertile genius enabled him to marshal the leading facts of the theory, and to impress upon them his own personality in a manner that was scarcely within the reach of any other man. He contrived to impart a glamour to those abstract depths of the subject to which few mathematicians have sufficient faith and energy to penetrate. Since that day the scientific world has been yearly expecting his collected papers. There is no doubt that their appearance will greatly stimulate interest and research in Higher Arithmetic. The reports of the British Association are not sufficiently accessible. Doubtless the papers will soon emerge from the hands of those upon whom has devolved the responsibility of their production. In the meantime we welcome Part I. of the present work.

Theory of Numbers.

By G. B. Mathews Part I. (Cambridge: Deighton, Bell and Co., 1892.)