A REVIEW of these beautifully printed publications of the Cambridge Press necessarily constitutes in some measure a survey of the proceedings of the Fifth International Congress of Mathematicians. Although more than a year has elapsed since these meetings were held at Cambridge, it may not yet be too late to form an opinion on the work that was then done, and its influences on the progress of mathematical science, and on the position of mathematics in Great Britain. These are subjects on which no two people can be expected to hold the. same opinions, and it is therefore of great importance that a reviewer should be able to state his own views without prejudice to those held by other members present at the Congress, readers of the proceedings, or, indeed, anyone else. Proceedings of the Fifth International Congress of Mathematicians. (Cambridge, August 22-28, 1912.) Edited by Prof. E. W. Hobson Prof. A. E. H. Love. Vol. i., Part i., Report of the Congress. Part ii., Lectures: Communications (Section I.) Pp. 500. Vol. ii., Communications to Sections II–IV. Pp. 657. (Cambridge University Press, 1913.) Price 30s. net, two vols.)