REVIEWS 



MATHEMATICS 



History of the Theory of Numbers : Vol. I, Divisibility and Primality. 



By Leonard Eugene Dickson, Professor of Mathematics in the 

 University of Chicago. [Pp. xii + 486.] (Washington : Carnegie Institu- 

 tion of Washington, 1919.) 



One of the most encouraging developments of the present day is the return 

 to an interest in the historical development of mathematics which had ap- 

 parently disappeared since the appearance of such works as Todhunter and 

 Pearson's History of the Theory of Elasticity. Recently the revival of this 

 interest has been quite definite, at least as regards the history of mathematics in 

 general. The present volume is notable in that it gives a connected account 

 of the historical development of one special branch of pure mathematics, and that, 

 as it happens, the most progressive one at the present day. Mathematicians 

 now owe a great debt to the Carnegie Institution of Washington — a debt which 

 we may hope will be extended by the production of similar volumes dealing from 

 the historical standpoint with other branches of mathematics which, like the one 

 at present before us, are now scattered throughout scientific periodicals in such 

 a way that their order of development cannot readily be appreciated by a 

 student. 



Any attempt to indicate in detail the contents of the present work would 

 hardly be possible here. It is perhaps sufficient to say that it is complete and 

 apparently exhaustive and that the grouping together of related investigations 

 appears throughout to be the most natural one. The most striking developments 

 now taking place are well represented, and in particular comprehensive reference 

 is made to some of the more remarkable theorems obtained quite recently by 

 Landau, Hardy, Littlewood and Tchebychef. The manner in which the further 

 development of the theory of numbers has tended to centre round the properties 

 of the Zeta function will be quite clear to the reader. For an account which is 

 by its nature largely bibliography the work is very pleasant to read, and it should 

 be an indispensable addition to any mathematical library. 



Dorothy Wrinch. 



Matrices and Determinoids. Vol. II. By C. E. Cullis, M.A., Ph.D., Hardinge 

 Professor of Higher Mathematics in the University of Calcutta. [Pp. xxiii + 

 555.] (Cambridge : at the University Press, 1918. Price 42J. net.) 



In view of the far-reaching advantages in the treatment of determinants derived 

 from the use of matrices, it has always been a serious drawback that, in the 

 treatment usually presented in treatises on algebra, the older methods have been 



497 



