SCIENCE PROGRESS 



RECENT ADVANCES IN SCIENCE 



MATHEItHATICS. By F. Puryer White, M.A„ St. John's College, 

 Cambridge. 



The German Encyclopcedia of Mathematics was begun in the 

 closing years of the last century, but so far only volume i 

 (Arithmetic and Algebra) and the first division of volume 2 

 (Analysis, Real Numbers) have been completely published. 

 During the present year, however, considerable progress has 

 been made. In Analysis, L. Bieberbach (Heft 4) gives an 

 account of recent investigations in the theory of functions of 

 a complex variable, to supplement Osgood's article, which 

 appeared in 1900. In Geometry four parts have appeared : 

 M. Zacharias and W. F. Meyer (III. i. 6) conclude their article 

 on " Synthetic Geometry " (EucHdean and non-Euclidean), 

 G. Berkhan and W. F. Meyer (III. i. 7) write on recent " Geo- 

 metry of the Triangle," H. Rothe (III. i . 7) on Grassmann's 

 " Ausdehnungslehre," C. Segre (IV. 2. 7) on the algebraic geo- 

 metry of hyperspace, and E. Salkowski (III. 3. 5) on triply- 

 orthogonal systems of surfaces. 



Several mathematical journals have ceased publication, 

 largely no doubt owing to the enormous cost of production ; a 

 list is appended, with the last volume in each case : 



Archiv der Mathematik (28, 1920). 

 Bibliotheca Mathematica (14, 19 14-15). 

 Nouvelles Annates de Mathematiques (79, 1920). 

 Zeitsckrift fur Mathematik und Physik (64, 191 7). 



The Mathematische Annalen, after fifty years' publication by 

 Teubner of Leipzig, has now, beginning with volume 81, been 

 transferred to the firm of Springer in Berlin ; it will in future 

 not be strictly limited to Pure Mathematics. 



Nature, for August 11, 1921, contains a list, probably in- 

 complete, of leading German scientists who died during the 

 war. Of mathematicians it includes R. Dedekind (February 

 1916), R. Helmert (June 191 7), G. Frobenius (August 19 17); 

 and G. Cantor (January 191 8). 



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