542 



SCIENCE 



[N. S. Vol. LIII. No. 1381 



have been published since 1910, a detailed 

 examination of those articles would be impos- 

 sible. I have, as a matter of fact, obtained 

 what I believe to be a fairly complete list of 

 these artcles, and made a rough classification 

 of them according to subject matter. Perhaps 

 a quantitative comparison, based on numbers 

 of pages, would have been more informative 

 than one based merely on numbers of titles, 

 but this too would have been open to criti- 

 cism, and somewhat more difficult to obtain 

 and digest. If you will bear in mind the 

 meaning of the figures given, I have little fear 

 that you will over-estimate their significance, 

 or infer that I have any disposition to propose 

 any quantitative test as the sole measure of 

 the excellence of an individual's scientific out- 

 put. On the contrary, I should prefer six 

 pages of Fredholm's in the Proceedings of the 

 Eoyal Academy of Science of Sweden of 1900 

 to scores of titles and many hundred pages 

 that might be picked out from journals on the 

 other side, or this side, of the water. 



The limitations on the statistical field before 

 us must first be stated. It iacludes no his- 

 torical, biographical, or philosophical contri- 

 butions, and only such in applied mathematics 

 as were contributed by men primarily mathe- 

 maticians, or appeared in journals devoted en- 

 tirely to mathematics. It does not, moreover, 

 contain articles contributed to journals of 

 primarily didactic emphasis. Otherwise, it is 

 intended to be complete, and contains contri- 

 butions to a considerable number of foreign 

 periodicals. 



I wish to consider first the distribution of 

 effort amongst various sub-fields of mathe- 

 matics, and then to comment on some other 

 aspects of interest presented by the data col- 

 lected. In the matter of classification, in ad- 

 dition to certain customary headings, I have 

 endeavored to separate out a few other classes 

 of subjects of interest for the purposes in 

 hand: first, certain topics whose present vi- 

 tality and interest among mathematicians gen- 

 erally have been pointed out by Bliss, Van 

 Vleck and others on occasions similar to this, 

 and secondly some topics characteristically 

 American in that Americans have taken a sig- 

 nificant or preponderant part in their develop- 



m.ent. The distribution of titles among the 

 headings selected follows, the numbers given 

 being the percentages of the total number of 

 titles foimd, or 1,258. 



Algebra 



Groups 8.9 



Theory of numbers (ineludiug theory 



of irrationals) 6.0 



Theory of equations, matrices and 



determinants 4.8 



Higher complex algebras 1.8 



Modular analysis 1.7 



Invariants 1.4 



Combinatory analysis . . . . • 1.1 



Probabilities and statistics 0.5 



Analysis 



Theory of functions of one or more 



complex variables 6.4 



Theory of functions of a real va- 

 riable 6.0 



Differential equations 4.3 



Sturmian problems, including Fourier 



Series 3.9 



General analysis, calcul fonetionel.. 2.9 



Integral equations 2.5 



Calculus of variations 2.3 



Analysis situs 2.1 



Theory of integration (Lebesgue, 



etc.) 2.0 



Difference equations 1-2 



Functions of infinitely many va- 

 riables 1-1 



Point sets 1-0 



Other analysis 5.3 



41.» 



Geometry 



Metric differential geometry 6.0 



Analytical geometry of curves and 



surfaces 5-7 



Greometry of hyperspace 2.0 



Geometric transformations 1.4 



Projective differential geometry .... 1.7 

 Configurations of a finite number of 



elements 1-0 



Geometry of forms 0.9 



Modular geometry 0.8 



Congruences and complexes 0.6 



Projective geometry (other than dif- 

 ferential) 0.6 



Non-Euclidian geometry 0.5 



Other geometry 1-0 



22.2 



