December 15, 1916] 



SCIENCE 



837 



mathematics ' sake and those interested in 

 creating a tool with which to attack some 

 other science. The search after truth — 

 geographical, religious, scientific — has al- 

 ways lured men. The desire to create, to 

 build some new thing, is continually find- 

 ing outlet in invention, in exploration, and 

 jn scientific research. That desire which 

 sends some men to the poles of the earth, 

 to the tops of mountains, or to the heart 

 of the desert, sends other men over the 

 mountain tops of geometry, or among the 

 pitfalls of analysis, or through the laby- 

 rinth of point sets, to some hitherto un- 

 trodden field of mathematics. The mathe- 

 matician creates an intellectual fabric 

 which is just as real and just as beautiful 

 to him as the tapestry is to the weaver. 

 Some put forth their effort in any field that 

 attracts; others, the utilitarians, choose 

 parts which they think will be fruitful in 

 applications. 



Knowledge of pure science precedes its 

 application. The properties of conic sec- 

 tions were well known before Kepler and 

 Newton wanted to use them in their theo- 

 ries of planetary motion. The infinitesimal 

 calculus was developed before and not 

 after it was needed in physics. The differ- 

 ential equation had to be understood before 

 it could be applied. Mathematicians have 

 ready now the integral equation and the 

 difference equation which, I believe, have 

 only made a beginning in their service to 

 science. It may be the man who is not seek- 

 ing utilitarian ends who discovers the most 

 useful facts. Roentgen was not seeking an 

 aid for the medical profession when he dis- 

 covered the X-rays. That man who reads 

 carefully the history of scientific discovery 

 and its application will not criticize any 

 worker for choosing a field which is ap- 

 parently remote from usefulness. 



How many are working in mathematics, 

 what have they done and what are they do- 



ing? There are some six or eight of the 

 more important mathematical societies in 

 various parts of the world with a total 

 membership of over three thousand. These 

 societies comprise in their membership 

 practically all the research workers, be- 

 sides many others not so engaged. The 

 Subject Index of the Royal Society of Lon- 

 don Catalogue of Scientific Papers, volume 

 1, which gives practically a complete list 

 of mathematical articles which appeared 

 during the nineteenth century, says in its 

 preface that it contains 38,748 entries re- 

 ferring to articles in 701 serials and has re- 

 jected 750 as having no scientific value. G. 

 Valentin, of Berlin, has collected a list of 

 150,000 titles of books and articles pub- 

 lished before the beginning of the twentieth 

 century. The Jahrbuch uber die Fort- 

 schritte der Mathematik is a yearly review 

 and each year publishes a volume of about 

 1,000 pages with very short reviews of 

 books and of papers published in about 200 

 serials. A very conservative estimate would 

 be that each year there appear 2,000 ar- 

 ticles, in addition to the books which con- 

 tain no new matter. Professor G. A. 

 Miller, of Illinois University, estimates that 

 there was published during the first fifteen 

 years of the present century about one 

 fifth as much mathematical research as dur- 

 ing all time before. Mathematicians have 

 varied greatly in their productivity. At 

 one extremity is Galois, killed in a duel 

 before he was twenty-one years old, whose 

 essential contribution to mathematics re- 

 quires about sixty pages of print; and at 

 the other are Cauchy, whose works are ex- 

 pected to fill twenty-seven volumes when 

 printed, and Euler, the printing of whose 

 work as planned will fill forty-five large 

 volumes. 



Now, what relation can this science 

 which deals with the abstract have to do 

 with the natural sciences which deal with 



