MODERN MATHEMATICAL BESEARCH MILLER. 197 



were called mathematics, fiaOrj/jLara, by the ancient Greeks. The 

 mathematical investigator of the present day is pushing these thought 

 roads into domains which were totally unknown to the older mathe- 

 maticians. Whetlfer it will ever be possible to penetrate all scientific 

 knowledge in this way and thus to unify all the advanced scientific 

 subjects of study under the general term of mathematics, as v/as the 

 case with the ancient Greeks,^ is a question of deep interest. 



The scientific world has devoted much attention to the collection 

 and the classification of facts relative to material things and has 

 secured already an immensely valuable store of such knowledge. As 

 the nimiber of these facts increases, stronger and stronger means of 

 intellectual penetration are needed. In many cases mathematics has 

 already provided such means in a large measure; and, judging from 

 the past, one may reasonably expect that the demand for such means 

 v/ill continue to increase as long as scientific knowledge continues to 

 grow. On the other hand, the domain of logic has been v/idely 

 extended through the work of Russell, Poincare, and others; and 

 Russell's conclusion that any false proposition implies all other prop- 

 ositions whether true or false is of great general interest. 



During the last two or three centuries there has been a most 

 remarkable increase in facilities for publication. Not only have 

 academies and societies started journals for the use of their members, 

 but numerous journals, inviting suitable contributions from the public 

 have arisen. The oldest of the latter type is the Journal des S^avans, 

 which was started at Paris in 1665, while the Transactions of the 

 Royal Society of London, started in the same year, should probably 

 be regarded as the oldest of the former type. These journals have 

 done an inestimable amount of good for the growth of knowledge 

 and the spread of the spirit of investigation. At the present time 

 more than 2,000 articles which are supposed to be contributions to 

 knowledge in pure mathematics appear annually in such periodicals. 

 In addition to these there is a growing annual list of books. 



The great extent of the fields of mathematics and the rapid growth 

 of this literature have made it very desirable to secure means of 

 judging more easily the relative merit of various publications. ♦Along 

 this line our facilities are still very meager and many serious diffi- 

 culties present themselves. In America we have the book reviews 

 and the indirect means provided by the meetings of various societies 

 and by such publications as the ''American Men of Science." 



The most important aid to judge contemporaneous work is fur- 

 nished by a German publication known as the Jahrbuch iiber die 

 Fortschritte der Mathcmatik. In this work there appear annually 

 about 1,000 pages of reviews of boqks and articles published two or 

 thi-ee years earlier. These re^^ews are prepared by about 60 different 



1 The term mathematics was first used with Its present restricted meaning by the Peripatetic School. 

 Cantor, " Vorlesungen iiber Geschichte der Mathematik," vol. 1 (1907), p. 216. 



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