RECENT ADVANCES IN SCIENCE 189 



MATHEMATICS. By Philip E. B. Jourdain, M.A., Cambridge. 



In the present summary, those references which consist of a 

 number in parentheses after a man's name refer to the pages 

 of the last number which has appeared of the Revue Semestrielle 

 (191 9, 27, pt. 1). This number is supposed to contain an 

 account of publications in mathematics from April to October, 

 191 8 — though many of the papers reviewed in it are of earlier 

 date (cf. Science Progress, 191 9, 13, 520). 



Education. — R. C. Archibald has published, with the co- 

 operation of D. E. Smith, W. F. Osgood, and J. W. A. Young, 

 a report on mathematical teaching in the countries represented 

 in the International Commission on the Teaching of Mathe- 

 matics of which the organisation was begun at the Congress 

 at Rome in 1908. At present 18 countries have already pub- 

 lished 178 reports ; Germany has published 50, Great Britain 

 34, and the United States 14. This report is the fifteenth of 

 those published by the United States, and is entitled The 

 Training of Teachers of Mathematics (Washington : Depart- 

 ment of the Interior : Bureau of Education, 191 8). 



Hints for a lecture at an undergraduate mathematical club 

 (cf. Science Progress, 191 9, 13, 521) on the history of in- 

 vestigations on the number tt are given in Amer. Math. Monthly 

 (191 9, 26, 209-12). W. Dieck (22) writes on the foundations 

 of geometry as an introduction to the theory of knowledge 

 which is suitable for schools. Other papers of interest to 

 teachers of mathematics are by C. Andriessen (31) and 

 W. Lorey (31). 



History. — A new publication devoted to the history of 

 science is the Archivio di Storia delta Scienza, a quarterly pub- 

 lished at Rome and edited by Aldo Mieli, of which the first 

 number appeared in March 1919. The articles and notes which 

 are of the greatest interest in the present connection are as 

 follows : A. Favaro (1, 28-38) gives the forty-first article of 

 his series on the friends and correspondents of Galileo : the 

 article is on Matteo Carosio, and a note is given with detailed 

 references to the previous forty articles of the series. G. 

 Loria (ibid. 39-47) has a note discussing Cajori's remarks in 

 Science for 191 8 on a history of mathematics in the nineteenth 

 century. It is of interest that a methodical bibliography on 

 works of the history of science published in Italy will be under- 



