RECENT ADVANCES IN SCIENCE 



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



Education. — In the number of the Mathematical Gazette for 

 March 191 8 there are several papers read at the annual meeting 

 of the Mathematical Association in January 191 8 which are 

 of great interest in educational questions. T. P. Nunn gives 

 a presidential address on " Mathematics and Individuality," 

 W. P. Milne discusses the graphical treatment of power-series 

 and the uses and functions of a school mathematical library, 

 S. Brodetsky discusses nomography, and G. Goodwill gives 

 some suggestions for a " presentment of mathematics in closer 

 touch with reality." 



For use in preparing a subject for discussion in an under- 

 graduate mathematical club is given, in the Amer. Math. 

 Monthly (191 8, 25, 276-82), a very full set of references to 

 literature on some integrals and spirals considered by Euler, 

 Fresnel, and others (cf. Science Progress, 191 8, 13, 177). 



History. — H. G. Zeuthen published (191 7) in Danish a work 

 on the history of mathematics from Plato to Euclid, of which 

 an account is given by D. E. Smith (Bull. Amer. Math. Soc. 

 191 8, 24, 407-10). The same subject also comes into Zeuthen's 

 able and interesting article (Scientia, 191 8, 24, 257-69) on the 

 definitions of Euclid. 



G. R. Kaye (ibid. 53-5) supports Carra da Vaux's theory, 

 given in Scientia of 191 6, of the Greek origin of our numeration, 

 and of its passage through Persia to India and Arabia, by his 

 own results found in a wholly different way and published 

 in 1907, 1908, 191 1, and in his Indian Mathematics of 1915 

 (cf. Science Progress, 191 6, 10, 503-4). 



D. E. Smith and J. Ginsburg (Amer. Math. Monthly, 191 8, 

 25, 99-108) give an extensively annotated translation of Rabbi 

 ben Ezra's (Abraham ibn Ezra's) introduction to his translation 

 into Hebrew of a book on the astronomical tables of Mohammed 

 ibn Musa al Khowarizmi, on account of the light it throws on 

 23 345 



