SCIENCE PROGRESS 



RECENT ADVANCES IN SCIENCE 



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



One of the most remarkable things about the last number 

 published of the Revue semestrielle des publications mathematiques 

 (191 7, 25 [2]) is the exceedingly small space devoted to publica- 

 tions from Germany. In fact, though the papers in mathe- 

 matics from October 19 16 to April 191 7 are supposed to be 

 indexed in the number referred to, only just over three pages 

 out of the sixty-four are devoted to an account of recent Ger- 

 man work, and some of this was published in 1915. The case 

 is apparently better as regards Austria-Hungary, for about 

 ten pages are devoted to mathematical literature from that 

 Empire, — but most of these papers were published in 191 5. 

 It is probably unsafe to conclude from this fact that the 

 actual production of mathematical work in the Central Empires 

 has been very much smaller of late than in the rest of the 

 world, but still the fact is remarkable. 



Educational Note. — A. F. Frumveller (Amer. Math. Monthly, 

 19 1 7, 24, 409-20) gives a full development, with many illus- 

 trations, of the making of graphs of f(x) for complex numbers, 

 which is of interest to teachers when they have to teach the 

 theory of functions. 



History. — K. Sethe (Schr. der wiss. Ges. zu Strassburg, 19 16, 

 25) studies the art of calculation with the ancient Egyptians. 



A. C. Bose (Bull. Calcutta Math. Soc. 19 16, 6, 13-31) con- 

 tinues an account of John Napier's life and work. 



G. Milhaud (Scientia, 19 18, 23, 1-8, 77-90) gives a very 

 valuable sketch of the work of Descartes during the memor- 

 able winter of 1619-20, which is based on both the known 

 documents and some very likely conjectures. The first part 

 is on the discovery of Descartes' Method and his ideal of a 

 " Mathesis," and the second part is on his first work in analysis 

 and geometry. Cf . also the papers of Milhaud in Scientia ( 1 9 1 6, 

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