RECENT ADVANCES IN SCIENCE 1 



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



Prof. Emil Lampe of Berlin, the editor of the well-known 

 Jahrbuch uber die Fortschritte der Mathematik, recently wrote to 

 the writer of this report that all the German mathematical 

 periodicals are still published in spite of the war. The great 

 trouble is that there is a shortage of compositors, so that, for 

 example, the last part of the Jahrbuch for 191 2, which would 

 normally have appeared in May of this year, is probably 

 delayed until August. However, we cannot, as a rule, get any 

 idea over here as to what is being done by Germany in the 

 world of mathematics. The task of settling accounts after 

 the war will no doubt be an arduous one here as elsewhere. 



Strictly speaking, the death of a mathematician is not a pro- 

 gress in mathematics. Yet deaths of great men remind us of 

 some progress they took part in ; and so we must here record 

 the death of Morgan Crofton (1826 — 19 15), perhaps best 

 known for his article " Probability " in the ninth edition of 

 the Encyclopaedia Britannica. 



Logic and the Principles of Mathematics. — In Prof. J . Brough's 

 study (Proc. Aristot. Soc. 1914, 14, 152) of some points in the 

 logical doctrines of the authors in the first volume of the 

 Encyclopaedia of the Philosophical Sciences, mentioned in 

 Science Progress for July 191 5, p. 115, there is some mention 

 of Couturat's article on mathematical logic, but the points 

 touched on do not seem to be of much interest to mathematical 

 logicians. The first important contributions to these branches 

 of mathematics which must be noticed are three papers by 

 Dr. Norbert Wiener {Proc. Camb. Phil. Soc. 1914, 17, 387, 

 441, and 191 5, 18, 14). Wiener noticed that certain points in 

 the logic of relations as given by Whitehead and Russell in 

 their Principia Mathematica are simplified if we practically 

 revert to Schroder's treatment, given in the third volume 

 ( 1 895) of his Algebra der Logik, of a relation as a class of couples. 



1 To be continued every quarter. 

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