RECENT ADVANCES IN SCIENCE 1 



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



The war has had a disastrous effect on mathematical publica- 

 tions, at least abroad. No foreign periodicals, which contain 

 the great mass of mathematical literature usually put out, seem 

 to have been published of late, with the exception of some from 

 America, France, and Italy. The Comptes Rendus of the French 

 Academy seems to be the only scientific publication in France 

 which has appeared regularly. However — and this is of great 

 importance for all who are interested in the principles of 

 mathematics — the Revue de Metaphysique et de Morale, which, 

 in spite of its title, is by no means chiefly devoted to questions 

 of metaphysics or morals, is shortly to resume regular publi- 

 cation. To mathematical logic in particular the limitation of 

 discussion to a small group of nations is especially harmful. 

 The history of it shows that this is so in perhaps a better way 

 than that of any other scientific subject. The first really 

 adequate idea of a science of mathematical logic was due to a 

 German, Leibniz, but his idea of a "universal characteristic" 

 remained in part unpublished and almost entirely unnoticed 

 until Frege, another German, two hundred years afterwards, 

 developed the same idea in a narrower domain, but with even 

 greater subtlety. But since then no German has made any 

 important contributions to the subject, and only one Austrian. 

 With unexampled obtuseness, German mathematicians have 

 treated Frege's glorious logical and mathematical work with 

 that amused contempt that arises from ignorance. They even 

 call it " philosophy." And the modern developments — including 

 proper appreciation of Leibniz and Frege — are due almost 

 wholly to Frenchmen, Italians, Britons, and Americans. The 

 best popular work on the subject is due to a Frenchman, Louis 

 Couturat, who was killed by a motor car last August, but was 

 not a victim of the war. The work of Couturat has done very 

 much to convince those mathematicians who care to think that 



1 To be continued every quarter. 

 114 



