MATHEMATICS 51 



earliest dawn of history : Pythagorus ; Euclid ; Archimedes, — 

 known for other feats; Omar Khayyam, — known better for 

 a set of verses ; Descartes ; Leibnitz ; Newton ; Lagrange. I 

 have omitted most, even the prominent names of history. 

 In modern times, of the few whom I can hope to make stay 

 with you are : Abel, the founder of modern mathematics, 

 who died of abuse, an outcast; Galois, a spectacular youth, 

 killed in a duel at 18 years of age ; Gauss ; Cauchy ; Riemann ; 

 Lord Kelvin; Kowalewski, one of the few women who ha§i 

 attained equal rank with men in dispensing with any prefix 

 to her name; Klein; Poincare; Hilbert; Osgood, the only 

 American I shall mention; — certainly more than these would 

 confuse your minds rather than enlighten them. 



PROGRESS AND PRESENT ACTIVITY 



Perhaps you will be surprised to know that the last few 

 men whose names I have mentioned are actually alive, that 

 they have actually added to mathematical knowledge, that 

 mathematics is not all known, and that some of it has been 

 very recently discovered. I have already indicated the tre- 

 mendous enlargement of the fundamental ideas in mathe- 

 matics, and the enormous extent of the existing literature. It 

 will be easy for you to understand that mathematics at pre- 

 sent has passed the stage of instant expression in the popular 

 sense of newspaper exploitation, so that its progress is popu- 

 larly unknown. I can only explain that the extent of current 

 literature in mathematics, — I mean that the extent of new 

 development of previously unknown things is greater by far 

 than at any other previous stage in history. There are over 

 twenty-five journals, now published, which are devoted ex- 

 clusively to mathematics, besides more than a hundred general 

 scientific journals devoted partially to mathematics. The 

 importance from a scientific standpoint of the develop- 

 ments actually being made at this time is greater than that 

 at any previous similar stage. These lie, of course, beyond 



