50 UNIVERSITY OF MISSOURI BULLETIN 



on the other, with an enormous range of practical appHca- 

 tions between them, human achievements without number de- 

 pend utterly upon mathematics, and are utterly impossible 

 without it. I would note, however, that mathematics is merely 

 neceessary to these discoveries, — it is not sufficient. For the 

 discoveries themselves, it is necessary always that some genius 

 arise who can apply the conclusions which mathematics has 

 reached to the practical ends of life, in the building of a 

 bridge, in the construction of an engine, in the taking of 

 observations with a sextant from a frozen polar sea. 



HISTORY 



The history of mathematics is as long as the history of 

 mankind, for perhaps we should not wish to recognize an 

 ancestor to whom the mere notion of counting was too 

 abstruse. Indeed, the history of mathematics goes back of 

 written history. Its first chapters are evolved rather from 

 the reason than from history. Coming down to written his- 

 tory, we know that geometry arose as a necessity for the mea- 

 surement of land in the peculiarly shaped alluvial regions 

 near the Nile. Perhaps this is typical in that every branch 

 of mathematics has seen at least its genesis in a pressing 

 need of the race. 



Of the vital steps in the formation of mathematics I 

 may note swiftly these : the idea of number itself, the distinc- 

 tion of the difference between one number and some different 

 number; the Arabian notation for number, which really arose 

 in India; the first Egyptian survey, which was the foundation 

 of geometry; the Grecian school of logic which formed geo- 

 metry into a precise doctrine as it stands today ; the invention 

 of algebra by the Arabians; the junction of algebra and geo- 

 metry in analytics; the invention of the calculus; and, last, 

 the enormous expansion of recent times forced by the neces- 

 sities of science and of engineering. 



Among the names of famous men, I may recall from the 



