TENDENCIES IN MATHEMATICAL SCIENCE 327 



at the courts of St. Petersburg and Berlin. In spite of partial 

 and ultimately complete blindness, his scientific productivity was 

 enormous, and one of the most ambitious scientific undertakings 

 of our own time is the publication of his complete works in 45 

 volumes, by international cooperation. Our college mathematics 

 algebra, analytic geometry, and the calculus owes its pres- 

 ent shape largely to his works. 



Euler's Complete Introduction to Algebra was one of the most 

 influential books on algebra in the eighteenth century, and not the 

 least because it is written with extraordinary clearness and in easily 

 intelligible form. Euler was at that time already totally blind. He 

 picked out a young man whom he had brought with him from Berlin 

 as an attendant and who could reckon tolerably, but who otherwise 

 had no understanding of mathematics. He was a tailor by trade 

 and of moderate intellectual capacity. To him Euler dictated this 

 book, and the amanuensis not only understood everything well but 

 in a short time acquired the power to carry out difficult algebraic 

 processes by himself with much facility. It was this book which 

 completing the development begun by Vieta made algebra an inter- 

 national mathematical shorthand. 



Euler formulated the idea of function which has proved so fun- 

 damental in modern mathematics, both pure and applied. His 

 work also contains the first systematic treatment of the calculus 

 of variations, which is defined as "the method of finding the 

 change caused in an expression containing any number of variables 

 when one lets all or any of the variables change" or more geo- 

 metrically " a method of finding curves having a particular prop- 

 erty in the highest or the lowest degree." 



In other fields Euler " was the first to treat the vibrations of light 

 analytically and to deduce the equation of the curve of vibration as 

 dependent upon elasticity and density. . . . He deduced the law of 

 refraction analytically and explained that the rays of greater wave- 

 length must suffer the least deviation. . . . He studied dispersion 

 in the search for a corrective for chromatic aberration, which Newton 

 had declared unattainable. ... It was this investigation that in- 



