ANNIVERSARY ADDRESS. 11 



involved the invention of more general and therefore more powerful 

 methods ; but to this task the Greek was unequal. 



The Romans contributed relatively nothing; their giant Boetius 

 [475 - 525 A.D.] compared with the Greek masters, was a pigmy; 

 and mathematical inspiration vanished from the western world, 

 to more feebly reappear in the eastern, in Hindustan. The Hindu 

 however regarded arithmetic, algebra, and geometry merely as aids 

 to astronomy; a science in which, as the irony of fate determined 

 he was to win no distinction. The historically oldest of Indian 

 mathematicians or rather astronomers, Aryabhata [476 - 550 A.D. ] 

 assigned the value 3*1416 for the Ludolphian number. This, 

 however, had been previously given by Ptolemseus as 3? 8'. 30" or 

 3 + 6i7 + "36-00 *.e., 3*1416. To Aryabhata, though the evidence 

 is not quite decisive, probably belongs the credit of inventing the 

 fundamental principles of our present system of arithmetical 

 notation, the contribution of which to the general progress of 

 intelligence, would be difficult to estimate. Coming to us through 

 the Arab, it has improperly been called the Arabic system. 

 Mathematics attained its highest position in India about 630 A.D. 

 when flourished Brahmagupta [born 598 A.D.], the 12th and 18th 

 chapters of whose work, 'Brahma-sphuta-siddhanta,' contains what 

 of mathematics was then known to Hindustan. The Hindu was 

 remarkable for skill in calculation, for being the first to recognise 

 the existence of negative quantities, and for the development of 

 general methods of solving indeterminate equations ; his taste lay 

 rather in the direction of algebra and trigonometry than in 

 geometry, for Hindu geometry was poor. That both the form and 

 spirit, however, of modern arithmetic and algebra are essentially 

 Hindu, is sufficient evidence of the reality of our debt to his genius. 



From India the torch of science passed to the ascendant Arab 

 when at the close of the reign of Abu Ja'far ibn Mohammed, or 

 Almansur [772 A.D. ] Hindu mathematics was studied at Baghdad, 

 and a Hindu astronomer translated into Arabic the astronomical 

 tables of his country. The oriental superstition that the progress 

 of human affairs was associated with celestial portents, and the 



