(xix ) INTRODUCTION BY DAVID EUGENE SMITH, PROFESSOR OF MATHEMATICS IN TEACHERS' COLLEGE, COLUMBIA UNIVERSITY, NEW YORK. We have so long been accustomed to think of Pataliputra on the Ganges and of Ujjain over towards the western coast of India as the ancient habitats of Hindu mathematics, that we experience a kind of surprise at the idea that other centres equally important existed among the multitude of cities of that great empire. In the same way we have known for a century, chiefly through the labours of such scholars as Colebrooke and Taylor, the works of Aryabhata, Brahmagupta, and Bhaskara, and have come to feel that to these men alone are due the noteworthy contributions to be found in native Hindu mathematics. Of course a little reflec tion shows this conclusion to be an incorrect one. Other great schools, particularly of astronomy, did exist, and other scholars taught and wrote and added their quota, small or large, to make up the sum total. It has, however, been a little discouraging that native scholars under the English supremacy have done so little to bring to light the ancient mathematical material known to exist and to make it known to the Western world. This neglect has not certainly been owing to the absence of material, for Sanskrit mathematical manuscripts are known, as are also Persian, Arabic, Chfhese, and Japanese; and many of these are well worth translating from the historical standpoint. It has rather been owing to the fact that it, is hard to find a man with the requisite scholarship, who can afford to give his time to what is necessarily a labour of love.
