Philosophical foundations of a general theory of numbers

This paper considers how Indian mathematicians have traditionally cognised numbers and their operations, and what bearing it has on problems faced by modern number theories. The discussion is not merely an exposition of the traditional Indian view. The Indian conceptions have the potentiality of generating alternative perspectives which may be conducive to providing solutions to modern problems or in striking our new paths. It is these alternatives that this paper seeks In explore. It considers not just algorithm of numbers but their philosophical foundations. Since algorithms and axioms are finally based on philosophical ground beliefs, it is only by analysis of these beliefs that clarity can be achieved for alternative conceptions. Before discussing the Indian views and their consequences, it first states the general problems about numbers posed by the western tradition for which solutions have been sought and discusses the attempted solutions to the important problems. It is only in the light of this that the Indian alternative can be properly appreciated.