ABSTRACT
Many of the commonly available books on history of mathematics declare or imply that Indian mathematics, whatever be its other achievements, did not not have any notion of proof. To illustrate, with two examples, the first taken from one of the better known texts on the history of mathematics, Kline (1972) writes:
There is much good procedure and technical facility, but no evidence that they (i.e., the Indians) considered proof at all. They had rules, but apparently no logical scruples. Moreover, no general methods or new viewpoints were arrived at in any area of mathematics. It is fairly certain that the Hindus (i.e., the Indians) did not appreciate the significance of their own contributions. The few good ideas they had, such as separate symbols for the numbers, were introduced causally with no realisation that they were valuable innovations. They were not sensitive to mathematical values. (Kline, 1972, p. 190)
A more recent opinion is that of Lloyd (1990) who writes:It would appear that before, in, and after the Sulbasutra [the earliest known evidence of mathematics from India], right down to the modern representatives of that tradition, we are dealing with men who tolerate, on occasion, rough and ready techniques. They are in fact interested in practical results and show no direct concern with proof procedures as such at all. (Lloyd, 1990, p. 104)
These quotations raise a number of fundamental questions: What is mathematics? How is it created? How is its quality to be assessed? But a more general question is: How do mathematicians produce information about mathematical objects? Underlying all these questions is the issue of proof, often perceived as a litmus test of whether we are ‘doing’ real mathematics or doing it well.