FROM ACCOUNTING TO NEGATIVE NUMBERS: A SIGNAL CONTRIBUTION OF MEDIEVAL INDIA TO MATHEMATICS

The major object of this paper is to present evidence for arguing that the highly developed Hindu accounting tradition, beginning with Kautilya's Arthasãstra about 300 B. C., or even earlier, may have had a part in the more receptive attitude of medieval Indian mathematicians, compared to Europeans, in accepting negative numbers. The Hindus justified this attitude by arguing that having a debt is the inverse of possessing an asset; thus, attributing a negative number to a debt but a positive one to an asset. To advance the argument, the paper shows that the accounting aspect of debt is at least as basic as its legalistic one. Indeed, the former can be traced to the 4th millennium B. C. or earlier, while the first known legal codes go back only to the 3rd millennium B. C. However, there are other angles from which to examine the relation between accounting and negative numbers. Some accountants [e. g., Peters and Emery, 1978] believe that the long-standing hesitation of European mathematicians to accept negative numbers contributed to the accountants' debit/credit scheme, while others [e. g, Scorgie, 1989] deny this view. But this controversy concerns rather the influence of negative numbers upon accounting. It neglects to investigate the reverse possibility; namely, the influence of accounting upon the Indian mathematicians' early acceptance of negative numbers. Thus, this paper first reviews concisely, for the sake of contrast, the arguments between Peters and Emery [1978] and Scorgie [1989]; then it elaborates on the long-standing resistance of Western mathematicians to legitimizing negative numbers (which, in its entirety, did not happen before the 19th century); and, finally, it discusses the very different attitude of medieval Indian mathematicians, who were the first to accept negative magnitudes as numbers (e. g., Brahmagupta, 7th century A. D., Bh.skara, 12th century A. D.). Their interpretation of a negative number as representing "debt" as a basic accounting and legal notion may have been conditioned by the longstanding accounting tradition of India since the 3rd century B. C. or before.