Academic journal article The Accounting Historians Journal

From Accounting to Negative Numbers: A Signal Contribution of Medieval India to Mathematics

Academic journal article The Accounting Historians Journal

From Accounting to Negative Numbers: A Signal Contribution of Medieval India to Mathematics

Article excerpt

Abstract: The major object of this paper is to present evidence for arguing that the highly developed Hindu accounting tradition, beginning with Kautilya's Artha/astra 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., Bhaskara, 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.

Acknowledgments: Financial support from the Social Sciences and Humanities Research Council of Canada for this paper is gratefully acknowledged. I also want to express my thanks to the editorial team, including two reviewers and the editor, for valuable advice and stimulating my thoughts.

Probing more deeply into mathematical history shows that accounting aspects may have played an important role in medieval India through the earliest acceptance of negative numbers. This deserves at least as much attention as did the controversy between Peters and Emery [1978] and Scorgie [1989] as to whether or not the avoidance of negative numbers by Western mathematicians influenced the development of double-entry bookkeeping in Renaissance Europe. Peters and Emery [1978] tried to show that due to the rejection of negative numbers by Renaissance mathematicians, account balances had to be kept positive; e.g., relying on the "basic balance sheet equation" A = L + OE, instead of A - L = OE. One might counter this argument by pointing out that the balance sheet equation (A = L + OE) is more likely to have resulted from entering every transaction twice, and on opposite sides, via the trial balance because mathematicians and even accountants of this time were already sophisticated enough to know that the equation A - L = OE is an equivalent transposition of A = L + OE. But neither of these equations, nor a balance sheet, are mentioned in Pacioli's Summa [1494]. There one encounters merely the Profit and Loss account and the trial balance as well as the inventory, which also served as a starting basis for opening the accounts, thus approaching the notion of balance sheet. This "need for a bookkeeping system free of negative balances," in turn, was supposed to have led in commerce and in Fra Luca Pacioli's Summa [1494] to the notions of debits (Per) and credits (A) instead of regarding the values of assets as positive and those of all equities as negative. …

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