Everyday Equations
The word algorithm, which is commonly used for any systematic procedure of computation, has an interesting history. It derives from the medieval word "algorism", which referred to the process of doing arithmetic by means of Indian numerals (the so called "Hindu-Arabic numerals") following the Indian methods of calculation based on the decimal place value system. The word algorism itself is a corruption of the name of the Central Asian mathematician al Khwarizmi (c 825) whose book on the Indian method of reckoning (Hisab al Hind) was the source from which the Indian methods of calculation reached the western world. The "algorists" in medieval Europe, who computed by algorism were at a great advantage compared to those who used the abacus or any other system of numeration such as the Roman system.
“It is India that gave us the ingenious method of expressing all numbers by means of 10 symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”
The term “mathematics” is derived from the Greek word “mathema” which means knowledge or learning. The Indian term for this discipline is “ganita” which means calculation or computation. Indian mathematics, ganita, is quintessentially a science of computation. Indian mathematical texts are not just a collection of propositions or theorems about mathematical entities, they are more in the nature of a compendia of systematic and efficient procedures for computation (with numbers, geometrical figures and algebraic symbols standing for a class of mathematical objects and so on) as applicable to diverse problems. Thus, a majority of the sutras or verses of a classical Indian mathematical text are in the form of prescriptions or rules — they are referred to by the traditional commentators as vidhi, prakriya orkarana-sutras — rules that characterise systematic procedures.
This approach is not special to mathematics alone, but common to most Indian knowledge systems — the sastras. The canonical texts of different disciplines in Indian tradition present rules which are generally called sutras or lakshanas. Most of these rules serve to characterise systematic procedures (referred to variously as vidhi, kriya or prakriya, sadhana, karma or parikarma, karana etc) which are designed to accomplish specific ends. In this way, the Indian sastras are always rooted in vyavahara or practical applications. This approach of Indian sastras allows them to have a great degree of flexibility in devising multiple approaches to the solutions of problems and not get bogged down by any dogma of inviolability of the fundamental truths posited or derived in any specific theoretical formulation employed in the discipline concerned. While the canonical texts of Indian sastras clearly assert the validity and the efficacy of the various procedures enunciated in them, they also simultaneously emphasise that these procedures are only upaya, or means for accomplishing specific ends, and there are no other restrictions which need to be imposed on them. The texts also declare that one is free to take recourse to any other set of systematic procedures, if they are equally efficacious in accomplishing the given ends.
It is the algorithmic approach that distinguishes the ancient Indian texts of geometry, the Sulvasutras (prior to 800 BCE), which deal with the construction of yajna-vedis (altars). While Sulvasutras do contain the earliest available statement of the so-called Pythagoras theorem — they state it in the form “the square made by the diagonal of a rectangle is equal to the sum of the squares made by its sides” — the main purpose of the Sulvasutras is to describe systematic procedures for constructing and transforming geometrical figures using a rajju (rope) and sanku (pole).
Source: Excerpted from an article by MD Srinivas, chairman of Centre for Policy Studies, Chennai http://www.mydigitalfc.com/indian-knowledge-series/everyday-equations-188