Panini

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By Krishna Maheshwari


Panini is thought to have been born in Shalatula, a town near Attock, on the Indus river in present day Pakistan. Experts guess at the dates of his life, ranging from 4th-7th century BCE. The extent of work which he undertook is also debated. What is in little doubt, however, is that he was one of the most innovative people in the development of knowledge.

Panini was a Sanskrit grammarian and developed a comprehensive theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of his time and Panini is considered to be one of the fathers of the language because he was the first to formally define its grammar (and his grammar was the first and to date, the only one of its kind for a spoken language). The word "Sanskrit" itself means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.

Panini's major work was a treatise entitled Astadhyayi (or Astaka). It consists of eight chapters, each subdivided into quarter chapters. In this work, Panini distinguishes between the language of sacred texts and the language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. He started by categorizing 1,700 basic elements (nouns, verbs, vowels, consonants) into classes. The construction of sentences, compound nouns etc. is also explained as ordered rules operating on underlying structures in a manner similar to modern language theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph[1] writes:

[Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systematization of its grammar by Panini. ... On the basis of just under 4,000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.

Joseph goes on to argue that algebraic reasoning, the way of representing numbers by words, and ultimately the development of modern number systems in ancient India, are linked through the structure of language.

There are other works which are closely associated with the Astadhyayi but it is debated whether these works were authored by Panini or others who proceeded him.

It is extremely difficult to date Panini. There are ten scholars mentioned by Panini in his work who must have preceded him. However, there is no knowledge of when any of them lived. Panini also uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. However, nothing conclusive has been found.

Similarly, references to Panini by others are also confusing and no conclusive evidence has been found linking those references to the date of Panini.

An evaluation of Panini's contribution by Cardona states[2]:

Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.

Panini's contribution to science

A particularly important development in the history of Indian science that was to have a profound impact on all mathematical treatises that followed was the pioneering work in the field of Sanskrit grammar and linguistics. Panini expounded a comprehensive and scientific theory of phonetics, phonology and morphology, as well as language theory.

Today, Panini's constructions are seen as comparable to modern definitions of a mathematical function. Ingerman[3] finds Panini's notation to be equivalent in its power to that of Backus - inventor of the Backus Normal Form used to describe the syntax of modern computer languages. Thus Panini's work provided an example of a scientific notational model that could have propelled later mathematicians to use abstract notations in characterizing algebraic equations and presenting algebraic theorems and results in a scientific format.

References & Citations

  1. G G Joseph, The crest of the peacock (London, 1991).
  2. G Cardona, Panini : a survey of research (Paris, 1976).
  3. Ingerman, "Panini-Backus form", Communications of the ACM 10 (3)(1967), 137.
  • Shishir Thadani, "History of Mathematics", [1]
  • J J O'Connor and E F Robertson, "Panini", [2]