## 15 Sep Panini and Formal Scientific Notation

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 by Panini (6th C BC) in the field of Sanskrit grammar and linguistics.

Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan.

Besides expounding a comprehensive and scientific theory of phonetics, phonology and morphology, Panini provided formal production rules and definitions describing Sanskrit grammar in his treatise called Asthadhyayi.

Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini’s notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today’s theoretical computer science should have their origin with an Indian genius around 2500 years ago.

Basic elements such as vowels and consonants, parts of speech such as nouns and verbs were placed in classes. The construction of compound words and sentences was elaborated through ordered rules operating on underlying structures in a manner similar to formal language theory.

Today, Panini’s constructions can also be seen as comparable to modern definitions of a mathematical function. G G Joseph, in The crest of the peacock, argues that the algebraic nature of Indian mathematics arises as a consequence of the structure of the Sanskrit language.

Ingerman in his paper titled Panini-Backus form 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.

(Exerpts from Indic Mathematics – India and the Scientific Revolution By David Gray, PhD)

By Prachodayat Team

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