Panini: numbers from language
A biography of Panini, the great Indian grammatician and thinker, suggests that modern number systems, like grammar, came from the analysis of Sanskrit language.
Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.
A treatise called Astadhyayi (or Astaka ) is Panini’s major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini’s constructions are similar to the way that a mathematical function is defined today. Joseph writes in [ [Sanskrit’s] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. … On the basis of just under 4000 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 make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.
G G Joseph, The crest of the peacock (London, 1991).