Pānini (पाणिनि)  was an ancient Indian grammarian (c. 520–460 BC, but estimates range from the 7th or even earlier as far back as the 17th century BCE, to 4th centuries BCE pprior to the evolution of Classical Sanskrit) who lived in Gandhara and is most famous for his grammar of Sanskrit, particularly for his formulation of the 3,959 rules of Sanskrit morphology in the text Ashtādhyāyī.

Pānini's grammar of Sanskrit is highly systematised and technical. Inherent in its analytic approach are the concepts of the phoneme, the morpheme and the root, only recognized by Western linguists some two millennia later. His rules have a reputation for perfection — that is, they are claimed to describe Sanskrit morphology fully, without any redundancy. A consequence of his grammar's focus on brevity is its highly unintuitive structure, reminiscent of contemporary "machine language" (as opposed to "human readable" programming languages). His sophisticated logical rules and technique have been widely influential in ancient and modern linguistics.

It was Panini who first enunciated  that grammatically, Sanskrit has eight cases for the noun (nominative, accusative, genitive, dative, ablative, instrumental, vocative, and locative), three genders (masculine, feminine, and neuter), three numbers for verbs, nouns, pronouns, and adjectives (singular, dual, and plural), and three voices for the verb (active, middle, and passive). The language is very highly inflected. The ancient Indian scripts known as the Brahmi and Kharosthi alphabets have been employed to record Sanskrit. Both Brahmi and Kharosthi are thought to be of Semitic origin. The Devanagari characters, which are descended from Brahmi, also were, and still are, used for writing Sanskrit. The comparison of Sanskrit with the languages of Europe, especially by Sir William Jones, opened the way to the scientific study of language in Europe in the 18th cent. In fact it would not be too far fetched to say that the study of Grammar began in Europe after the discovery of Sanskrit. We doff our hats to this extraordinarily  brilliant individual who achieved so much with so little nearly 4 millennia ago.

Pānini, and the later Indian linguist Bhartrihari, may have had a significant influence on many of the foundational ideas proposed by Ferdinand de Saussure, professor of Sanskrit, who is widely considered the father of modern structural linguistics.

 

Nilakantha Somayaji (1444 - 1545) of the Kerala school In the 19th century, the prevailing belief among the historians of science was that Mathematics and Astronomy in the Indian subcontinent had gone into hibernation after Bhaskaracharya in the 12th century. The credit for demonstrating that this was not so must surely go to Charles M Whish, Esq., a civil servant in the East-India Company. In 1832 he brought to the attention of the historians the magnificent achievements of the Kerala School which flourished from the 14th to 17th century. (Whish's paper, On the Hindu Quadrature of the circle, has been reproduced in A modern introduction to ancient Indian mathematics, T S Bhanumurthy, Wiley Eastern, as an appendix.) Among the major figures of this school are Madhava (1350-1410) of Sangamagrama , Paramesvara (1360-1455), Nilakantha Somayaji (1444-1545) and Jyesthadeva (c.1500-1600) whose significant contributions to mathematics include infinite series expansions of trigonometric functions and very accurate approximations to p. The most comprehensive work of the Kerala school available to us is the Tantrasangraha of Nilakantha Somayaji along with commentaries on it by some of his followers. Fortunately the biographical details of Nilakantha are well recorded. He was born on Wednesday, June 14, 1444, and was a resident of Trkkantiyur (Sanskritised into Sri -Kundapura ), near Tirur, Ponnai taluk, South Malabar. His teachers were Ravi with whom he studied Vedanta , and Damodara , son of Paramesvara, who initiated him into Astronomy and the underlying mathematical principles. That Nilakantha lived upto a ripe old age, even to become a centenarian, is attested by a contemporary reference made to him in a Malayalam work on astrology Prasnasara composed in 1542-43. Nilakantha 's writings substantiate his knowledge of several branches of Indian philosophy and culture. It is said that he could refer to a Mimam& sa authority to establish his view-point in a debate and with equal felicity apply a grammatical dictum to the same purpose. Sundararaja , a contemporary Tamil astronomer, refers to Nilakantha as sad - darshani - parangata , one who had mastered the six systems of Indian philosophy. Another major work of Nilakantha is his Bhasya on Aryabhatiyam of Aryabhata (476 A.D). The lucid manner in which difficult concepts and cryptic astronomical calculations from Aryabhatiyam are explained, the wealth of quotations, and the results of personal investigation amply justify Nilakantha referring to his work as a Mahabhasya . The Tantrasangraha of Nilakantha Somayaji along with commentaries on it by some of his followers has been critically edited by K V Sharma. Another source book, also by K V Sharma, is A History of the Kerala School of Hindu Astronomy ; both these books have been published by the V V B Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur, Punjab.     References Books:   G Cardona, Panini : a survey of research (Paris, 1976). G G Joseph, The crest of the peacock (London, 1991). Articles:   P Z Ingerman, 'Panini-Backus form' suggested, Communications of the ACM 10 (3)(1967), 137.   Apastambha Author of SulvaSutras References Books:   G G Joseph, The crest of the peacock (London, 1991). Articles:   R P Kulkarni, The value of p known to Sulbasutrakaras, Indian J. Hist. Sci. 13 (1) (1978), 32-41. G Kumari, Some significant results of algebra of pre-Aryabhata era, Math. Ed. (Siwan) 14 (1) (1980), B5-B13. A E Raik and V N Ilin, A reconstruction of the solution of certain problems from the Apastamba Sulba Sutra Apastamba (Russian), in A P Juskevic, S S Demidov, F A Medvedev and E I Slavutin, Studies in the history of mathematics 19 'Nauka' (Moscow, 1974), 220-222; 302. November 2000 Baudhayana   Dharmasutras: The Law Codes of Apastamba, Gautama, Baudhayana, and Vasistha by Patrick Olivelle, 01 January, 2000 Baudhayanadharmasutram: Govindasvami racita Vivarana vrtti sahita by Baudhayana, 1999 Layout and construction of citisaccording to Baudhayana-, Manava-, and Apastamba-lbasutras (Research Unit series / Bhandarkar Oriental Research Institute) by Raghunatha Purushottama Kulakarni, 1987 Dharmasutras: The Law Codes of Apastamba, Gautama, Baudhayana, and Vasistha by Patrick Olivelle, 01 January, 2000 Baudhayanadharmasutram: Govindasvami racita Vivarana vrtti sahita by Baudhayana, 1999 Layout and construction of citisaccording to Baudhayana-, Manava-, and Apastamba-sulbasutras (Research Unit series / Bhandarkar Oriental Research Institute) by Raghunatha Purushottama Kulakarni, 1987     Bhartrihari