Kātyāyana
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Kātyāyana (कात्यायन) also spelled as Katyayana ( century BCE) was a Sanskrit grammarian,
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and Vedic priest who lived in
ancient India Anatomically modern humans first arrived on the Indian subcontinent between 73,000 and 55,000 years ago. The earliest known human remains in South Asia date to 30,000 years ago. Sedentism, Sedentariness began in South Asia around 7000 BCE; ...
.


Origins

According to some legends, he was born in the Katya lineage originating from Vishwamitra, thus called Katyayana. The Kathāsaritsāgara mentions Kātyāyana as another name of Vararuci, a re-incarnation of Lord
Shiva Shiva (; , ), also known as Mahadeva (; , , Help:IPA/Sanskrit, ɐɦaːd̪eːʋɐh and Hara, is one of the Hindu deities, principal deities of Hinduism. He is the God in Hinduism, Supreme Being in Shaivism, one of the major traditions w ...
's gana or follower Pushpadanta. The story also mentions him learning grammar from Shiva's son
Kartikeya Kartikeya (/Sanskrit phonology, kɑɾt̪ɪkejə/; ), also known as Skanda (Sanskrit phonology, /skən̪d̪ə/), Subrahmanya (/Sanskrit phonology, sʊbɾəɦməɲjə/, /ɕʊ-/), Shanmukha (Sanskrit phonology, /ɕɑnmʊkʰə/) and Murugan ...
which is corroborated in the Garuda Purana where
Kartikeya Kartikeya (/Sanskrit phonology, kɑɾt̪ɪkejə/; ), also known as Skanda (Sanskrit phonology, /skən̪d̪ə/), Subrahmanya (/Sanskrit phonology, sʊbɾəɦməɲjə/, /ɕʊ-/), Shanmukha (Sanskrit phonology, /ɕɑnmʊkʰə/) and Murugan ...
(also called Kumara) teaches Katyayana the rules of grammar in a way that it could be understood even by children. It may be that his full name was in fact Vararuci Kātyāyana.


Relation to Goddess Katyayini

In texts like Kalika Purana, it is mentioned that he worshipped Mother Goddess to be born as his daughter hence she came to be known as Katyayani or the "daughter of Katyayan" who is worshipped on the sixth day of Navratri festival. According to the Vamana Purana once the gods had gathered together to discuss the atrocities of the demon Mahishasura and their anger manifested itself in the form of energy rays. The rays crystallized in the hermitage of Kātyāyana
Rishi In Indian religions, a ''rishi'' ( ) is an accomplished and enlightened person. They find mention in various Vedic texts. Rishis are believed to have composed hymns of the Vedas. The Post-Vedic tradition of Hinduism regards the rishis as "gre ...
, who gave it proper form therefore she is also called Katyayani.


Works

He is known for two works: * The '' Vārttikakāra'', an elaboration on Pāṇini grammar. Along with the '' Mahābhāṣya'' of Patañjali, this text became a core part of the '' Vyākaraṇa'' (
grammar In linguistics, grammar is the set of rules for how a natural language is structured, as demonstrated by its speakers or writers. Grammar rules may concern the use of clauses, phrases, and words. The term may also refer to the study of such rul ...
) canon. This was one of the six Vedangas, and constituted compulsory education for students in the following twelve centuries. * He also composed one of the later Śulbasūtras, a series of nine texts on the geometry of altar constructions, dealing with rectangles, right-sided triangles, rhombuses, etc.


Views

Kātyāyana's views on the sentence-meaning connection tended towards naturalism. Kātyāyana believed, that the word-meaning relationship was not a result of human convention. For Kātyāyana, word-meaning relations were ''siddha'', given to us, eternal. Though the object a word is referring to is non-eternal, the substance of its meaning, like a lump of gold used to make different ornaments, remains undistorted, and is therefore permanent. Realizing that each word represented a categorization, he came up with the following conundrum (following Bimal Krishna Matilal): :"If the 'basis' for the use of the word 'cow' is ''cowhood'' (a universal) what would be the 'basis' for the use of the word 'cowhood'? Clearly, this leads to infinite regress. Kātyāyana's solution to this was to restrict the universal category to that of the word itself — the ''basis'' for the use of any word is to be the very same word-universal itself." This view may have been the nucleus of the Sphoṭa doctrine enunciated by Bhartṛhari in the 5th century, in which he elaborates the word-universal as the superposition of two structures — the meaning-universal or the
semantic Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
structure (''artha-jāti'') is superposed on the sound-universal or the phonological structure (''śabda-jāti''). In the tradition of scholars like Pingala, Kātyāyana was also interested in mathematics. Here his text on the sulvasutras dealt with
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, and extended the treatment of the Pythagorean theorem as first presented in 800 BCE by Baudhayana.Pingree (1981), p. 6 Kātyāyana belonged to the Aindra School of Grammar.


Notes


References

* Joseph, George Gheverguese: The Crest of the Peacock: Non-European Roots of Mathematics * Pingree, David
''Jyotihsastra: Astral and Mathematical Literature''
Otto Harrassowitz. Wiesbaden, 1981. .


External links

* {{DEFAULTSORT:Katyayana Ancient Sanskrit grammarians Ancient Indian mathematicians 3rd-century BC writers Indian Sanskrit scholars 2nd-century BC mathematicians Ancient Indian mathematical works 3rd-century BC clergy 3rd-century BC mathematicians