According to some legends, he was born in the Katya lineage originating from Vishwamitra, thus called Katyayan. The Kathāsaritsāgara mentions Katyayan as another name of Vararuchi, a re-incarnation of Lord Shiva's gana or follower Pushpadanta. The story also mentions him learning grammar from Shiva's son Kartikeya which is corroborated in the Garuda Purana where Kartikeya teaches Katyayana the rules of grammar in a way that it could be understood even by children.
The Vārttikakāra, an elaboration on Pāṇini grammar. Along with the Mahābhāṣya of Patañjali, this text became a core part of the Vyākaraṇa 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 : 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 structure is superposed on the sound-universal or the phonological structure. In the tradition of scholars like Pingala, Kātyāyana was also interested in mathematics. Here his text on the sulvasutras dealt with geometry, and extended the treatment of the Pythagorean theorem as first presented in 800 BCE by Baudhayana. Kātyāyana belonged to the Aindra School of Grammar and may have lived towards the Punjab region of the Indian Subcontinent.
