Kātyāyana (कात्यायन) also spelled as Katyayana (est. c. 6th to 3rd century BCE) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India. 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'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 (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, 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) 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