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Katyayana was a Sanskrit Grammarian and mathematician who lived in North India during the 2nd century BCE.
Apart from his Varttika, an elaboration on Panini's grammar, he also composed one of the later Sulba-sutras, a series of nine texts on the geometry dealing with rectangles, right-sided triangles, rhombuses, etc.
As regards his grammatical treatise, Katyayana's views on the word-meaning connection tended towards naturalism. Katyayana believed, like Plato, that the word-meaning relationship was not a result of human convention. For Katyayana, 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 undestroyed, and is therefore permanent.
Realizing that each word represented a categorization, he came up with the following conundrum:
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. Katyayana'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 sphota doctrine enunciated by Bhartrhari in the 5th Century, in which he elaborates the word-universal as the superposition of two structures - the meaning-universal or the semantic structure (artha-jati) is superposed on the sound-universal or the phonological structure (sabda-jati)
In the tradition of scholars like Pingala, Katyayana was also interested in mathematics. Here his text on the Sulva-sutras dealt with geometry, and extended the treatment of the Pythagorean theorem as first presented in 800 BC by Baudhayana.
