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Kātyāyana (c. 3rd century BC) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India.

He is known for two works:

• The Varttika, an elaboration on Panini's grammar. Along with the Mahā-bhāsya of Patanjali, this text became a core part of the vyākarana (grammar) canon. This was one of the six Vedangas, and constituted compulsory education for Brahman students in the following twelve centuries.
• He also composed one of the later Sulba Sutras, a series of nine texts on the geometry of altar constructions, dealing with rectangles, right-sided triangles, rhombuses, etc.

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 (following 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. 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 Bhartrihari in the 5th c., in which he elaborates the word-universal as the superposition of two structures - the meaning-universal or the semantic structure (artha-jāti) is superposed on the sound-universal or the phonological structure (shabda-jāti)

In the tradition of scholars like Pingala, Katyayana 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 BC by Baudhayana.

Katyayana belonged to the Aindra school of grammarians and may have lived towards the North west of the Indian subcontinent.

• Panini (grammarian)
• Indian mathematicians

See the article Indian Sulbasutras for more information on the Sulbasutras in general and the mathematical results which they contain.

• O'Connor, John J; Edmund F. Robertson "Katyayana". MacTutor History of Mathematics archive.  
• Matilal, Bimal Krishna (1990/2001), The word and the world: India's contribution to the study of language, Oxford University Press, ISBN 0-19-565512-5.

• Katyayana and Advaita