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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.

Contents

See also

References

External links

See also

★ Panini (grammarian)

★ Indian mathematicians
We cannot attempt to write a biography of Katyayana since essentially nothing is known of him except that he was the author of a Sulbasutra which is much later than the Sulbasutras of Baudhayana and Apastamba. It would also be fair to say that Katyayana's Sulbasutra is the least interesting from a mathematical point of view of the three best known Sulbasutras. It adds very little to that of Apastamba written several hundreds of years earlier. We do not know Katyayana's dates accurately enough to even guess at a life span for him, which is why we have given the same approximate birth year as death year.
Katyayana was neither a mathematician in the sense that we would understand it today, nor a scribe who simply copied manuscripts like Ahmes. He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and to improve and expand on the rules which had been given by his predecessors. Katyayana would have been a priest instructing the people in the ways of conducting the religious rites he describes.
Katyayana lived in a period when the religious rites that the Sulbasutras were written to support were becoming less influential. People were turning to other religions and perhaps this lack of vigour in the religion at this time partly explains why several hundreds of years after Apastamba Katyayana adds little of importance to the Sulbasutra which he wrote.
See the article Indian Sulbasutras for more information on the Sulbasutras in general and the mathematical results which they contain.

References

★

★ .

External links

★ Katyayana and Advaita

★ Katyayana and vegetarianism