(Article I.4.) Mahāvīra’s Geometrical Problems Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages

Abstract

The first part of the article presents, as necessary background, the development of the Near Eastern surveyors’ riddle tradition, from its pre-Old-Babylonian beginnings, over innovations that may go back to the fifth or fourth century BCE, until those that can be dated to the Seleucid-Demotic periods. It also gives a brief description of its impact on Greek theoretical as well as Pythagoreanizing and so-called practical mathematics.

The second part looks at the geometry chapter of Mahāvīra’s Ganita-sāra-saṅgraha. It finds clear borrowings, respecting the phases of the Near Eastern development, each of the three sections of the chapter corresponding to one of the Near Eastern phases; surprisingly, the borrowings often point more clearly to the Mediterranean offset of Near Eastern practices than to these practices themselves. The borrowings can be seen to have been regarded by Mahavira as part of age-old and venerated Jaina tradition – which implies that the borrowings did not come from the Islamic culture of Mahāvīra’s own century.

Originally published in Ivor Grattan-Guinness & B. S. Yadav (eds), History of the Mathematical Sciences, pp. 83–95. New Delhi: Hindustan Book Agency, 2004.

Small corrections of style made tacitly

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