Jyotihshastra: Astral and Mathematical Literature c5.s1.22

c5.s1.22

Perhaps contemporary with Śrīdhara is the work on mathematics preserved in the Bakhshālī manuscript;¹⁸ though some scholars would date it as early as 200 A.D. on the basis of its symbols, its language, its meter, and its references, none of their arguments is very persuasive. The work is earlier than the manuscript, which is written in "early" Śāradā and may therefore have been copied in the eighth, ninth, or tenth century. Arguments based on its relation to extant Sanskrit texts on gaṇita appear to me rather unreliable since we have so little from an early period to compare it with, and since it is clearly not in the main tradition of these texts. However, the fact that it is composed of sūtrāṇi and udāharaṇāni in verse with symbolic statements and prose solutions of the examples as are the works of Śrīdhara makes me believe that it follows the same model as does he. Aside from Āryabhaṭa and Brahmagupta, who did not follow this model, the only mathematicians earlier than Śrīdhara that we know of are Maskari, Pūraṇa, Pūtana, and Mudgala whom the earlier Bhāskara mentions,¹⁹ and Nārmada whom Śrīdhara himself mentions,²⁰ while Lalla was probably contemporary with Śrīdhara.²¹ The tradition, then, of works on gaṇita based on the classification into parikarmāṇi and vyavahārāḥ (the latter are specifically ascribed to Maskari, Pūraṇa, and Mudgala by Bhāskara) was not a very long one; the treatment of rules and examples offered by Śrīdhara and the Bakhshālī manuscript was probably even shorter, though no certain terminus post quem can be attached to it. The subjects treated in the Bakhshālī manuscript include the rule of three, series, square-roots, mixtures (miśraka), simultaneous equations, and quadratic equations; presumably the rest of the traditional contents of a work on gaṇita once were present when the manuscript was complete.