A new theoretical approach to sample problems and deductive reasoning in Sanskrit mathematical texts

Geometry is the earliest recorded branch of Indian mathematics. Mathematics of the Vedic period consists of those geometric techniques needed for the construction of the altars and fire-places described by the priestly hereditary class for the performance of their rites. The link between geometry and ritual suggests that mathematical accuracy was considered of the utmost importance in this context. The study of rational figures in the Sanskrit work Ganita Sara Samgraha, to which Mahaviracarya, a ninth-century CE Jaina mathematician, dedicates a special treatment, reveals striking parallelism with the earlier geometry developed in connection with the Vedic sacrifice. Mahavira makes extensive use of the uddesaka or 'sample problem', and I suggest a new way of interpreting the uddesaka as a significant device for constructing an 'actual proof' which validates and links a mathematical rule to its unmentioned premises and provides a system of knowledge based on deductive syllogism.