Exploring what could have been the particularity of Sanskrit mathematical commentaries in the larger landscape of the scholarly commentaries of South Asia, this chapter explores how Prthūdaka (ca. 850) carries out ‘explanations’ on two mathematical verses of Brahmagupta's Theoretical Astronomical Treatise of the True Brahma [School] (Brahmasphuṭasiddhānta-628) concerning progressions. As the commentator explores in many different ways the scope of the rule, a multiplicity of meanings is drawn out, among which one may find the interpretation of a progression as a pile of areas of rectangles within a ‘proof’, or the reading of one procedure as being an algebraical consequence of a previous one. It is within examples and their variations that such mathematical explorations are made, and these may very well be the textual particularity of mathematical commentaries in South Asia.

The foremost historiographic challenge in interpreting pre-modern Indian mathematics is arguably not anachronism so much as anachorism, the blurring of geographical or cultural rather than chronological distinctions. For example, historians struggle constantly with ways to avoid or explain calling Indian analyses of right-triangle relations “Pythagorean”, or using the term “Diophantine equations” for the type of problems designated in Sanskrit as \kuttaka\ or \varga-\prakrti. Nonetheless, the combination of anachronism and anachorism provides the study of Indian mathematics with a powerful lens, which clarifies even as it distorts. This paper will address such trade-offs between popular misconceptions and deeper insights, especially in the application of concepts from the historiography of early modern European calculus to infinitesimal methods used in Sanskrit mathematics of the early to mid-second millennium.