Multiplying Integers: On the Diverse Practices of Medieval Sanskrit Authors

Abstract

We examine the diverse ways Brahmagupta (628 CE), Mahāvīra (ca. 850), and their commentators understood how a multiplication could be executed. We describe a variety of algorithms. We note how commentators give us clues to how numbers are shaped for execution, how the procedure is displayed on a working surface, etc. We attempt to evaluate in which ways resources of the decimal place value notation were used. The current historiography of elementary operations in Sanskrit sources is also revised along the way. 1 The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement n. 269804. We would like to thank the invaluable remarks and comments of S.