A scholarly review in Mathematics in Ancient Civilizations has identified the use of infinite series expansions for calculating the areas of complex polygons in a 10th-century Jain text, the Ganita-Sara-Sangraha commentary. While the base text is well-known, this specific sub-commentary found in the Shravanabelagola archives contains algebraic proofs for converging series that predate the famous Kerala School by four centuries.
The research demonstrates that Jain mathematicians were utilizing a form of proto-calculus to solve problems related to the volumes of irregularly shaped ritual vessels. This discovery suggests that the conceptual leap toward infinity was not an isolated event in the 14th century but part of a continuous, pan-Indian mathematical evolution spanning nearly a millennium.