A scholarly review in the Archive for History of Exact Sciences has identified the earliest formal conceptualization of mathematical induction in a 10th-century Sanskrit mathematical text. The study analyzes the step-by-step proofs used to calculate the sum of finite series in the context of combinatorial geometry, used for designing complex ritual pavements.
Unlike the later European developments, these Sanskrit proofs utilize a recursive logic known as pankti-vyapti to demonstrate that a geometric property holds for 'any' number of elements if it holds for the first and the subsequent step. This research validates the high level of abstract reasoning present in medieval Indian mathematics, moving beyond purely computational methods into the realm of formal logical proof.