History of Mathematics Seminar

During the 14th to the 16th centuries CE, a succession of Indian scholars, collectively referred to as the Kerala school, made remarkable contributions in the fields of mathematics and astronomy. Mādhava of Saṅgamagrāma, a gifted mathematician and astronomer, is considered the founder of this school, and is perhaps best known for discovering an infinite series for pi, among other achievements. Subsequently, Mādhava's lineage of disciples, consisting of illustrious names such as Parameśvara, Dāmodara, Nīlakaṇṭha, Jyeṣṭhadeva, Śaṅkara Vāriyar, Citrabhānu, Acyuta Piṣaraṭi etc., made numerous important contributions of their own in the fields of mathematics and astronomy. Later scholars of the Kerala school flourished up to the 19th century. This talk will provide a historical overview of the Kerala school and highlight its important contributions.

How should we interpret past mathematicians who may use the same vocabulary as us but with different meanings, or whose philosophical outlooks differ from ours? Errors aside, it is often assumed that past mathematicians largely made true claims—but what exactly justifies that assumption?

In this talk, we will explore these questions through general philosophical considerations and four case studies: arithmetic in Book IX of Euclid's Elements, 19th-century analysis, 18th-century geometry, and 19th-century matricial algebra. In each case, we encounter a significant challenge to supposing that the mathematicians in question made true claims. We will show how these challenges can be addressed and overcome.