How did the school of Madhava in Kerala develop infinite series?

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Indian mathematics The evolution of Hindu-Arabic numerals from Brahmi through Devanagari and Arabic to European scripts.

The school of Madhava in Kerala made pioneering contributions to mathematics by developing infinite series and utilizing infinitesimal quantities long before similar concepts emerged in European analysis.1

Working in the late 14th century, Madhava established the foundation for these advancements, which were later expanded upon by his successors, including Jyesthadeva, Nilakantha, and Sankara. These mathematicians derived power series for trigonometric functions such as the sine, cosine, and arctangent. By applying these series, they were able to calculate the value of π to 11 decimal places.1

The school is notable for its rigorous approach, as followers provided ingenious geometric demonstrations to support these analytical findings. This tradition was maintained through a rare, documented lineage of direct teacher-pupil relationships that persisted from the late 1300s through at least the early 1600s.1