The sum of the series in the brackets adds up to π/4, and is famous as the Gregory Leibniz series.

Madhava’s series was quoted and a proof (upapatti) also given a century later by Jyeshtadeva.

Parameshvara – Like Brahmagupta providing a sphuTam to Paitamaha Siddhaanta, Parameshvara observed that over time, predictions of earlier astronomers did not agree with observed positions based on calculations. In such a situation, he observed, one must adjust one’s methods and calculations, because planets and stars will conform to them.

He titled his book Drg Ganitam. This title, which means Observed Calculations, is a popular phrase for jyotisham in south India, though the author himself has faded from public memory. His shishya NilakanTha referred to him as Paschimaam Bodhi, the western scholar.

Nilakantha Somayaaji – More unknown than even Brahmagupta, was a polymath like Varahamihira. He was a scholar of Shad darshana (the six philosophies of Hinduism, and also in vyaakarana, chandas, the Bhagavata and various such literature. He also studied Vedanga Jyotisha, Pancha Siddhaantika, Brhat Samhita etc.

This historical curiosity and scholarship may have shined in other scholars, too, but in Nilakantha, we have contemporary evidence. He was also a prolific composer, of several texts.

He was a friend a Sundararaja, a jyotisha of the neighboring Tamil Nadu, and took the effort to compile a written list of answers for questions posed by the former, compiled into a book called Sundararaja Prashnottara.

Aficionados of European science may be reminded of the extensive correspondence of Franklin, Newton, Darwin, Humboldt etc.

A ninth century mathematician called Virasena in his commentary Dhavala gave this equation, that the sum of all powers of 1/4 is 1/3. One sees the reflection of this in Madhava’s several infinite series. Nilakantha questioned this apparent absurdity. How does the sum of this infinite series increase to that finite value (1/3), and that it reaches finite value?