Madhava of Sangamagrama, who lived from about 1340 to 1425, is remembered as the founder of the Kerala school of astronomy and mathematics in southern India. Later Kerala scholars quoted him on the circumference of a circle 9×10¹¹ units across. His figure was 2827433388233. Rounded to the nearest whole number, the true answer ends in 231, so Madhava was out by two.
That small miss is now a research puzzle. A paper tested the infinite series for π that tradition credits to Madhava. Except in one unlikely case, none of them reproduces his number, and the paper concludes that how he reached it remains unanswered.
Who quoted the number
Madhava’s own words on the circle come to us second-hand. Nilakantha Somayaji and Sankara Variar, both later members of the Kerala school, are the ones who report the value in his name.
A much later member of the same school did better. Sankara Varman, who lived from 1774 to 1839, wrote a verse treatise called the Sadratnamala in 1819. In it he gave the circumference of a circle 10¹⁷ units across, and his figure is correct to the nearest integer. That is the same as knowing π to 17 decimal places.
The paper’s author is careful about how much that feat means on its own terms. Set beside William Shanks’s 507 decimal places in 1853, 17 places carries little mathematical weight. What stands out is the form. Varman wrote the whole Sadratnamala as Sanskrit verse in the old Kerala manner, although Western-style mathematics books had by then reached India.
The paper shows one route to Varman’s answer. Start from the series now called the Madhava-Gregory series, applied to π/6 as the arctangent of one over the square root of three. Then drop the fractional part after every operation. Done that way, by hand, the sum lands on Varman’s value.
How much is known about the man
Very little. An updated biography posted to arXiv says almost nothing about his life can be stated with certainty. Inside Kerala’s own traditions he was better known as an astronomer and astrologer than as a mathematician. Ulloor S. Parameswara Aiyer’s five-volume history of Kerala literature, published between 1953 and 1957, calls him a daivajña, an astrologer-astronomer.
Local legend places his home village, Sangamagrama, at the town of Irinjalakuda, about 60 km north of Cochin. The biography’s author notes that recent scholarship disputes this. One undated document, held at the Oriental Institute in Baroda as number 9886, lists a line of scholars from Govinda Bhattatiri, born in 1237, to Acyuta Pisharati, who died in 1621. Madhava is the ninth name on it.
That entry names him as the author of several works. It lists the Venvaroha, the Muhurttamadhaviyam, the Prasnamadhaviyam and a calendar work, the Aganita-panchangam. Even his face is a guess. The portrait now used for him is an artist’s impression, released in 2014 by Madhava Ganitha Kendram, a volunteer group in Kochi working to revive his work.
When the West heard of him
The first person to bring the Kerala school to European mathematicians was C. M. Whish, a civil servant with the East India Company’s Madras establishment. He knew Sankara Varman personally, and wrote that the Sadratnamala was full of “fluxional forms and series”.
Yet Whish’s 1834 paper on Kerala mathematics never mentions Madhava. His name first appeared in print outside Sanskrit only in 1948, in a Malayalam commentary on the Yuktibhasa. Recognition of him as one of India’s greatest mathematicians came only in the second half of the twentieth century.
Much of what is known about the founder of the Kerala school still rests on one undated list. His best-known circle value is two units wrong, and the method behind it is still unknown.
