Madhava, mathematician
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A backgrounder
Sreerag PS, Sep 1, 2024: The Times of India
So, who got there first? Was it Isaac Newton? Or was it Gottfried Leibniz? This had led to one of the ugliest spats in the scientific community, in the early 18th century, with supporters of Newton claiming he was the first to discover calculus, and those in the Leibniz camp saying that this was ridiculous, it was Leibniz who had cracked calculus first.
Four hundred years later, with passions having long cooled after neutral observers reached the conclusion that both Newton and Leibniz had discovered calculus independently — Leibniz beginning with integration and Newton with differentiation — there are now claims that perhaps it was Madhava from Kerala who had got there before both Newton and Leibniz, sometime in the 14th century.
Kerala School Of Mathematics
A recent publication, titled ‘The Secret Lives of Numbers: A Global History of Mathematics & Its Unsung Trailblazers’ by Kate Kitagawa and Timothy Revell has piqued the interest of the Western world. “The ancient Greeks are put on a pedestal as somehow being the originator of modern mathematics, yet so much of what is now incorporated into our global knowledge comes from many other places too, including ancient China, India and the Arabian peninsula,” write Kitagawa and Revell in the prelude to their book.
So, determined to give credit where it is due, the writers dwell at length on the brilliant mathematician Madhava, who was born in a village in central Kerala in 1340. “And what was needed to deduce these formulas (that Madhava wrote)?” ask the writers. “Calculus. Or certainly the basics of calculus,” they conclude.
International Recognition
In recent years, the international community has begun to recognise Madhava’s contributions, renaming several mathematical theorems in his honour, such as the Madhava-Leibniz series on infinity. Back home though, there’s been little effort to protect and retrieve Madhava’s works, which could be vital for future explorations in mathematics.
However, over the past 12 years, a gradual but persistent movement has begun in Kerala, spearheaded by a group of academics who are trying to recover Madhava’s writings on palm leaves and making them accessible for future scholars.
Litty Chacko, a Malayalam teacher at St Joseph College, Irinjalakkuda, leads this movement, supported by her former colleagues, Aneesh EM, a teacher of zoology, and Mangalammal NR, a retired mathematics professor. Their quest to understand Madhava’s life and work is opening new avenues in the study of mathematical history.
“It was Madhava who determined the value of Pi up to 10 decimal places. [Pi is the ratio of a circle’s circumference to its diameter.] Mathematics until then existed in finite series; it was Madhava who introduced the concept of an infinite se- ries. Additionally, sine and cosine tables were affirmed by the theorems of Madhava, decades before Newton, Leibniz and Copernicus,” says Chacko.
Wrote 8 Books, 3 Missing
But Madhava’s contributions to mathematics went largely unrecognised for centuries. According to historical accounts, Madhava founded the Kerala School of Astronomy and Mathematics and is credited with writing eight books, though only five have been found so far. His remaining works, including a work called ‘Golavada’ that his disciples consider his magnum opus, have not been traced yet.
Recently, Chacko authored a book titled ‘Sangamagrama Madhavante Randu Krithikal (Two Works of Sangamagrama Madhava)’ which was published by the National Book Trust. This features, for the first time, Madhava’s work Lagnaprakaranam. The team of academics found the manuscript at an antique seller’s in Irinjalakkuda in 2018. They also found some other manuscripts with the same seller. These are commentaries on astronomy, purportedly written by Madhava.
“We could undertake this long research partly due to our curiosity about the subject and partly due to our friend- ship,” says Aneesh. He says, as a zoologist, he contributed to the research by developing techniques to ensure that the palm leaves featuring Madhava’s works remain accessible for future generations. Aneesh’s team is using techniques from archaezoology to ascertain the actual age of the materials they’ve collected. “We’ve also developed materials using nanoparticles in our lab to preserve the palm leaves without affecting the text written on them,” says Aneesh, who currently works at the department of zoology, University of Calicut.
Meanwhile, Mangalammal, the mathematician in the group, says that deciphering the available work they have found would require a larger team of experts across multiple domains, including math- ematics, astronomy and Sanskrit. “In ancient India, mathematics was not an individual subject; it was always combined with concepts of astrology and astronomy. Understanding the meaning of Madhava’s works requires expertise in mathematics, Sanskrit, and Jyotisa (astrology/astronomy),” says Mangalammal.
Watching Stars From A Temple
At Irinjadappilly Mana in Kallettumkara near Irinjalakkuda, where Madhava probably lived, tales of his achievements are popular even today, Chacko says. Locals here believe that Madhava conducted his space observations at a Shree Krishna temple here. “In Nandinagiri script, it is written that this peeth (seat) was used by Madhava for his space observations, but no attempt has been made to ascertain the period during which these stone inscriptions were created,” Chacko says.
‘The Crest of the Peacock: Non-European Roots of Mathematics’, a book authored by George Gheverghese Joseph and published by Princeton University, suggests that Indian knowledge systems, including Madhava’s works, likely travelled to Europe through Christian missionaries who arrived from the West. Joseph cites several instances of Jesuits from European nations who sought assistance from Brahmins and the Cochin royal family in translating Sanskrit manuscripts into European languages.
“This knowledge acquisition began with the very arrival of Jesuits in Kerala. The translation of local sciences into European languages before their transmission to Europe was epitomised by Garcia da Orta’s popular work, ‘Colloquios dos simples e drogas he cousas mediçinas da India’, published in Goa in 1563. There may have been other, similar publications that remain inaccessible, possibly due to linguistic and nationalistic reasons,” writes Joseph in his book.
According to researchers, India has yet to develop detailed cataloguing systems like those found in libraries abroad, and many working in this field lack the knowledge and skills in archival management. “Managing archives in our country remains a significant barrier to our research. There is an urgent need to develop expertise in manuscript preservation and make these records accessible to the public,” says Chacko.
The researchers say by collaborating with the govt of India, their team is trying to bring back the manuscripts of Kerala School of Astronomy and Mathematics to India. “I am aware that libraries in Germany, the Vatican and Lisbon have huge collections of manuscripts from Kerala, especially on Jyotisa. We are sure that we will also be able to retrieve the ‘Golavada’, in the coming years,” says Chacko.
Kerala School Of Mathematics
MADHAVA SERIES | Madhava developed an infinite series expansion for trigonometric functions such as sine, cosine, and arctangent, which are similar to the modern-day Taylor series. These expansions were groundbreaking in the study of trigonometry and laid the foundation for further advancements in the discipline.
FINDING APPROXIMATE VALUE FOR π | His works provided a series for calculating π (Pi) which converges to the true value of π faster than the method used by ancient Greeks. A specific series for π, which later became famous as the Gregory-Leibniz series, was originally discovered by Madhava.
CALCULUS FOUNDATIONS | Madhava’s work laid the groundwork for the development of calculus, predating similar work in Europe by a few centuries. The Madhava series provides a foundation for calculus, which, very broadly, is the study of continuous change and a bedrock in mathematics.
KERALA SCHOOL OF MATHEMATICS | Madhava is considered the founder of the Kerala School of Mathematics, whose disciples continued to develop and refine his mathematical ideas for centuries.
