KOCHI: The story of pi is one of great intrigue. On a cosmological plane, this natural constant is believed to hold secrets of the universe, evident in the spiral patterns of galaxies and the way matter is distributed. In quantum mechanics, pi offers insights into the subatomic world.
Physicists such as Werner Heisenberg, Albert Einstein, and Johannes Kepler have depended on it for the ‘Uncertainty Principle’, the ‘General Theory of Relativity’, and the ‘Laws of Planetary Motion.’ Pi is seen as an intrinsic part of universal geometry, governing everything from the macroscopic world to the DNA’s inner structure. And its history spans ancient civilisations: the Sumerians, Babylonians, and Bharat.
To a mathematician, pi is an infinite, irrational number often approximated as 22/7 or in decimal as 3.14159… extending into an infinite sequence of digits. Several cultures approximated pi to different decimal places.
This mystery number has a notable Kerala connection as well. In the 14th century, Sangamagrama Madhava, a mathematician from Irinjalakuda in Thrissur, became the first to approximate pi correctly up to 11 decimal places.
Madhava’s achievements go beyond the value of pi. He developed calculus series for sine, cosine, and arctangent functions long before these concepts appeared in the works of 17th-century mathematicians James Gregory, Gottfried Wilhelm Leibniz, and Isaac Newton.
This revelation has shifted traditional beliefs, as Leibniz and Newton are regarded as the fathers of calculus. Today, Madhava’s contributions are recognised in the naming of certain infinite series based on trigonometric and calculus functions, now known as the ‘Madhava-Newton’, ‘Madhava-Leibniz’, and ‘Madhava-Gregory’ series.
‘Kerala School of Mathematics’
Madhava’s work highlights ancient Kerala’s prominence in mathematics and astronomy, giving rise to the term ‘Kerala School of Mathematics’.
This school includes scholars such as Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, and Achyutha Panikkar. Among them, Melpathur Narayana Bhattathiri, famous to Malayalis as the author of the devotional work ‘Narayaneeyam’, was a mathematical linguist who contributed significantly to the school.
Madhava’s work is referenced in the writings of these scholars. However, much of his original work has been lost, or yet to be unearthed.
While outside Kerala, within India and abroad, Madhava’s contributions have been well-celebrated, the state is now slowly embracing his legacy.
And that brings us to Litty Chacko, a Malayalam professor at St Joseph’s College in Irinjalakuda, who has spent 15 years uncovering Madhava’s life and contributions.
“In my college, the mathematics department was quite strong, and we hosted many international seminars. Many international speakers came because they had heard of Irinjalakuda as Madhava’s birthplace. That intrigued me,” she says, on how her research began.
“I have always had a passion for heritage. I wanted to learn more about him. I visited his ancestral home near Irinjalakuda, met many people, and explored numerous manuscripts. The journey has been incredible, allowing me to know more about him and related history that is nowhere in our textbooks.”
Litty had a clear goal: finding the eight books Madhava is credited with, as mentioned by his successors.
“It was during these journeys that I discovered ‘Lagnaprakarana’ [an important astronomical text] for the first time. I found it written in a notebook, but it had several errors. I spent two years working on it, refining it, and eventually publishing it,” she says.
When the UGC called for new course proposals, Litty incorporated a manuscript management course alongside Malayalam. This helped establish a lab for manuscript preservation at her college. It also created a dedicated space for studying inscriptions, allowing her to deepen her focus on Madhava’s work. She terms it as a “calling”.
“While maths was not my field, I felt a pull inside to prove Madhava’s existence, compile his works, and promote the depth of his contributions, focusing on preserving his legacy and heritage,” she reflects.
Her next mission is to pin-point Madhava’s astronomical observatory. “It is widely believed that a temple and two stones, near the ‘mana’, mark the vananireekshanasala’s (observatory) location. However, I found no concrete evidence there,” says Litty.
“But there certainly must be an observatory associated with Madhava… bringing clarity to this became my next goal.”
For this, she turned to the works of manuscriptologist K V Sarma, internet archives, and other resources. She plans to compile her findings into a resource for studying the ancient local heritage. “It will gather studies in mathematics and astronomy for broader accessibility,” she says.
English education was promoted as superior
Among the discoveries is ‘Golavadha’, considered Madhava’s masterpiece. Sarma’s research describes Madhava’s disciples’ reverence for the work, yet no one knows what it precisely contains as it seems lost to time. Litty believes it may exist “somewhere”.
“If not here, it could be in Europe, as a foundational text likely influencing later mathematical works claimed by the West. They surely must have read this one,” she says.
The colonial era’s onset accelerated the decay of Indian scientific heritage. Palm-leaf manuscripts were neglected, and the class system alienated knowledge from the masses, stopping these works from entering folklore or daily life.
“Sanskrit was largely inaccessible to the public. English education was promoted as superior, leading to the dismissal of traditional knowledge systems,” Litty says.
Litty’s searches in various ‘manas’ (traditional homes) unearthed several unpublished and untitled works left to ruin. “Through these studies and conversations, I realised Madhava could not be studied in isolation. It involves Malayalam, Sanskrit, mathematics, astronomy, Ayurveda, Tantra, and more. Such a multidisciplinary approach is absent in our syllabus,” says Litty.
“I believe documenting branches of Asian science is vital for progress. I began with Ayurveda’s ‘Ashtavaidya’ tradition, and plan to proceed with Tantra next. My aim is to establish a foundation, paving a clear path for future researchers.”
Madhava’s global recognition led to the creation of a collective called Madhava Ganitha Kendram in 2012. Since then, the Kendram, based in Ernakulam, has organised events and created programmes about his work. However, A Vinod Karuvarakundu, the Kendram’s director, points out that the state is yet to establish a memorial at Madhava’s birthplace.
“Just as Shankaracharya is globally recognised as a philosopher, Madhava should be celebrated as one of the greatest mathematicians,” he says. “We also need a robust research structure to delve deeper into Madhava’s contributions.”
There is, however, a centre called the Kerala School of Mathematics, established in Kozhikode in 2007 by the Kerala State Council for Science, Technology and Environment and the Department of Atomic Energy. It aims “to revive the glory of a similar school that flourished between the 14th and 16th centuries in Kerala’”.
But, the centre is said to be focused more on current mathematics rather than historical research.
Ironically, it was an English civil servant, Charles Matthew Whish (1794-1833), who first introduced the existence of the ‘Kerala School of Mathematics and Astronomy’ to the West.
“Since Charles Whish’s discovery, many scholars have explored Madhava’s contributions. However, a systematic study of his mathematical work is still lacking,” says Vinod. “An ecosystem for decoding the manuscripts’ coded language and an organised inventory of available copies are necessary.”
Sooraj R S, who is part of a project cell at Sree Sankaracharya University of Sanskrit, Kalady, has researched how historians approach Madhava. He agrees the study should be multidisciplinary.
“My background is in Sanskrit, and I used historiography theory in my research. In-depth analysis of Madhava’s work is limited here, as I am not very familiar with mathematical theories,” he rues. “Studies should consider figures beyond Madhava as well. This scientific heritage should be included in the curriculum. Too often, a trend emerges where interest in certain figures spikes, only to wane quickly. It would be unfortunate if Madhava’s legacy followed this pattern.”
Rajasekhar P Vaikom, who has published an interpretation of ‘Yuktibhasa’ (a treatise by Jyeshtadeva from the Kerala School), highlights two issues regarding traditional knowledge systems in India. “There are two contradictory trends when it comes to traditional knowledge in India. One is to exaggerate it, and the other, a more malevolent one, is to trivialise it,” he says.
“If we can encourage the younger generation to study these contributions scientifically and understand the pedagogies and derivations from different historical periods, an appreciation of these systems could ensue. Without this, all that is genuine also risks being labelled as superstition.”
Research institutions outside Kerala, such as International Centre for Theoretical Sciences, Bengaluru, and colleges under Delhi University, have been organising seminars and outreach sessions on Madhava.
Spurred by this, the Kerala government has taken note of the genius. Higher Education Minister R Bindu recently said at an international seminar organised by the Government Sanskrit College in March that there were plans to set up a mathematical research institute at Kallettumkara, considered to be Madhava’s native place. History awaits.
With inputs from Aparna Nair