The methods and findings of pre-modern Indian mathematicians remain poorly understood. Priya Nambrath, a doctoral candidate in the School of Arts & Sciences’ Department of South Asia Studies, wants to change that.
2 min. read
Add zero and one to get one, one and one to get two, one and two to get three, two and three to get five. Most of us know this—that each successive number is the sum of the two numbers that came before it—as the Fibonacci sequence, named after a 12th-century Italian mathematician. But as early as 200 BCE, an Indian poet and mathematician named Acharya Pingala used that sequential concept to analyze poetry, and 7th-century scholar Virahanka later described it in more detail.
Priya Nambrath studied astronomical data tables in a medieval Sanskrit text at the Oriental Research Institute and Manuscripts Library in Thiruvananthapuram, India.
(Image Courtesy of Priya Nambrath)
In fact, the use of math on the Indian subcontinent stretches back more than 3,000 years, and curiosity about this ancient and understudied history is at the center of Priya Nambrath’s research. As a fifth-year doctoral candidate in the Department of South Asia Studies in Penn’s School of Arts & Sciences, Nambrath is studying the applied practice of mathematics during medieval and premodern times in what is now Kerala, a state in southwestern India.
It’s “a deeply grounded and long-lasting mathematical tradition,” she says, one in which people drew on local religious and metaphysical themes, as well as the rhythm and structure of Sanskrit poetry. In the process, they uncovered many ideas and approaches long before Europeans did—discoveries that go largely underrecognized: “For the most part,” Nambrath says, “even students in India are not taught this aspect of cultural and intellectual history.”
A nine-month Fulbright Research Fellowship gave Nambrath the opportunity to travel to the Indian cities of Thiruvananthapuram, Chennai, and Pune, where she visited manuscript archives to examine medieval mathematical and astronomical texts written on palm leaf. Nambrath also accessed late 19th-century print editions of Sanskrit and vernacular mathematical works, among many others.
“This research involved a lot of time spent in several different archives and dealing with different categories of archival material,” she says. From December 2023 to September 2024, Nambrath visited manuscript libraries in India, where she identified a few mathematical texts that had not been previously studied or translated. Those texts provided insights into “a medieval system of pedagogy,” Nambrath says, one that incorporated local approaches to mathematics.
She also found that European colonial scholars struggled to completely understand Indian math. One stumbling block, she observed, was cultural prejudice and a sense of mathematical superiority. But Nambrath surmises they may also have been flummoxed by how different it was from anything they’d encountered, something she ran into herself. “My STEM background had encouraged me to think of mathematics as a kind of universal language, not susceptible to cultural and historical nuance like art, music, and literature,” she says. “But what I was seeing in Indian mathematical texts convinced me otherwise.”
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