A majority of source texts of Indian mathematics and astronomy are written in the verse format. Hence, they and even their prose commentaries, make use of a variety of numeration systems in which linguistic phrases—syllables, words, or set of sounds—are employed to represent arbitrary numerical values. The bhūta-saṅkhyā, Āryabhaṭīya, and kaṭapayādi systems of numeration are well known and have been discussed in many scholarly and popular books and articles.
In their Talk for THT, Dr V Ramanathan of IIT-BHU, Dr Venketeswara Pai of IISER Pune and Prof M D Srinivas of CPS, Chennai examine a less-known but significant system developed within the Tamil Astronomy tradition. They discuss the 12th–13th century astronomical work Cūḍāmaṇi Uḷḷamuḍaiyān by Tirukkoṭṭiyūr Nambi, which uses a vowel-based numeration scheme (uyirēḻuttu) to encode arbitrary numbers by a method that is significantly distinct from systems mentioned above. In particular, they explain its use in encoding lunar longitudes and its application in the formulation of the 248 Candravākyas (sometimes referred to as the Pañcāṅgavākyas) in Tamil.
Their online talk in English titled "Uyirēḻuttu: A System of Numeration Used in Tamil Astronomy Texts" is at 5.30 pm IST on Saturday, May 3, 2025.
About the Speakers:
Dr. V. Ramanathan is a physical chemist in the Department of Chemistry at IIT(BHU) Varanasi and heading the IKS Center of the institute. He carried out his post-doctoral research works in University of Stuttgart in Germany, University of Basel in Switzerland and Seoul National University in South Korea. He obtained his PhD from IIT Kanpur, India. His areas of current academic research are Raman imaging and spectroscopy, SERS and computational chemistry. His other research interest lies in studying the scientific heritage of India. He is a Fulbright scholar and a former core committee member of Indian National Young Academy of Science (a body of Indian National Science Academy (INSA).
Dr. Venketeswara Pai is a renowned scholar in the field of Indian mathematics and astronomy, with expertise in Sanskrit scientific literature, manuscript studies, and traditional knowledge systems. As a faculty member at IISER Pune, he has made significant contributions to the study of historical mathematical texts, their interpretations, and their relevance within the broader framework of Indian Knowledge Systems (IKS). He has done extensive research on Indian astronomical treatise making use of his strong background in philology and mathematical analysis and computation. Dr. Pai has authored numerous articles in peer-reviewed journals and books, receiving prestigious awards for his research in Indian astronomy and mathematics.
Prof. M. D Srinivas is Chairman of Centre for Policy Studies at Chennai, a Research institute which he founded along with Dr. J. K. Bajaj and a few colleagues with the objective of comprehending India from an Indian perspective. After completing his PhD in University of Rochester, New York, USA, Srinivas taught at the Department of Theoretical Physics, University of Madras during 1976-1996. His areas of interest are: Conceptual and mathematical foundations of quantum mechanics; Indian scientific tradition, especially Indian mathematics and astronomy; and Society, polity and economy of India in the Eighteenth century. He has published significant works in all these fields. He was selected a Fellow of Indian National Science Academy in 2023 for his work on History and Philosophy of Science. His name has been included among the list of Padma Shri awardees this year.
