The Jain Legacy of Mathematics

SHRI RATNAKUMAR SHAH has undertaken a comprehensive study of nearly all the major Jain scriptures, meticulously extracting their inherent mathematical content. It is noteworthy that throughout the thousands of pages of mathematical material contained in these ancient scriptures, not a single instance presents mathematics in the conventional form of equations. Instead, the content is conveyed descriptively through poetic verses and prose-without the use of numerical values or symbolic equations.

For any scholar to identify and extract mathematical concepts from such texts originally written in Prakrit (a precursor to Sanskrit) or preserved in translations into other Indian languages and then translate them into modern mathematical expressions with numbers and equations, is an exceptionally complex and monumental task.

In this book, Shri Ratnakumar Shah presents a carefully curated collection of essays that explore the key mathematical concepts found in major Jain scriptures dating from 500 BCE to about 1000 A.D. The original mathematical content in these texts is expressed through elaborate sentences or evocative poetic stanzas in Prakrit, the linguistic predecessor of Sanskrit. Shri Shah has accomplished the formidable task of converting these ancient descriptions into contemporary mathematical forms, employing equations with numbers and symbols that are accessible and comprehensible to modern readers. His achievement not only illuminates the mathematical richness of Jain literature but also significantly aids future scholars in this emerging field of study.

PANKAJKUMAR K. SHAH holds Master of Science degrees in Mechanical and Nuclear Engineering, as well as an MBA from leading U.S. universities. He is a prominent international consultant specializing in the design of nuclear reactor vessels and other critical components of nuclear power plants.

He is also a noted author and researcher in Jain studies. Mr. Shah published one of the earliest groundbreaking books on Jain astronomy, Bridging the Cosmos - Ancient Jain Scriptures Revealed Through Modern Astronomy.

In 2020, he organized the First International Symposium on Jainism and Mathematics and co-edited its proceedings, later published in 2022 under the title Mathematics in Ancient Jain Literature.

In 2022, he also organized the first-ever symposium on the Nirvan Dating of Jain Tirthankar Mahavir Swami in Pune, India. The proceedings were published in 2024 under the title Nirvan Dating Tirthankar Swami.

RATNAKUMAR S. SHAH (b. 11 June 1937), after completing his M.A. in Applied. Mathematics from Pune University in 1960, served as Lecturer in Mathematics and Astronomy at Fergusson College, Pune. He later joined the Life Insurance Corporation of India as an Officer, from where he retired as Executive Director in 1995.

He has authored several books on Insurance, Statistics, Dynamics, Quantitative Techniques, and related subjects. After working as a consultant to private insurers until 2007 (at the age of 70), he turned his focus to the study of Jaina Mathematics. To date, he has published more than 19 research papers, either in national and international journals or presented at national and international conferences. Ten of these mathematical contributions have been selected and reproduced in this volume.

Recently, he completed a research monograph titled Mathematics of the Karma Theory of the Jainas, sponsored by Kundakunda Jñānapitha, Indore. This work is so comprehensive that it may be regarded as a textbook on the history of Jaina mathematics and is being published by the sponsors.

He has also completed editing and translating into English two Agamic works-Anuyogadvārasūtra and Jambuddiva-pannattisutta-both of which contain highly advanced mathematical concepts for their time. These works, prepared on behalf of Jain Viśva Bharati, Ladnun, Rajasthan, India, are currently in press and will be available soon. Additionally, he is editing and translating (into English) the ancient Agamic work Sura/Candapannatti, an advanced treatise on mathematics and astronomy. This project is now in its final stages and will be published shortly.