Psycho‑Social Aspects of Jaina Mathematics

Summary

The article "Psycho‑Social Aspects of Jaina Mathematics" by S. S. Lishk and Smt. Amarjit Kaur offers an interdisciplinary examination of how the Jaina way of life influenced the development of mathematical ideas and how mathematical concepts shaped Jaina society. The authors argue that the general psychology of Jain monks—grounded in truthfulness, non‑violence and disciplined asceticism—created a conducive environment for the emergence of a sophisticated mathematical tradition. They note that Jaina canonical literature was compiled after centuries of oral transmission, reflecting a long-standing emphasis on memorisation and systematic analysis. Two important traditions of commentary, the Dhavalā and Jaya‑dhavalā, preserve these early teachings. The article surveys principal Jaina mathematical and cosmological texts such as the Sūrya‑prajñapti, Jambūdvīpa‑prajñapti and Candraprajñapti, which describe the structure of the cosmos, the dimensions of Jambūdvīpa (the central continent), and the motions of the sun and moon using numerical and geometrical models. Jaina mathematicians introduced concepts of infinity, very large numbers and permutations long before similar ideas appeared in other cultures. They used technical terminology such as karma‑pāhuda and kaṣāya‑pāhuda and developed methods for calculating time units (muhūrta) and spatial measures. The authors point to the Jaina innovation of dividing the zodiacal circle into 360 degrees, suggesting that such knowledge was unique to Jaina texts and predated similar divisions elsewhere. The article also discusses the socio‑religious implications of these mathematical endeavours: Jaina monks needed precise astronomical knowledge to determine auspicious times (tithis) for rituals, to adhere to strict rules of conduct (e.g., avoiding harm during nocturnal activities) and to develop philosophical doctrines like karma theory that require an understanding of particles (paramāṇu) and time cycles. Mathematical rigor was therefore intertwined with ethical practice. Moreover, the authors argue that the Jaina emphasis on intellectual inquiry inspired followers to establish educational institutes and research centres. They highlight the work of scholars like L. C. Jain, R. C. Gupta and S. S. Lishk in bringing Jaina mathematical heritage to modern audiences. Concluding, the article calls for the creation of a dedicated research institute for Jaina Mathematical Sciences to preserve ancient knowledge, inspire further study and demonstrate how mathematical thinking can contribute to social and spiritual development. It suggests that recognising the psycho‑social roots of Jaina mathematics helps us appreciate the broader cultural context in which mathematical ideas flourish.