Survey Of The Work Done On Jain Mathematics

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The article "Survey of the Work Done on Jain Mathematics" by Anupam Jain aims to highlight the significant contributions of ancient Jain literature to the field of mathematics and to compile an up-to-date list of research conducted on the subject. The author emphasizes that Jain literature, encompassing religious and secular texts, is vast and has made substantial contributions to various branches of knowledge, including mathematics.

Key Points and Findings:

• Richness of Jain Mathematical Literature: Jain philosophy has not only contributed to spiritual concepts but also to various scientific fields like mathematics, physics, chemistry, zoology, botany, and astronomy. Ancient Jain texts, written in Prakrit and Apabhramsha languages, contain valuable material on traditional and modern mathematics, despite some texts being lost or unexplored.
• Early Jain Texts and Their Mathematical Content:
  • Early texts like Sūryaprajñapti, Sūtrākṛtāṅga, Sthānāṅga Sūtra, Bhagvatī Sūtra, Jivābhigama Sūtra, Uttarādhyayana Sūtra, Anuyogadvāra Sūtra, and Jambūdvīpa Prajñapati (along with commentaries by Shīlāṅka, Abhēdeva Sūri, Hēmacandra Sūri, and Malaigiri) contain significant information on:
    • Eight fundamental operations.
    • Fractions.
    • Combinations and permutations.
    • Laws of indices.
    • Number systems.
    • Decimal place value system.
    • Plane and solid geometry.
  • Tattvārtha Sūtra by Umāswami (or Umaswati) in Sanskrit is noted as an important religious work. Its commentaries also reveal geometrical formulas, measurement lists, and rudimentary concepts of Newton's first law of motion and the law of conservation of energy.
• Later Jain Mathematical Works: Texts like Kaṣāyapāhuda by Guṇadhara, Śatakaṅḍāgama by Puṣpadanta and Bhūtabali, Mahābandha, Tilloyapaṇṇatti by Yativṛṣabha, Dhavalā and Jayadhavalā by Vīrasēna, Gommasāra, Trilōkasāra, and Khaṇḍasāra by Nēmicandra Siddhānta Chakravarti, and works by Todarmal contain discussions on:
  • Traditional mathematics.
  • Set theory.
  • Theory of transfinite and transcendental numbers.
  • Theory of relativity (though using different terminology).
  • The work of Professor L.C. Jain in relating the Karma theory to modern system theory is specifically highlighted.
• Significant Jain Mathematicians and Their Contributions: The article mentions the significant work of Jain mathematicians like Shrīdhara (circa 750 A.D.), Mahāvīra (circa 850 A.D.), and Simhatilaka Sūri (13th century A.D.) in the broader context of Indian Mathematics. It also points to many other lesser-known mathematical texts and commentaries by scholars like Rājāditya, Ṭhakkara Pherū, Shraṣṭhi Chandra, Mahāmodaśaya, Lalcandra, and Hemarāja, which require further research.
• Need for a Comprehensive Survey: The author notes that a substantial amount of research on Jain mathematics has been conducted over the past fifty years by both known and unknown scholars. However, much of this work has not been published in standard mathematical journals or history of mathematics publications, being spread across various magazines and souvenirs. This makes it difficult for new researchers to access and build upon existing knowledge, leading to wasted time and effort.
• Purpose of the Article: The article is an "humble attempt" to create a list of works done by various researchers for the convenience of scholars, aiming to address the fragmentation of knowledge in this field.
• Disclaimer: The provided list is not claimed to be exhaustive, and the author welcomes suggestions for additions.

In essence, Anupam Jain's "Survey of the Work Done on Jain Mathematics" serves as a foundational document, calling attention to the rich but often scattered body of Jain mathematical literature and research. It aims to guide future scholars by providing a curated bibliography and underscoring the historical importance of Jain contributions to mathematics.