On Mathematical Contents Of Jaina Prakrit Texts

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This paper, a brief survey of the mathematical content within Jaina Prakrit texts, highlights the profound and often overlooked mathematical achievements of the Jaina tradition, particularly the Digambara Jaina School. The author, L.C. Jain, emphasizes that these texts offer a rich source of mathematical knowledge that can be foundational for understanding the evolution of scientific thought.

Key Arguments and Themes:

• Jainism's Mathematical Prowess: The paper argues that Jaina scholars made significant contributions to mathematics, particularly in arithmetic, algebra, and geometry, often tinged with philosophical and cosmological underpinnings. This is likened to the reverence for Greek logical systems by Albert Einstein.
• Prakrit Texts as Mathematical Repositories: The Prakrit texts, especially those within the Karananuyoga (Cosmology) and Dravyanuyoga (Metaphysics), are presented as containing mathematical significance. The Karnataka Vritti of Gommatasara is cited as an example of sophisticated mathematical details linked to the Jaina Karma philosophy.
• Symbolism and Algebra: The paper points out the peculiar use of mathematical manipulation through symbols in the Digambara Jaina School, originating around the period of Kundkundacharya. This symbolic approach is seen as a precursor to modern algebraic notation.
• Historical Context and Chronology: The paper places Jaina mathematical activity within historical periods, particularly around the Christian era and the period of Mahaviracharya and Sridharacharya. It acknowledges controversies regarding chronology but emphasizes the existence of revolutionary mathematical talent.
• Unification in Jaina Mathematical Theory: The paper suggests that the Jaina School, through its mathematical theory of karma, attempted to provide a unified theory for biological phenomena, akin to modern physics' pursuit of a "Theory of Everything." This unification is achieved by depicting several processes through single manipulations.
• Computerization Potential: A significant focus is placed on the potential for computerizing the vast mathematical data found in these texts. The author suggests that terms related to finite and transfinite cardinals, ordinals, and sequences (like those in Trilokasara) can be coded into high-level computer languages (Fortran, Mathematica, C++).
• Mathematical Concepts Identified: The paper lists numerous mathematical terms from Jaina Prakrit texts, many of which are marked with asterisks to denote their calculable measure. These include:
  • Number Systems: Finite and transfinite cardinals and ordinals, place value system, the use of zero.
  • Operations: The eight parikarmas (operations) like addition, subtraction, square roots, cube roots, etc., which dealt with both finite and transfinite quantities.
  • Set Theory Concepts: Various types of sets (rasis), sequences (dharas), minimum and maximum values, domains and ranges.
  • Geometry and Trigonometry: Concepts like trikona-yantra (triangular matrix) for variations in mass, configurations, energy levels, and lifetimes of karma particles.
  • Measures and Units: Terms like salaka (counting rod), Muhurta, Samaya, Pradesa, Varga, Vargana, Rajju, Yojana, etc.
  • Algebraic Concepts: Yavat-tavat (variables), Addha, Uddhara, Vyavahara.
• Notable Figures and Texts: The paper mentions key figures like Mahaviracharya (author of Ganitasara Samgraha) and Kundkundacharya, and seminal texts such as Gommatasara, Labdhisara, Trilokasara, Suryaprajnapti, Tiloyapannatti, Satkhandagama, and Kasayaphuda.
• Call for Scholarship: The author advocates for a concerted effort by scholars of Jainism and Prakrit to delve into these texts, translate them, and elucidate their historical and theoretical significance. There's a critique of the mere republication of already published works, urging a focus on translating unpublished scientific works.
• Foreign Scholarly Interest: The paper acknowledges the contributions of foreign scholars in bringing attention to these Jaina mathematical traditions but stresses the need for self-reliance in present times.

In essence, the paper by L.C. Jain serves as a compelling argument for recognizing the Jaina tradition as a vital contributor to the history of mathematics. It underscores the complexity, sophistication, and the unique philosophical integration of mathematical concepts within Jaina Prakrit texts, while also highlighting their potential relevance for modern computational approaches.