Prachin Jain Sahitya Me Ganitiya Shabdavali - Book Summary

Here's a comprehensive summary of the provided Jain text, "Prachin Jain Sahitya me Ganitiya Shabdavali" by Prem Suman Jain, focusing on mathematical terminology in early Jain literature:

The article, "Mathematical Terminology in Early Jain Literature" by Dr. Prem Suman Jain, highlights the significant and often overlooked contribution of Jain literature to the field of mathematics in ancient India. The author asserts that Jain texts, spanning various Indian languages, contain a rich treasury of mathematical principles and technical vocabulary that offer valuable insights into the history of Indian mathematics.

Key Contributions and Texts:

Early Mathematical Foundation: Jain texts like the Shatkhandagama and Sthananga Sutra are identified as crucial for understanding early Indian mathematical concepts.
Comprehensive Mathematical Content: Tiloypannatti is noted for its extensive content in both mathematics and geography.
Pre-Hellenistic Influence: Works such as Suryaprajnapti and Chandraprajnapti are significant as they predate Greek influence on Indian literature, making their mathematical contributions foundational and original.
Adding New Dimensions to Indian Mathematics: The author emphasizes that mathematical material found in texts like Bhagavati Sutra, Anuyogadvara Sutra, Uttaradhyayana Sutra, and Tattvartha Sutra adds new facts to the history of ancient Indian mathematics.
Mahaviracharya's Prominence: The article dedicates considerable attention to Mahaviracharya, a Jain acharya, whose work Ganitasara-Sangraha (Collection of Mathematical Essence) is described as one of the best books on arithmetic.
- LCM Rule: Mahaviracharya presented the rule for the Least Common Multiple (LCM) in the 8th century, a rule that was only introduced in Europe in the 15th century.
- Detailed Treatment of Fractions and Series: The book is praised for its detailed and extensive treatment of fractions, series, and arithmetic problems, surpassing other works in its scope.
- Mathematical Pervasiveness: Mahaviracharya held the belief that mathematics underlies all existence in the universe, famously stating: "What use is much elaborate speech? In this moving and unmoving tri-lok (universe), whatever exists, all that exists without mathematics."
Bhagvat Gita's Mathematical Usage: The text acknowledges the use of mathematics (Sankhyana) in all worldly, Vedic, and other regular activities. The Acharanga Niyukti (5.50) specifically states that every Jain acharya should study mathematics.
Mahaviracharya's Algebra: Mahaviracharya also authored a book on algebra called Trinshika, a manuscript of which is found in a Jaipur library.
Thakkar Pheru's Contribution: The Jain householder scholar Thakkar Pheru wrote Ganitasara-Kaumudi between V.S. 1372-1380 in Prakrit. Although it shares similarities with Bhaskaracharya's Lilavati, it introduces many new topics and holds significant cultural importance. It remains unpublished.
Pallilal Anantpal's "Patiganita": The householder Jain scholar Pallilal Anantpal wrote a work called Patiganita, alongside 5-6 other Jain mathematical compositions.
Shridhara's Advancements: Jain acharya Shridhara built upon Mahaviracharya's work by writing Trinshatika, Patiganita, and an algebra text (now unavailable), introducing new principles in the history of mathematics.
- Quadratic Equations: Shridhara propounded the rule for solving quadratic equations.
- Geometric Treatment of Algebra: Uniquely, Shridhara also provided a geometric treatment for algebraic topics.

Mathematical Terminology and its Significance:

Mathematics as an Independent Discipline: The mathematical terminology found in Jain works reveals that mathematics (Ganita) was considered an independent field of study, not merely a tool for astrology or geography.
"Ganitanuyoga": This importance led to the creation of a separate section in Jain literature called Ganitanuyoga. Muni Shri Kanhaiyalal 'Kamal' compiled mathematical content from all Agam scriptures under this name.
Scholarly Expertise Required: The author stresses that the correct utilization of mathematical content from Jain texts requires expertise in both mathematics and Jain philosophy.
Key Scholars: While many scholars, both monastic and lay, have contributed, Professor Lakshmi Chandra Jain is recognized as a foundational figure whose writings have introduced Western scholars to the valuable principles of Jain mathematics.

Examples of Mathematical Terms and Concepts:

The article provides a detailed list of mathematical terms found in various Jain texts, categorized by the respective sutra or text:

Suryaprajnapti: Terms related to shapes and geometrical concepts like tribhuj (triangle), samachatursra (square), panchkon (pentagon), vishanchatursra (irregular quadrilateral), samachatuskon (rectangle), and geometrical measurements.
Sthananga Sutra: Terms like Parikarma (arithmetic operation), Vyavahara (calculation), Rajjus (line segment/rope), Rashi (collection/aggregate), Kalasavarna (fraction), Yavatatavat (as much as), Varga (square), Varga Ganita (calculation of squares), and Sukshma (minute).
Bhagavati Sutra: Sankhyea (countable), Asankhyea (uncountable), Samyoga (combination/permutation), Tryasra (triangle), Chaturasra (quadrilateral), Ayata (rectangle), Vrutta (circle), Parimandala (ellipse), Pratara (plane).
Uttaradhyayana Sutra: Varga (square), Ghata (cube), Vargavarga (biquadrate, i.e., power of 4).
Anuyogadvara Sutra: Bhagavata (division), Praman (measure), Kshetra Praman (area measurement), Dravya Praman (quantity measurement).
Algebraic Terms (powers): Ghata (cube), Ghata Tryasra (tetrahedron), Ghata Chatusra (cube), Ghatayata (cuboid), Ghatavritta (cylinder), Ghataparimandala (cone), Valayavritta (ring/torus), Valayatyasra (triangular ring), Valayachatusra (square ring). Also, Ghanavarga (power of 6) and Ghanavargavarga (power of 12).
Measurement Terms: Rasaman (taste measurement), Suchiyangula (finger measurement), Pratarangula (area finger measurement).
Time and Quantity: Kala Praman (time measurement), Bhava Praman (state measurement), Mana (measure), Unmana (customary measure), Avamana (linear measure), Ganima (numerical measure), Pratiman (standard measure), Dhanyaman (grain measure).
Tattvartha Sutra: Vrutta Parikshepa (circumference of a circle), Jiva (chord), Ishu (arrow/sagitta), Vishkambha (diameter), Dhanukashtha (bow/arc).
Jambudvipasamaas: Unnata (elevation), Ekeekaran (unification), Karana Sutra (formula for calculation), Guna (multiplication), Gunottara (geometric progression).

Origin of Mathematical Terms:

The article argues that many terms related to geometry and algebra, such as kona (angle), pati (board/slate), shreni (series), and jiva (chord), likely entered Sanskrit from Prakrit Jain texts.
The word Jiva is identified as originating in Prakrit Jain texts and later evolving into Jya in Sanskrit, eventually traveling to Arabia and then to Europe.
The term kona (angle) is presented as a native Indian word, challenging the theory that it originated from the Greek word "gonia." The author suggests the opposite might be true, with the term influencing Greek.
The term Ayata (rectangle) is found in its current mathematical sense in texts like Bhagavati Sutra and Anuyogadvara Sutra.

Mahaviracharya's Vocabulary:

The article highlights that most modern numerical terms are derived from Ganitasara-Sangraha, with Mahaviracharya using nearly all modern numerical terms except for "neel" (blue).
Specific terms from Ganitasara-Sangraha include Sankalita (sum), Ghanangula (cubic finger), Pratham Varga (first square), Dwitiya Varga (second square), Tritiya Varga (third square), Pancham Varga (fifth square), Pratham Vargamool (first square root), etc., Vriddhayuttar (increasing), heenottar (decreasing), nimna (lower/concave), ardhavritta (semicircle), bahhu (radius), bhedgunan (fractional multiplication), vishkambha (diameter), vyasardha (radius), niruddha (restricted), prushtha (surface), prachaya (accumulation/summation), masikavriddhi (monthly interest), mishradhan (mixed principal and interest), ghanivrutta (cylindrical volume), samavritta (regular polygon), chaya (combination), and shatavriddhi (percentage).

Shridhara's Lexicon:

Shridhara also contributed specific terms such as chaya (combination), sankalita (sum), sansthanak (arrangement), aaya (profit), vyaya (loss), sama (even), and vishama (odd).

Cultural and Linguistic Insights:

Problem Formulation: Jain mathematical problems are noted for their philosophical influence, focusing on elements like lotuses, bees, lakes, and charitable donations, rather than potentially problematic themes like the sale of women or animals found in other ancient texts. An example of a problem involving bees and lotuses from Ganita-Tilaka is provided.
Linguistic Evolution of Terms: The article emphasizes the importance of linguistic study of mathematical terminology, tracing the journey of words over millennia. The example of "Oanama Si Dham" evolving from "Om Namah Siddham" highlights this.
Word Origins and Meanings: The etymology of words like "Vanara" (monkey) is explored, suggesting "Va" means similar and "Nara" means human, implying a creature resembling humans. The agricultural term "Karis" in Prakrit becoming "Arisi" in Tamil (meaning rice) and then "Rice" in English due to trade is also presented.
Evolution of "Byaj" (Interest): The transformation of the word for interest is traced from "Kusid" to "Vriddhi," and then to "Byaj" in Sanskrit, which originally meant trickery, eventually settling on the modern meaning of interest, particularly in Gujarat.
The Lotus Symbol: The frequent use of words related to lotuses in Jain mathematical texts suggests a deep connection between lotus symbolism and Jain philosophy.
Reinterpretation of Terms: Jain texts offer new interpretations of mathematical terms, aiding in understanding their specialized meanings. The definition of "Rajjus" in Ratna Sankaya is given as the distance covered by a 1000-bhar iron ball thrown by a powerful deity in 6 months, 6 days, 6 pahars, and 6 ghadis.

Conclusion:

The author concludes by advocating for the collection and comparative study of the vast mathematical terminology found in Jain literature with modern mathematics. This endeavor, the author suggests, will not only illuminate the contributions of Jain acharyas but also shed new light on India's cultural history, highlighting the interconnectedness of mathematics, language, and society.