Jain Ganit Parampara Aur Sahitya

Here's a comprehensive summary of the Jain text "Jain Ganit Parampara aur Sahitya" by Savitri Bhatnagar, based on the provided pages:

The book "Jain Ganit Parampara aur Sahitya" (Jain Mathematical Tradition and Literature) by Vaidya Savitri Devi Bhatnagar highlights the significant and unforgettable contributions of Jain scholars to mathematics and astronomy. It emphasizes the inherent connection between these two disciplines in ancient Indian texts.

Early Mentions and Foundations:

• Samavāyāṅgasūtra and Aupapātikāsūtra list mathematics among the 72 arts (kalās).
• There's a mention of the first Tirthankara educating his daughter Sundari in mathematics.
• The art of "liking" (lipi) includes knowledge of scripts, with "ankalipi" (numerals like 1, 2) and "gaṇitalipi" (symbols for addition, subtraction, multiplication, division) being part of 18 types of scripts.
• Gaṇitānuyoga is one of the four types of anuyogas (categories of Jain literature), which includes the texts Sūryaprajñapti and Candraprājñapti.
• Mathematics is also referred to as "saṅkhyāna." The Sthānāṅgasūtra (10/747) enumerates ten types of saṅkhyāna (mathematics): Parikarma, Vyavahāra, Rajju (Geometry), Kalāsavaṇṇa (Kalāsarvarna), Jāvaṁ, Tāvaṁ, Varga (Square), Dhana (Cube), Vargāvaraga, and Vikalpa.
• The Vyākhyāprajñapti (2/1) and Uttarādhyayanasūtra (25/7, 36) list "saṅkhyāna" (mathematics) and "joisa" (astronomy) among the fourteen types of vidyāsthānas (fields of knowledge).
• Lord Mahavir himself was proficient in mathematics and astronomy, as mentioned in the Kalpasūtra (1/10).
• In the Śvetāmbara tradition, the Upāṅga texts Sūryaprajñapti and Candraprājñapti describe mathematics in relation to the movements of the sun, moon, constellations, and stars.
• In the Digambara tradition, the commentary on Ācārya Dharasena's Paṭṭāgama by Ācārya Vīrasena (approx. 660 CE) mentions "Parikarma" in its mathematical discourse.
• "Parikarma" is also listed as one of the five divisions of the twelfth Anga, Dṛṣṭivāda. It encompassed scriptural knowledge and mathematics. The five divisions of Parikarma were Sūryaprajñapti, Candraprājñapti, Jambuprājñapti, Dvīpasāgara-prājñapti, and Vyākhyā-prājñapti. The first four contain mathematical sutras.
• Digambara literature is categorized into Angapraviṣṭa (12 Angas) and Angabāhya. Within this framework, literature is further divided into four anuyogas: Prathamānuyoga (epics, biographies), Karaṇānuyoga (mathematics and astronomy), Caraṇānuyoga (conduct rules), and Dravyanuyoga (philosophy, soul, matter, karma, logic). Karaṇānuyoga texts describe the geography of the universe (lower, middle, and upper worlds, islands, oceans, mountains, rivers) using mathematical principles and illustrate the evolution of mathematical concepts.

Key Later Works and Authors:

The text then introduces prominent mathematicians and their works from later periods:

• Tiloyapaṇṇatti (6th Century CE) by Yativṛṣabha: Considered the oldest text presenting trilo-kosmology (description of the three worlds). Written in Prakrit gāthās with some Prakrit prose, it contains 18,000 ślokas and 5677 gāthās, rich with numerical references. Its main sections describe the different worlds and their inhabitants. It's estimated to have been composed between 500-800 CE, likely in the 6th century.
• Gaṇitasāra-saṅgraha (around 850 CE) by Mahāvirācārya: A valuable work by this Digambara Jain scholar from South India, who was patronized by the Rashtrakuta king Amoghavarsha. The book begins with salutations to Lord Mahavir and Jinen-dra (as the light of mathematics) and includes six verses praising King Amoghavarsha. The text highlights Amoghavarsha's spiritual inclinations, his conquest of inner enemies (lust, anger, etc.), and his attainment of liberation. Mahavirācārya states that the origin of mathematics comes from the teachings of the Tirthankaras. The work emphasizes the omnipresence of mathematics in all aspects of life, from mundane activities to Vedic rituals, arts, sciences, and even astronomical calculations. It mentions numbers up to 24 kinds (e.g., eka, daśa, śata, sahasra, lakṣa, koṭi, arbud, nyarbud, kharva, mahākharva, padma, mahāpadma, kṣoṇī, mahākṣoṇī, śaṅkha, mahāśaṅkha, kṣiti, mahākṣiti, kṣobha, mahākṣobha). It uses special words for numbers and describes eight types of operations (addition, subtraction, multiplication, division, square, square root, cube, cube root), including concepts of zero and imaginary numbers. It also presents original methods for division of fractions and the invention of the least common multiple. The book contains principles of geometry and algebra, specific methods for trigonometry, and clarifies equations with practical examples. Its techniques for solving indeterminate equations (samakuttikaraṇa, viṣamakuttikaraṇa, miśrakuttikaraṇa) are noteworthy. This work is considered more extensive than Bhaskaracharya's Lilavati. Mahavirācārya also utilized Śrīdhara's Śatika. The book is highly regarded in South India and has Sanskrit commentaries by Varadarāja and others, with Telugu and Kannada translations and commentaries.
• Ṣaṭtriṁśikā (around 850 CE) by Mahāvirācārya: A shorter work by Mahavirācārya focusing on algebraic practices.
• Other Works of Mahavirācārya: Vyavahāraganita, Kṣetraganita, Vyavahāraratna, Jaina-gaṇita-sūtra-ṭīkodāharaṇa, and Lilāvatī (comprising 1177, i.e., 1120 CE). These are all in Kannada and attributed to the poet-scholar Rājāditya, who was the chief court pandit of King Viṣṇuvardhana around 1120 CE. He is considered the first scholar to write mathematical treatises in Kannada.
• Pāṭīganita (1204 CE) by Anantapāla: A Jain householder scholar who also composed the epic Nemicarita. His brother Dhanapāla created Tilakamañjarīkathāsāra in 1261 VS.
• Koṣṭhaka-cintāmaṇi (13th Century CE) by Śīlasiṁhasūri: A Jain Ācārya, this work in Prakrit, consisting of 150 verses, deals with magic squares, where numbers arranged in grids add up to the same sum from all sides, and includes various mantras. It also has a Sanskrit commentary.
• Gaṇitasāṅgraha by Yatācārya: An ancient Jain monk.
• Kṣetra Tichandra: Mentioned in Jinaratnakośa.
• Iṣṭapañcaviṁśatikā by Muni Teja Siṁha: A short work of 26 verses on mathematics by a monk of the Lonkāgaccha.
• Gaṇitasāra-ṭīkā by Siddhasūri: A commentary on Śrīdhara's Gaṇitasāra by a Muni of the Upakeśagaccha.
• Gaṇitasāra-vṛtti (1273 CE) by Saṁhatilakasūri: A scholar of astronomy and mathematics, whose guru was Vibudhacandra sūri. This commentary on Śrīpati's Gaṇitasāra (1330 VS) utilizes Lilāvatī and Triśatikā. He also wrote Bhuvanadīpakavṛtti on astronomy and other works.
• Siddha Bhū-paddhati (Unknown Author): An ancient treatise on practical geometry. Ācārya Vīrasena wrote a commentary on it. Vīrasena (born 765 VS, died 880 VS) was a disciple of Ānanda, guru of Jinasenācārya, and great-guru of Guṇabhadra. His commentary on the Digambara Āgama text Ṣaṭkhaṇḍāgama (Karma Prābhṛta) called Dhavalā (written in 873 VS) contains significant mathematical details. He also began a commentary on Kasāya-pāhuḍ called Jayadhavalā, but died before completing it.
• Gaṇita Sūtra (Unknown Author): A work by a Digambara Jain muni, with a manuscript in the Jain Siddhanta Bhavan, Arrah.
• Yantrarāja (1270 CE) by Mahendrasūri: A useful work on Brahmavidyā (though this seems to be a misprint and likely relates to mechanical devices or geometry).
• Gaṇitasārakāumudī (Early 14th Century CE) by Ṭhakkura Pherū: A Jain śrāvaka from Rajasthan, born into the Dhaddha clan of the Śrīmāl family. This work, composed between 1372-1380 VS, is unpublished. Ṭhakkura Pherū was the treasurer to Sultan Alauddin Khilji of Delhi. The work, in Prakrit, is based on Bhaskaracharya's Lilāvatī and Mahavirācārya's Gaṇitasāra-saṅgraha. It follows a similar subject division to Lilāvatī and includes diagrams for the Kṣetra Vyavahāra prakaraṇa, introducing new terms. His other works include Vāstusāra, Jyotiṣsāra, Ratnaparīkṣā, Dravyaparīkṣā (numismatics), Bhūgarbhaprakāśa, Dhātūtpatti, and Yugapradhāna Caupaī.
• Lilāvatīgaṇita (1682 CE) by Kavi Lālachanda: A resident of Bikaner, whose initiated name was Labhavardhana. This work was composed in Hindi verses in 1682 CE. He also wrote Aṅkaprasāra and works on astronomy like Svarodayabhāṣā and Śakuna Dīpikā Caupaī.
• Aṅkaprastāra (1704 CE) by Kavi Lālachanda: As mentioned above.
• Aicavaḍi: A mathematical text in Tamil language, a Jain work with significant usage in business practices.

The text concludes by noting that apart from the mentioned works, there are other mathematical treatises, many of which are primarily focused on mathematical astronomy. It reiterates that in ancient Indian tradition, mathematics was extensively used for understanding the structure of the three worlds, interpreting astronomical principles, and calculating the apportionment and results of karma. Mathematics also found extensive application in architecture (Vāstuśāstra), sculpture (Śilpaśāstra), Ayurveda, and other disciplines.