Survey of the Work done on Jain Mathematics

Author(s): Anupam Jain
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf
Catalog link: https://jainqq.org/explore/250332/1

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Survey of the Work Done on Jain Mathematics
Sh. ANUPAM JAIN
ABSTRACT - In this article the author has drawn the attention of Scholars on the history of Mathematics
towards the original source books on ancient Jain Mathematics. Attempt has been made to compile an almost upto-date list of the works done by various researchers on the subject.
The Jain literature, both religious as well as otherwise is indeed extremely vast and varied. In line with the corresponding literature of the vedic Hindus and the Buddhists, the Jainas have contributed a great deal to different branches of knowledge such as Grammar, Poetics, Koshas, Stories, Religion, Cosmology, Cosmography and indeed all the physical and social sciences known to us today. Language and Literature, Philosophy and Ethics, Fine Arts and Science, History and Culture of India inherited the rich literature of Jainism through the course of development of the original canon over the centuries.
Jain philosophy has propounded not only a unique theory of the soul and karma, but its contribution in the field of Science (Mathematics, Physics, Chemistry, Zoology, Botany, Astronomy etc.) is also very significant. The ancient Jain literature composed in Prakrit (Shorshaini & Ardhamagdhi) and Apbhransha languages contains significant material about the traditional as well as modern Mathematics. A systematic development of mathematical thought may be traced in the available Jain literature inspite of the fact that so many mathematical and conanical texts have either been lost or are still lying unexplored it.1
Early Jaina Texts Sürya prajnapti, Sūtrakritānga, Sthānānga Sūtra (Thānam), Bhagwati, Sutra (Vyākhyā Prajnapti), Jivābhigama Sutra Uttarādhyayan Sūtra, Anuyogadvara Sūtra, Jamboodvipa Prajnapati and its commentaries written by Shilänka (9th C. A. D.), Abhaideva Sūri (11th C. A. D.), Hemchandra Susi (11th C. A. D.) and Malaigiri (12th C. A. D.) contain many important rules and descriptions about eight fundamental operations, frictions, combinations and permutations, law of indices, numbers, decimal place value system etc. A lot of material about plane as well as solid geometry is also available. Tattvārtha Sutra of Umāswami (Umaswati ?) is the first authentic religious work of the Jainas composed in Sanskrit Some available commentaries, namely, tattvärtha-dhigama Bhâsya (Umaswati), Sarvärtha Siddhi (Puivapāda) Tattvärtha Rājvårtka (Akalank), Tattvärtha Shloka Vartic (Vidyanand) etc, contain many Geometrical formula and list of measurement. Concepts of Newton's first law of motion and law of conservation of energy are also available in rough form.
An idea of the un-explored Jain Mathematical Works can be had from the Author's Article on 'Some unknown Jain Mathematical Works' (Hindi) Ganita Bharti (Bulletin of Indian Soc. for History of Mathematics) 4 (1, 2) PP. 61-71 Jan-Apr.-1982. The Dates of these texts are controversial but in any way it can't be prior than 500 B.C. and later than 500 A.D.
2.
Aare fourg
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Kasävapāhuda of Gunadhara (150 B. C.), Shatakhandagama of Pushpadanta and Bhuta Bali (Ist C. A. D.) together with Mahabandha, Tilloyapannatti of Yativrashabha (2nd-5th C. A. D), Dhawala of Virasen (9th C.A.D.) Jaidhawala of Jinasen (9th C.A.D.), Gommatsāra, Triloksara & Khapanasara of Nemichandra Siddhanta Chakravarti (10-11th C.A.D.), Samyaggyan Chandrika with Artha Sandristhi Adhikars of Todarmala (17th C.A.D.) contain not only traditional mathematics, but also a detailed description of set theory, theory of transfinite and transidental numbers, theory of relativity etc. in quite a different terminology. The efforts of Prof. L. C. Jain to expose the mathematical aspect of Karma theory, which is parallel to recently developed system, theory are particularly noteworthy.1
The work of Jain mathematicians Sridhara? (750 A.D. ?), Mahavira (850 A.D.) and Simhatilak Suri (13th C.A.D.) etc. has been considered very significant in the field of Indian Mathematics. So many other mathematical texts and commen tries written by Rajaditya (11th C.A.D.), Thakkar Feru (1372 A.D.). Shrasthi Chandra, Mahimodaya, Lalchandra, Madhav Chandra, Hemrāja etc. are yet to catch the attention of research workers in this field. In my opinicn all these texts or commentaries are of much significance and may help to solve many historical problems. The details about all these manuscripts have been given by the author in another article.3
Evidently ancient Jain literature has considerable materials for the research scholars of History of Mathematics.
In the last fifty years lot of work has been done in this subject by known as well as unknown scholars. Not all this has unfortunately appeared in standard Mathematical publication or in the Journals on History of Mathematics. Major portion of this work is spread over various such magzines and souvenirs etc. which are generally not known to most of the scholars in the mathematical world. Hence the beginners in this field have to waste their valuable time and energy in collecting the information about the previous work done in this direction. In the absence of such information about the availability of relevant literature many researchers lose their interest and thus society in deprived of the knowledge gained by their predecessors. It is with this idea in mind that I have made an humble attempt to prepare a list of the works done by different workers and to present the same here for the convenience of other scholars.
The list as such has no claim for completeness. Any suggestions for fresh additions to this list would be most welcome by the author. 1. Agrawal, M.B. Lal
I. "Eratrat #ta fua 7**"
a fão To (TTT)-24-1 To 42-47 (1964) II. "fora gal strifag #far # 14 TTCIA"
TTTT facafau ant al 974-90 377, (1972) III. " fenfuata taa"
sit ta faalt tufa fa-at 177 (1979) IV. "a afu # peut s afe * a"-faalo v TT TTE STETT at foto 454-7791-7. 402-410
(1980)
1. See Jain, L.C.--Article No. XXIII in the list. 2. His religious belief is still controversial. 3. Jain, Anupam--Articles Nos. V, VI and VIII in the attached list.
आचार्यरत्न श्री देशभूषण जी महाराज मभिनन्दन अन्य

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y. faoi aaa" To TTTTT faca TF4-
F T-TO 646-662 (1982) 2. Bag, A.K. I. 'Mathematics in Ancient and Medievel India Chaukhamba Orientalia -Varanasi P. 344
(1979) 3. Bell, E.T. I. 'Development of Mathematics' Macgraw hill ----New York
1940 11. "Mahavira's Diophantine System B.C.M.S. (Calcutta) 28 pp. 121-122
(1946) 4. Boyer, C.B. I. A History of Mathematics' John Wiley & Sons-New York
1968 5. Cajori, F. 1. 'History of Mathematics' (IInd revised and enlarged) Macmillan New York-P. 1958 6.Chakravarti, I. Growth and Development of combination & Permutation in India' B.C.MS. Guru Govind (Calcutta)-24 pp. 7-88
(1932) II. 'Surds in Hindu Mathematics' Jou, of Department of Letters -Calcutta Univ. 24 pp. 9-58
(1934) 7. Das, S.R. I. Origin and Development of Hindu Numerals' I.H.O. (Poona)-3, pp. 97-120, 365.75 (1927) 8. Dikshit, i "Ta catfag" Tréfa fit for at sigara, 310- TTTTTTEET, face face S.B. Teat, TTTH ayu-30 To 147 1277, 713
1957 9. Duit, B.B. I. "On the Mahavira's Solution of Rational Traingles and Quadrilaterals' B.C.M.S. (Calcutta) 20-pp. 267-294
(1928) II. "The Jaina School of Mathematics' B.C.M.S. (Calcutta) 21-pp. 115-143
(1929) III. 'Geometry in Jain Cosmography' Quellin and Studien Zur Geschichte der Mathematic-Abtolung B Sec-1 pp. 245-254
(1930) IV. 'Mathematics of Nemichandra' The Jain Antiquary 1-II pp. 25-44
(1935) fara gara-wafar r oa" 340-3151a, a 1-7, ga 50-54 v. 'A Lost Jaina Treatise on Arthematics' The Jain Antiquary (Arrah) 2-11 pp. 38-41 (1936) VI. 'Sabda Sankhya Pranali' (Bengali) B.S.P.P.-(Bangiya Sahitya Parisad Patrika) B.S. pp. 8-30
(1930) VII. 'Aksara Samkhya Pranali (Bengali).B.S.P.P. B.S. pp. 22-50
(1936) VIII. Jain Sahitya Nama-Samkhya' (Bengali) Baogiya Sahitya Parishada Patrika (B.S.P.P.) B.S. pp. 28-39
(1937) IX. "Nama-Samkhya' (Bengali) B.S.-P.P.-B.S. pp. 7-27
(1937) X. Apkānām Vamto Gatih (Bengali) B.S.-PP.-B.S. pp. 7-30
(1937) Dutt B.B. & XI. History of Hindu Mathematics' (2 Vols) Motilal Bonarsidas-Lahore 1935-1937 Singh, A.N.
lind ed. (Combined) Asia Publishing House New Delhi-1962
प्रथम भाग का हिन्दी अनुवाद, अनु०-डा० कृपाशंकर शुक्ला, प्रकाशन ब्यूरो-उ० प्र० शासनलखनऊ
1967 XII. 'Hindu Geometry (ed. by K.S. Shukla) 1. J.H.S.-152 pp. 121-199
1980 10. Divedi, 1. "fa fr sfat" attua
1910 Sudhakar 11. "TOTT afrTort" 1889,7 Tr faut att ta ETUT-STTTT&T
1933 11. Eves,
*An Introduction to History of Mathematics' Holt, Rienholt and WinstonHarward
New York. 12. Gupta, I. Mahaviracharya on the Premeter and Area of an Ellipse M.E. (Shiwan)VIII-1 R.C. pp. 17-19
(1974) II. 'Circumference of the Jambuduipa in Jaina Cosmography' I.J.H.S.(Calcutta)-10 1 pp. 38-44
(1975) III. Mahāvirācārya's Bule for the Surface Area of a Spherical Segment-A new Interpretation Tulsi Prajna (Ladnu)-1-2 pp. 63-64
(1975) जैन प्राच्य विद्याएं
pois
1964

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(IV. 'Jaina Formula for the Area of a Circular Segment, Jain Journal (Calcutta)-XUI-3 pp. 89-94
(1979)
13. Jaggi, O.P. 14. Jain,
Anupam
15. Jain, B.C.
16. Jain, B.S.
17. Jain, G.R. 18. Jain, H.L 19. Jain, L.C
1. "Science and Technology in Medieval India Atma Ram & Sons - Delhi pp. 136-209 1977 I. “गणित के विकास में जैनाचार्यो का योगदान" (एम० फिल्० योजना विवरण का सारांश-मेरठ वि० वि०, मेरठ) गणित भारती (दिल्ली)-3 (112) पृ० 43-44
(1981) 11. 'प्राचीन भारतीय गणितज्ञ" अभिव्यक्ति (सलावा)-2 3047-51
(1981) III. महावीराचार्य व्यक्तित्व एवं कृतित्व"-जैन सन्देश (मथुरा) शोधांक-47 दिस० पृ० 258-260 (1981) IV. "ट्त्रिंशिका या ट्विशातिका" जैन सिद्धान्त भास्कर (आय)-34 (2) दिस० पृ. 31-40
(1981) v. "कतिपय अज्ञात जैन गणित ग्रंथ"-गणित भारती (दिल्ली)-4 (1, 2) पृ० 61-71
(1982) VI. "कन्नड साहित्य एवं गणित" सन्मति वाणी (इन्दौर)-11 (10) जन पृ० 8-12
(1982) VII. "जैन गणित के अध्ययन की आवश्यकता एवं उपयोगिता" सेठ सुनहरी लाल जैन अभि० ग्रंथ-पृ० 356-361
(1983) VIL. जैन गणितीय साहित्य ' तुलसी प्रज्ञा (लाडन) में प्रकाशनार्थ प्रेषित IX. "Mahäviracharya the men & the Mathematician' Accepted for Publication in Acta
Ciencia India (Meerut) 1. "गणित"_अन्तर्गत भारतीय संस्कृति के विकास में जैन तीर्थों का योगदान" अखिल विश्व जैन मिशन-अलीगंज (एटा)
(1961) 1. 'on the Ganita-Sar-Sangrah of Mahavira (850 A.D.)1 J.H.S. (Calcutta)-12-1 ___pp 17-32
1977 I. Cosmology Old and New' (2nd Revised) Bhartiya Jnanpith, New Delhi
1974 I. 'भारतीय संस्कृति में जैन धर्म का योगदान" मध्य प्रदेश शासन, साहित्य परिषद-भोपाल
1962 I. "तिलोयपण्णत्ति का गणित" जम्बुद्वीपपण्णत्ति संग्रहो के साथ प्रकाशित, जीवराज ग्रंथमाला____शोलापुर-पृ० 1-109
(1958) II. "लोकोत्तर गणित विज्ञान के शोध पथ-भिक्षु स्मृति ग्रंथ -- कलकत्ता प० 222-231
(1961) III. "गणितसारसंग्रह (महावीराचार्य कृत) विस्तृत प्रस्तावना, पाठ टिप्पणियों, परिशिष्टों सहित
[श्री एम० रंगाचार्य के अंग्रेजी संस्करण (1912) के आधार पर] संपादित एवं अनूदित हिन्दी संस्करण-जैन संस्कृति संरक्षक संघ, शोलापुर
(1963) IV. 'On the Jaina School of Mathematics' छोटे लाल स्मृति ग्रंथ-कलकत्ता अंग्रेजी विभाग पृ० 266-292
(1967) V. 'Researches on Jain Mathematics' Jnanpith Patrika-Sodha Visheshank (N. Delhi) Oct. Nov.-pp. 33-41
(1969) VI. "भारतीय गणित शास्त्र एवं जैन लोकोत्तर गणित' अनुसंधान पत्रिका-जैन विश्वभारती (लाडन) अप्रैल-जन, पृ० सं० 20-37
(1973) VII. 'Mathematical Foundation of Karma: Quantum System Theory' I Anusandhan Patrika, J.V.B. (Ladnu) Oct-Dec pp. 1-12
(1973) VIII. 'Set Theory in Jaina School of Mathematics' 1 J.H.S. (Calcutta) 8-I pp. 1-27 (1973) IX. 'Role of Mathematics in Jainology' Jou, of Birla Inst. of Arts & Music-Prachya Pratibha (Bhopal) 2-1 pp. 5.-52
(1975) X. 'Norms of Truth and non-violence for Karma Optimality'Tirthankar (Indore)-1-6 pp. 11-15
(1975)
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XI. Jaina School of Mathematics (A study in Chinese Influence and Tronsmission)'
Contribution of Jainism to Indian Culture-Motilal Bonarsidas-Varanasi pp. 206-220
(1975) XII. 'Scientific Socio Political Control and Karma System Theory' Tirthankar (Indore)-1-4 pp. 12-15
(1975) XIII. 'Zero's and Infinities of Ancient India' Tirthankar (Indore)-1-7-12 pp. 93-97, 106 (1975) XIV. 'On analytic Treatment of Transfinite Numbers in Dhavali’ Chainsukh Das Nyaytirth Smriti Granth-Jaipur, pp. 173-188
(1976) XV. 'On certain Mathematical Topics of Texts' 1.J.H.S. (Calcutta)-11-2 pp. 85-111 (1976) XVI. 'Principle of Relativity in Jaina School of Mathematics' Tulsi Prajna (Ladnu)-5 pp. 20-28
(1976) Tirthakar (Indore)-2-1 pp. 13-20, 21
(1976) XVII. The Jaina Theory of Ultimate Particles'
"जैन दर्शन एवं संस्कृति आधुनिक संदर्भ में" इन्दौर वि०वि०, इन्दौर द्वारा प्रकाशित पत्रिका में pp. 53-55(1976) XVIII. 'Distinct Features of Indian Astronomy upto Aryabhatta l' Prachya Pratibha (Bhopal)-1V-2 PP. 118-222
(1976) XIX. 'Mathematical Foundation of Karma System' Bhagwan Mahavir and his Relevence in Modern Times - Bikaner pp. 132-150
(1976) xx. "आधुनिक शोध के सन्दर्भ में जैन गणित"-सन्मति वाणी
(1976) XXI. Divergent Sequences Locating Transfinite sets in Triloksar' 1. J.H.S. (Calcutta)-12-1 pp. 59-75
(1977) XXII. "जैन गणित विज्ञान की शोध दिशायें"-महावीर जयन्ती स्मारिका-ग्वालियर-प० 281-290 (1977) XXIII. 'On the Contributions Transmissions and Influences of the Jaina School of Mathematical Sciences' Tulsi Prajna (Ladnu)-3-4 pp. 121-134
(1977) XXIV. 'Mathematical Contributions of Todarmala of Jaipur' The Jain Antiquary (Arrah) 30-1 pp. 10-122
(1977) Xxv. "जैन ज्योतिष एवं ज्योतिष शास्त्री"-मुनि द्वय अभि० ग्रंथ-जोधपुर प. 392-399
(1971) XXVI. 'Crisis in Mathematics Tirthakar (Indore)-3-1 pp. 16-18
(1977) XXVII. "पंडित परम्परा जोर जैन गणित विज्ञान" तीर्थकर (इन्दौर)-6-3 पृ० 73-78
(1978) XXVIII. "समयसार सप्तदशांगी टीका में गणितीय न्याय एवं दर्शन" श्रमण (वाराणसी) 29-9 पृ० 6-11 (1978) XXIX. "Perspective of System Theoretic Technique in Jaina School of Mathematics between 1400-1800 A.D.' 1. Jain Journal (Calcutta)-13-2 pp. 49-66
(1978) XXX. 'System Theory in Jaina School of Mathematics-I 1. J.H.S. (Calcutta) 14-1 p.29-63
(1979) XXX.
"आगमों में गणितीय सामग्री तथा उसका मूल्यांकन-तुलसी प्रज्ञा (लाडनूं ) खंड-6, अंक-9 पृ० 35-69
(1980) XXXII. "विज्ञान के परिप्रक्ष्य में जैन सिद्धान्त"-पं० बाबूलाल जैन जमादार अभि० ग्रन्थ, बड़ौत पृ० 165-169
(1981) xxxIII. "सिद्धान्त चक्रवर्ती नेमिचंद्राचार्य का गणितीय उपक्रम".भ. बाहुबली प्रतिष्ठापना सहस्राब्दि महोत्सव, महाभिषेक स्मारिका, नई दिल्ली पृ०स० 209-212
(1981) XXXIV. System Theory in Jainism and Science Paper Readin Jain Vidya Sangosthi ____Bombay 7-8 Sep.
(1982) xxxv. 'The Jaina School of Exact Science' (Five Volume) Due for Publication
XXXVI. 'The Jaina School of Exact Science' (Five volume) Due for Publication Jain, L.C & XXXVII. 'आधुनिक गणितीय शोध के सन्दर्भ में जैन गणित का पूर्वेक्षण'-तुलसी प्रज्ञा (लाड) 6 Ved. Prakash पृ० 67-78
(1976)
जैन प्राच्य विद्याएँ
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Jain, L.C.& XXXVIII. 'Contribution of Jainology to Indian Karma Structure Theory' Tulsi Prajna Jain C.K. (Ladnu) 7-5, 6, pp. 1-10
(1982) XXXIX. "जैनाचार्यों द्वारा कर्म सिद्धान्त के गणित का विकास" आ० श्रीधर्मसागरजी अभिननन्दन ग्रंथ, कलकत्ता पृ० 663-672
(1982) 20. Jain, N.C. I. "आचार्य नेमिचन्द्र एवं ज्योतिष शास्त्र" जैन सि० भा० (आरा) १०6-11
(1940) (Shashtri) II. "जैन गणित की महत्ता"-नाथूराम प्रेमी अभि० ग्रंथ-इन्दौर पृ० 713-723
(1945) III. "श्रीधराचार्य" जैन सि० भा० (आरा)14-1 पृ० 31-42
(1948) IV "भारतीय ज्योतिष का पोषक जैन ज्योतिष"-वर्णी अभि० ग्रंथ-सागर-प० 478-484
(1950) v. "ग्रीक पूर्व जैन ज्योतिष विचारधारा"-ब्र० चन्दाबाई अभि० ग्रंथ-आरा प०462-466 (1954) VI, "भारतीय ज्योतिष"-भारतीय ज्ञानपीठ-काशी प्रथम संस्करण
1958 VII. "जैन ज्योतिष साहित्य"-आचार्य भिक्षु स्मृति ग्रंथ-कलकत्ता पृ० 210-221
(1961) VIII. "आचार्यकल्प टोडरमल्ल की गणितीय उपलब्धि'"-वीरवाणी (जयपुर) टोडरमल्ल विशेषांक-मार्च पृ० 40-53
(1967) IX. “जैनाचार्यों द्वारा प्रस्तुत गणित की मौलिक उद्भावनायें"-महावीर जयन्ती स्मारिका-जयपुर पृ० 197-216
(1968) x. 'तिलोयपण्णत्ति में श्रेणी व्यवहार गणित सम्बन्धी दस सूत्रों की उत्पत्ति" जैन सि० भा. (आरा)-22-11 पृ० 42-50
(1968) 21. Jain, P.S. I. "अंक लिपि" ब्राह्मी विश्व की मूल लिपि पुस्तक-वीर निर्वाण ग्रंथ प्रकाशन समिति, इन्दौर पृ० 120-127 .
(1974) 22. Jha, G.S. I. Analytical Geometory in Ancient-Hindu Mathematics, M.E. (Shiwan) 12-Sec. ___B Bpp.25-27,38
(1978) 23. Jha, P. I. A Critical study of Brahmagupta and Mahavira and their contribution in the field of MathematicsIM.E.-12 (Shiwan) Sec. B. pp. 66-69
(1978) 24. Kapadia, I. Jain Hymns & Magic Square' 1.H.Q. (Poona) 10 pp. 148-154
(1936) H. R. II. Introduction of Ganit Tilak' Gaikwad Oriental Series-Baroda
(1937) III. History of Nagri Numerals' A.B.O.R.I. (Poona)-19 pp. 386-94
(1938,39) 25. Kaye,G.R. 'Indian Mathematics' Thakar Sprink & Co. Calcutta
1925 26. Kline, M. I. 'Development of Mathematical thoughts from Ancient to modern Time' Oxford University-Oxford
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