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  JAINAS ROLE IN DEVELOPMENT OF SCIENCE AND MATHEMATICS IN INDIA Dr.S.Panayappan INTRODUCTION The history of science in India has not received from the academic world, the attention it deserves. In this talk ,I will make an attempt to stimulate interest in this rich field. Ancient period corresponds up to 1200 AD, Medieval from 1200 AD to 1800 AD and Modern period from 1801 AD onwards Jaina tradition is confined from 8-th century until middle of 14-th century—i.e Ancient and Medieval periods JAINAS MATHEMATICS Jainas mathematics acts as a bridge between Vedic mathematics and modern mathematics. The Jaina School of Mathematics is an approved school in the field of ancient and medieval Indian Mathematics The Jaina school of Indian Mathematics could be divided into the canonical class and exclusive class. The former demonstrates canonical thoughts including on karma and cosmos theory using mathematics. The latter provides mathematics education to the contemporary civil life. Ganita-Sar-Samgraha of the Jain Monk Mahaviracharya (850AD) is the only treatise on mathematic that is available at present. The other mathematical treatises by the early monks have been lost. Jain canonical texts A’ga and Upa’ga contains valuable information in mathematics. The knowledge of ‘Sankhyana’(i.e. science of numbers) was considered to be one of the principal accomplishments of Jain priests CONTRIBUTION TO NUMBER THEORY The Jains were the first to conceive the idea of transfinite numbers,a concept which was brought to Europe by Cantor in the late 19-th century. Nearly 2000 years before Cantor, Jains had proposed the concepts. Jain mathematicians used very big numbers in their calculations while researching on the concepts of space time and matter.They have calculated the total age of the universe as 2 to the power of 588. In Jain Upanga agama surya Prajnpathi, all the numbers were classified into three sets: enumerable,innumerable and countable. Jains were the first to discard the idea that all the infinities were the same or equal. Five different infinities are recognized in Jainas works.: infinite in one and two directions, infinite in area, infinite everywhere and infinite perpetually. In the treatment of fractions, Mahaveera seems to be the first among the Indian Mathematicians,who used the method of Least Common Multiple (LCM) to shorten the process This is called niruddha.   WORK ON LOGARITHMS The concept of logarithms on base 10 was proposed by John Napier in 1614.Jains had developed the concept of logarithms more than 8 centuries before its invention in west Acharya Shri Virasena Ji Maharaj (792-853)was a Digambara monk and a noted mathematician. He worked on logarithms. He developed a concept ardacchedo --the number of times a number could be divided by 2,effectively base 2 logarithm. He also worked with logarithm in base 3 9trakecheda) and base 4 (caturta cheda) ON PERMUTATIONS AND COMBINATIONS The early Jainas seems to have a liking for the subject of permutations and combinations. Mahavira, the founder of Jainism was himself a great mathematician .In the Bhagawati Sutra he has set forth simple problems such as finding the number of combinations that can be obtained from a given number of categories, taken one at a time, two at a time three or more at a time The Jaina Commentator Silanka has quoted three rules regarding permutations and combinations. INVENTION OF ZERO The oldest reference to zero is in a Jain work ‘Lokvibhag’ which was written by a Jain ascetic Acharya Sarvanandi. Lokvibhag is a book on Jain cosmology written in Prakit language, translated in Sanskrit ,which is available now. CONCEPT OF IMAGINARY NUMBERS Mahavira remarked that ‘a negative number is non-square in nature from which no real square root can be derived.It is a clear recognition of imaginary quantities, centuries before their formal definition ON MENSURATION The ratio of circumference of a circle to its diameter was traditionally assumed to be 3.In Surya Prajanpti, a Jain text, it is square root of 10—a better value. It was known as Jain value for a long time in India. Jai texts from 6-th BC such as Surya Pragyapti describe ellipses. They have developed formula to find the length of circular arc in terms of corresponding chord and bow Formulae were known to them for the volume of frustrum of a cone,area subtended by a circular arc together with their chords and so on. JAINAS SCIENCE Propogation of sound and scattering of light have similar explanations in modern science and Jain science.  Cloning implies changing the genetic code of an existing egg i.e the same soul continues which confirms to the fundamental Jain principle. Emotional Quotient (E.Q) is both in contrast and complementary to Intelligence Quotient (I.Q).In these days much work is done in E.Q. and this is similar to samyaktva, dealt in Jain literature. Empathy,one of the key qualities in E.Q.is the ability to sense how other people feel,which is given in the definition of “ sravakya”—meaning Jain layman. A detailed description of atomic theory and theory of chemical combination is found in the oldest surviving Jain Philosophical text Tattvarthadhigama sutra (chapter5)of Jain Thinker and Acharya Umaswaati. RESEARCH GAPS AVAILABLE 1)Investigation of how vedic mathematics influenced Jaina mathematics 2)Investigation of their ability to develop various mensuration formulae-which were known only after the invention of calculus 3)Detailed study of Jain non-mathematical works to explore the mathematical content available 4)Comparing and contrasting the Jain principles with the laws of modern science and make attempts to bridge the gaps between them BIBLIOGRAPHY 1)L.C.Jain &K.M.Meena Jain -System theory in Jaina school of Mathematics, Indian J.Hist.Sci.24(3),1989,163-180 2)Joseph ,George Ghevergese:The crest of the pea-cock—Non-European roots of Mathematics,London,Penguin books 1994 3)Mardia.K.V:The scientific foundations of Jainism,Motilal Banarsidass,New Delhi ,1990 4)Panchastikaya Sara: ”Matter in reality cannot be created or destroyed-- it has only permanent sustainability : But through its modes it secures triple qualities of permanence, appearance and disappearance 5)Shiva Kumar : A note on glimpses of Indian Mathematics, International Journal of Innovation Technology and Research 2,No1,2014

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May 2, 2019

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May 2, 2019
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