Journey of Indian Mathematics from Vedic Era
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ESSENCE—IJERC International | Nidhi Handa Journal (2018) for Envir| IX (1):onmental 217—221 Rehabilitation and Conservation ISSN: 0975 — 6272 IX (1): 217— 221 www.essence—journal.com Original Research Article Journey of Indian Mathematics from Vedic Era Handa, Nidhi Department of Mathematics, Gurukul Kangri Vishwavidyalya, Haridwar, Uttarakhand, India Corresponding Author: [email protected] A R T I C L E I N F O Received: 28 January 2018 | Accepted: 30 April 2018 | Published Online: 15 August 2018 DOI: 10.31786/09756272.18.9.1.127 EOI: 10.11208/essence.18.9.1.127 Article is an Open Access Publication. This work is licensed under Attribution—Non Commercial 4.0 International (https://creativecommons.org/licenses/by/4.0/) ©The Authors (2018). Publishing Rights @ MANU—ICMANU & ESSENCE—IJERC. A B S T R A C T The paper points out how initially proposed theories by European scholars of Mathematics, consider- ing algebra and geometry of Greek and / or Old—Babylonian origin came to be discarded as studies expanded to Vedic works like Shatpath Brahamana and Taittiriya Samhita. K E Y W O R D S Indian Mathematics | Vedic Era | Ancient mathematics C I T A T I O N Handa, Nidhi (2018): Journey of Indian Mathematics from Vedic Era. ESSENCE Int. J. Env. Rehab. Conserv. IX (1): 217—221. https://doi.org/10.31786/09756272.18.9.1.127 https://eoi.citefactor.org/10.11208/essence.18.9.1.127 217 ESSENCE—IJERC | Nidhi Handa (2018) | IX (1): 217—221 Introduction Vedas, the paper presents the following points: Existence of Mathematics before Christ may be referred as foundation of Mathematics. 1. The numbers 1, 2, 3, ... 9, with 9 as the largest single digit find mention in the 1. Mathematics In Vedas (8000 B. C.) 'richaas' and mantras of the Vedas; Mathematics in Indus Valley Civilization (8000—3000B.C.) 2. There is enough evidence that a method to denote 'zero' was known to Vedic seers. 2. Pingala and Panini’S (2850 B.C.) 3. The Vedas refer to what in the modern 3. Śulbasūtras (1000—500 B.C.) terminology are called 'sequences of num- 4. Jain Mathematics (500—100 B.C.) bers'; The current scholarly outlook can rightly be 4. That the idea of fractions, both unit and called scientific. Therefore contemporary in- others, has also been found clear mention tellectuals have quite some interest in the his- in Vedas. tory of mathematics and science. Theories of Origin of Mathematics in *“For some, the failure to acknowledge the Greece and Babylonia success of non—Western cultures derives not The European renaissance of 1300 – 1600 just from ignorance, but from a conspiracy.” traced roots of everything to Ionian Greece, in *Dick Teresi— Lost Discoveries, Simon & particular to sixth century BC. Following Schuster, 2002: Pp—11 these lines, WWR Hall in 1901 wrote, “The The importance of the creation of zero mark history of Mathematics cannot with certainty can never be exaggerated. This giving to airy be traced back to any school or period before nothing, not merely a local habitation and a that of Ionian Greeks.” In these early years name, a picture, a symbol, but helpful power, of European intellectual growth, contributions is the characteristic of the Hindu race, whence of India were obviously not considered. After it sprang. It is like coining the nirvana into Sanskrit studies attracted some European dynamos. No single mathematical creation scholars, this situation was changed. In 1875 has been more potent for the general on—go G. Thibaut, a Sanskrit scholar with a view to of intelligence and power. inform the learned world about Indian mathe- matics, translated a large part of G. B. Halsted: On the Foundation and Tech- ‘Sulvasutras.’ nique of Mathematics In 1877 Cantor realizing the importance of It also brings out some references of Indian Thibaut’s work, began a comparative study of mathematicians spending time in China in Greek and Indian mathematics. Initially he eighth century and using Indian mathematics concluded that Indian geometry is derived there for calendrical purposes. Further, though from Alexandrian knowledge. However, some it is universally accepted that the present 25 years later, with greater study, he conclud- number system, called Hindu Numerals' origi- ed that the Indian geometry and Greek geom- nated in India. However, there is a lot of spec- etry are related. The process of assigning ulation as when and where did the so called dates were also picked up. Later Cantor even- 'Hindu Numerals' first came to be recorded tually conceded a much earlier date to Indian and used in Indian works. Going to the very geometry. roots, presenting direct internal evidence from 218 ESSENCE—IJERC | Nidhi Handa (2018) | IX (1): 217—221 In 1928 Neugebauer, published a paper in “Out of revenge of Parshuram’s father’s which he traced that the so called Pythagoras death, Parshuram attacked 21 times (to end theorem was known well over a thousand the seed of ks,triya) on ks,triya and made five years before Pythagoras, but in 1937 made a ponds full of their blood” hazard guess of geometry being of Babyloni- After following the simple processes shown an origin. in the śloka, we come to know Seidenberg (1978) expanded the study of Ve- 1 ÑRok fu% {kf=;ka & ÑRok (doing); fu (without);[{k¼”kwU;] dic sources, including ‘Shatpath Brahmana’ zero)] f=;ka (3, 6,9) means leaving 0,3,6,9 and ‘Taittiriya Samhita’ closely comparing ‘Greek and Vedic Mathematics’ as well as 2. leUr iapd & even numbers (2,4,8). After ‘Old— Babylonian and Vedic Mathematics, writing, 5, at the end of 2,4,8, we get the concluded as follows: numbers “… geometric algebra existed in India be- 3. pØs izHkq% & By following cyclic process and fore the classical period of Greece.” mutually changing (1 4 2\ 8 5 7) 2 and 4 get the sum one by one of first three numbers “A comparison of Pythagorean and Vedic with last three numbers so that mathematics together with some chronologi- (1+8,4+5,7+2=9) cal considerations showed … [that] a com- mon source for Pythagorean and Vedic math- 4. f=% lIr ÑRo% & Apply 3 to the beginning and ematics is to be sought either in Vedic mathe- 7 to the end 3.142857 is got. matics or in an older mathematics much like In this way, we see that the above stated ślo- it. The view that Vedic mathematics is a de- ka, we get the number which led to the gen- rivative of Old—Babylonian [is] rejected.” eral value of the proportion of the circumfer- Indian Mathematicians in China ence and diameter of the circle. Another interesting study has been brought According to R. D. Singh knowledge of sci- out by Nobel Laureate Amartya Sen (The Ar- ence is imparted in secret way, though they gumentative Indian, 2005). In a chapter on knew that this would help mankind in devel- ‘China and India’, he mentions, “Several In- opment of society. dian mathematicians and astronomers held Sen further writes: “Calendrical studies, in positions in China’s scientific establishment, which Indian astronomers located in China in and an Indian scientist, Gautam Siddhartha the eighth century, … were particularly in- (Qutan Xida, in Chinese) even became the volved, made good use of the progress of president of the official Board of Astronomy trigonometry that had already occurred in In- in China in the eighth century.” dia by then (going much beyond the original {Here one story of Parshuramji} seems to Greek roots of Indian trigonometry). The refer to the knowledge of the value of PIE movement east of Indian trigonometry to (p). It also refers to the curiosity for the value China was part of a global exchange of ideas of PIE. In other words, it lets us think that that also went west around that time. Indeed there has a tradition of mutual adjustment of this was also about the time when Indian trig- diśa, ksetra and pinda. onometry was having a major impact on the Arab world (with widely used Arabic transla- SLOKA f=% lIrÑRo i`fFkoha ÑRok fu% {kf=;ka izHkq%A leUri- tions of the works of Aryabhata, Varahami- Upds pØs ”kksf.krksnku ânku~ u`iAA ¼Hkkx0 9—16—19½ hira, Brahmagupta and others) which would 219 ESSENCE—IJERC | Nidhi Handa (2018) | IX (1): 217—221 later influence European mathematics as well, 800 BC and Apastambha 600 BC. Apas- through the Arabs.” tambha improved and expanded on the rules Sen points out, “Gautam (Qutan Xida) pro- given by Baudhayana. duced the great Chinese compendium of as- Some other major names in the history of tronomy Kaiyvan Zhanjing – an eighth— Hindu Mathematics century scientific classic. He was also en- Aryabhata 1 is a major name in world history gaged in adopting a number of Indian astro- of mathematics. According to internal evi- nomical works into Chinese. For example, dence he was born in 476 and died in the year Jiuzhi li, which draws on a particular plane- 550. His Aryabhatiya is available. It provides tary calendar in India (‘Navagraha calendar’) summary of Hindu mathematics known in his is clearly based on the classical Panchsid- time covering topics on arithmetic, algebra, dhantika, produced around 550 CE by plane trigonometry, continued fractions, Varahamihira. It is mainly an algorithmic quadratic equations, sums of power series and guide to computation, estimating such things a table of sines. as the duration of eclipses based on the diam- eter of the moon and other relevant parame- Varahamihir is practically the most famous ters. The techniques involved drew on meth- astrologer that we have known. Delhi’s ad- ods that were established by Aryabhata and joining area Mehrouli is named after him.