Mathematics in Sanskrit Literature © 2018 NJHSR

Home , Bijaganita, Ganita Kaumudi, Halayudha, Manava, Sridhara, Surya Siddhanta

National Journal of Hindi & Sanskrit Research

V.Ramesh Babu V.Ramesh Babu Associate Professor,

Dept of Mathematics, Rashtriya Sanskrit Vidyapeeth, I.Prologue Tirupati, Andhra Pradesh Stages of development of Mathematics in India

1.Indus valley Mathematics (2300 – 1700 B.C)

2.Mathematics in the age of Vedas (2000 – 800 B.C) 3.The age of vedangas/suthar period (800 -200 B.C)

4.Buddhist and Jaina’s schools (600 B.C – 300 A.D) 5.Preclassical age of epics and siddanthas (200 B.C – 320 A.D)

6.The classical period ( the golden age of mathematics) (320 – 750 A.D) 7.The new Jain writings upto Bhaskara II (750 – 1200 A.D) 8. Medieval Mathematics in North India (1200 – 1850 A.D)

9.The late Aryabhatiya school (Keral school) (1400 1850 A.D) 10.From the founding of the Universities to Freedom (1857 – 1947)

II. A List of Some Sanskrit Works In Mathematics

Aryabhatiya of Aryabhata 499 AD

Aryabhatiya Bhashya of Bhaskara I 629 AD Apasthamba Sulva Sutras 500 BC ca

Bijaganita of Bhaskara II 1150 AD Bakshali Manuscript 7th Century AD Br.Samhita of Varahamihira 587 AD d

BSS Baudayana Sulba Sutra 800 BC Ganita kaumudi of Narayana Pandita 1136 AD

Ganitasara Sangraha of Mahaviracharya 850 AD Ganita Tilaka of Sripati 1039 AD

Khanda Khadhyaka of Brahmagupta 628 AD Karana Paddhati of Putuman somayaji 1733 AD Katyana Sulba Sutras ca %th Century BC

Lilavati of Bhaskara II 1150 AD Laghu Bhaskariya of Bhaskara I 629 AD Maha Bhaskariya of Bhaskara I 629 AD

Mahasiddhanta of Aryabhata II 950 AD Manava Sulba Sutras 500 BC Correspondence: Arya Bhatiya Bhashya of Nilakanta 1500 AD V.Ramesh Babu Associate Professor, Pati ganita of Sridhara 750 AD Dept of Mathematics, Panchasiddhantika of Varahamihira 505 AD Rashtriya Sanskrit Vidyapeeth,

Tirupati, Andhra Pradesh Brahmasphuta Siddhata – A commentary of Pruthukasvami 850 AD Sishyadhiriddhida of Lalla 748 AD ~49~

National Journal of Hindi & Sanskrit Research

Siddhanta sekhara of Sripati 1039 AD Siddhanta Siromani of Bhaskara II 1150 AD Surya Siddhanta ? Trisatika of Sridhara 750 AD Tantra sangraha of Nilakanta 1500 AD Tantra Sangraha Vyakhya Yuktidipika of Sankara 1530 AD Vatesvara Siddhanta of Vatesvara 904 AD Yuktibhasa of Jyeshta deva ( Malayalam ) 1525 AD Ganita Sara Sangrahamu of Pavuluri Mallana 11th & 12th century AD

III. False Mathematical Eponyms for results attributable to Indian Mathematicians

S No. Indian work Western work 1. Baudhayana (BC 800) Pythagoras theorem 540 BC Bhuja-koti-karna-nyaya BSS-i-48, ASS i-4, KSS 2-7 2. Aryabhata (499 AD kuttaka solution of ax-by=±C Diophantine Equations (300 AD) Aii-32 and 33 3. Varahamihara (488 to 587 AD) Pascal triangle Blaise Pascal (1623- Losta or lostaka prastara B.S gandhayukthi adhya 1662) VS2 Meru in Halayudha’s (10th century) commentary on Pingala’s (200 BC) chandassaatra chapter 8 4. Pingalas (2nd century BC) binary system Leibliz (17th and 18th century) Germany 5. Heliocentric System of Aryabhata Copernicus – 16th century 476 – 550 A.D 1473—1543 A.D 6. Brahmagupta (628 AD Pell’s equation (1668 AD) Solution of varga prakrithi Nx2+1=y2 B.Sp.S.XVIII: 64-65 7. Brahmagupta’s formula for the area of a triangle as a Heron’s formula 1st Century AD special case of a cyclic quadrilateral with one side taken as Zero 8. Virahanka (600-800 AD) series Fubonacci (1170-1250 AD) 1,1,2,3,5,8……. Gopala and Hemachandra 10th century AD a,b,a+b, a+2b, 2a+2b 9. Mahaveera formula for Herigone’s formula GSS-VI, 218 Pierre Herigon (1634 AD)

10. Bhaskaracahrya’s (1114-1193 AD) Theorem on Rolle’s theorem (1652-1719 AD) retrograde motion 11. Nraryana Pandita (1356) method for finding for Fermat factorization method 1634 devisers of a number GK chapter XI-Vs 5 – 8

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12. Madhava of Sangama Grama (1340-1425 AD) Gregory series (1638-1675 )

13. Madhava Series for π Leibniz series (1646-1716)

14. Parameswara’s (1380-1460) SAJL Huiler’s Formula (1782 AD) Formula for the circum radius of a cyclic quadrilateral

IV. Epilogue

J .L. Wrote in his Discovery of India, “Till recently many Europeans thinkers imagined that everything that was worthwhile had its origins in Greece or Rome. Sir Henry Maine had said that except the blind forces on Nature nothing moves in this world which is not originally Greek. Our former Philosopher President Dr Sarvepalli Radhakrishnan had said, “The Europeans are apt to imagine that before the great Greek thinkers, Socrates, Plato and Aristotle, there was a crude confusion of thought, a sort of chaos without form or void. Such a view becomes only a provincialism. When we realize that systems of thought which influenced countless millions of human beings had been elaborated by people who never heard the names of Greek Thinkers. For these European scholar’s modern civilization appeared to be an outgrown colony of Hellas. The obvious Greek failings, their short comings and the unhealthy features of their civilization was rationalized and romanticized. But the American mathematician A. Seindenberg has demonstrated that the Sulba Sutras, the ancient Vedic mathematics inspired all the mathematical Sciences of the antique world from Babylonia, to Egypt and Greece. There is a great need for spreading authentic knowledge regarding various achievements of in India of the bygone times. Though studies and researches have been carried out in this direction in the past century and a half, and a great deal of material is accumulated, it is contained in rare books and journals which are hardly available. Only a small portion of this valuable stuff has reached the public. Time has come to make this body of knowledge accessible to the general public. To achieve this two things are essential. 1.Institutional arrangement devoted to the cause 2.Skilled writers to interpret the available stuff in terms of modern language in the concerned science in an authentic and reader friendly manner.

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