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Cultural Exchanges: India's Impact on European Mathematics, Science, and Politics

Explore the practical applications of Indian mathematics, science, and socio-political ideas in Europe, highlighting the influence of Indian inventions like zero, algebra, and astronomy on European advancements. Discover the cultural exchanges that shaped European civilization through Islamic, Byzantine, and Indian influences. Learn about the contributions of figures like Amir Khusro and Bhaskara, and the evolution of mathematical traditions from ancient Mesopotamia to the Kerala School. Delve into the political and social implications of religious toleration and racial divisions in Europe, as influenced by Indian and Chinese perspectives on governance. This in-depth analysis reveals the interconnected histories of India and Europe, shedding light on the transformative impact of cross-cultural interactions.

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Cultural Exchanges: India's Impact on European Mathematics, Science, and Politics

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  1. India in the Making of Europe

  2. Focus on the Practical • Not on Spiritual • Nor on straight exploitation and concentration of Wealth in Britain • But on the Application in Europe of Indian Mathematics, Science, technology and Socio-Political Ideas.

  3. Geographical Definitions of India and Europe • India Easy • Europe More Difficult

  4. ‘Europe’ as Cultural Entity • Created by Islam. • Byzantium and Western Europe Two largest fragments • Fancy Name For Christendom

  5. Three Gifts • Amir Khusro • Chess • Panchatantra (Fables) • (Arabic)Numbers

  6. Mathematics • Greek Disaster • Mesopotamian and Egyptian superior numbers, possibility of fractions and irrationals. • Platonic (Euclidian) geometry semi-religious, hostility to empiricism. • Cult of “Proof” axioms, deduction. • Indian drew on Greek but also on Mesopotamian “position.”

  7. Indian (Arabic) Numbers • Indian invention of zero • Al Khwarizim,780-850 Algebra • Egypto-Greek Geometry, • Arabic Algebra • Aral Sea, Uzbekistan • Fibonacci • Christian Resistance to “Infidel” numbers

  8. Indian Astronomy, Trigonometry • Ptolemy 2nd Century ? • Aryabhatta 3rd Century • Bhaskara (I) 6th Century • Origin of “sine” • Sanskrit Jya-ardha (Chord half) • Jya Arabic jiba/jaib “bay” Latin sinus

  9. Indian Mathematical Tradition • Bhaskara II 12th Century • Decline After Muslim Conquest • Kerala School • Madhava • Infinite Series • Series of Inverse tangent, • Power series of sine and cosine • Suspicion of “proof” • Diffusion, Independent invention • Complexity, Arbitrary nature,

  10. Transmission from Cochin to Rome • Jesuit College in Cochin 1552 • Sanskrit, Malayalam • Christopher Clavius 1537-1610 • Reformed mathematics • Problems with Calendar Reform • Navigation Vasco da Gama • Mercator • Matteo Ricci 1552-1610

  11. European mathematical breakthroughs of 17th century • Descartes, Co-ordinate geometry • Fermat, Diophantos • Infinite Series Bhaskara • Calculus, Newton, Leibniz

  12. Technology 12

  13. Sun Kings • Akbar, (1542-1605) • Mogul • Louis XIV (1638-1715) • Cardinal Mazarin 1602-1661

  14. Politics 2 Caste and Race • Vrna Colour • François Bernier, John Locke • “New Division of the Earth by the different species or races that inhabit it” • 1684 • Code Noir 1685

  15. Politics 3 Religious Toleration • François Bernier, John Locke • A Letter Concerning Toleration 1689 • Pierre Bayle • India/China

  16. Politics 3 Religious Toleration • François Bernier • John Locke • Pierre Bayle

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