The cauldron of history is stirred by the movement of people. Like leaves on some invisible wind of desire, adventurers and explorers have pollinated foreign cultures with ideas across millennia. It seems astonishing then, that the peacock of Indian mathematics remained unmolested by Greek geometry for 2,000 years.

The scholar TA Sarasvati Amma blamed this on the brahminical fixation with religious and social purpose, “...this leaning towards utilitarianism has had unfortunate results. The nonchalance with which the splendid achievements of Greek geometry were ignored, while the pseudo-science of Greek and Babylonian astrology was received with open hands, is perhaps the worst of these. It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.”

Fritz Staal even demarcates the main philosophical difference between Indian and Greek approaches to mathematics, saying — “The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry. Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.”

To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

So on one hand we have conic sections, the trajectories in which a lot of celestial and earthbound matter moved, and on the other we have the geometry of solids, which explained the structure of matter itself. Without these two pillars of classical physics, movement and matter, the Indian mathematicians could not possibly have triggered a scientific revolution; and as we know — they certainly didn’t. That these ideas remained undiscovered by Indian geometers is surprising; but not so much as the fact that early Greek works treating this subject never even reached India until late into the British Raj.

Another beguiling mystery is the astronomer-king of Jaipur, Maharaja Sawai Jaisingh II, who built the monumental solar observatory in the early 18th century. “Jai Singh’s career has been described as an enigma,” writes Virendra Nath Sharma, “... inspite of his close contacts with Europeans, Jai Singh’s endeavours reflect little or no influence of the astronomy of contemporary Europe. His instruments do not exploit refinements such as the telescopic sight, the micrometer, or the vernier. On the theoretical side, Jai Singh seems unaware of Kepler and Newton. A question is often raised: why did Jai Singh, an enlightened scholar, a man far ahead of his time, remain ignorant of or ignore the neo-astronomy of Europe, and instead attempt ‘to revive the spirit of Ulugh Beg’ at a time that seems, in retrospect — a century too late?”

Raymond Mercier of Cambridge further adds that, “In the Mughal period, for example, the work of Ulugh Beg of Samarkand was well-known, and parts of it (mainly the trigonometrical and geographical tables) were included in the Zîj of Jai Singh. The tables of sun, moon and planets, however, were taken over unaltered from Philippe de La Hire. By this time European astronomy had undergone revolutionary developments at the hands of Copernicus, Galileo, Kepler, Halley, and of course Newton. All of that was entirely unknown not only in Mughal India but in the rest of the Islamic world. The introduction of de La Hire’s tables alone proved to be of little consequence in the development of Mughal astronomy.”

One might even say that Jai Singh was as much of a historian as futurist or even mystic, and he never meant the instruments to have scientific value. However, because the next name in Indian science did not appear until 150 years later (in Jagadish Chandra Bose), he had a moral obligation to the transfer of knowledge from Europe that he failed to accomplish, with tragic consequences that resonate to this day.

( Rohit Gupta explores the history of science as Compasswallah; follow him on twitter >@fadesingh )

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