The Mathematical Marvel that was India

BHAIYYA JOSHI, Feb 19, 2004

THE ORIGIN OF MATHEMATICS by V. Lakshmikantham and S. Leela. University Press of America, Inc., Lanham, MD. Hardcover. 92 pages. www.univpress.com.

Long before the Egyptians, the Greeks, the Mayans, and the Sumerians began civiliz-ing their worlds, mathematics had flourished in India. Does this thesis seem incredible? No, this is not a rhetorical proclamation of some overzealous Indian chauvinists. Two India-born American university professors, V. Lakshmikantham and S. Leela, have documented extensive new data on ancient Indian mathematics and on the bankruptcy of the theory of Aryan invasion of India from the northern-central plains in Asia.

Along with their own meticulous research of original Sanskrit texts and related vernacular literature, the authors draw upon the works of a few European scholars. With the publication of this amazing monograph on Indian mathematics, the cloud of ignorance and deliberate misrepresentation of the many achievements in ancient India is beginning to lift. The authors remind us that the history taught even in Indian schools, colleges, and universities, is still filled with distortions that originated with the founding of the Indian Historical Society (IHS) in the late 18th-century Calcutta, overwhelmed by the prevailing colonial mentality.

These fabrications, passed on as the modern historiography for India, were officially inaugurated with the willful mix-up of Chandragupta Maurya (reigned 1534–1500 B.C.) and Chandragupta (327–320 B.C.) of the Gupta dynasty, by making the former a coeval of Alexander the Great, and by erasing the latter’s reference altogether. Thanks to the inventive and resourceful William Jones of the IHS, the entire chronology of events was summarily shortened by more than 1,200 years. Consequently, the times of ancient astronomers and mathematicians had to be moved into the Christian era. Another ambitious and influential Indologist, Max Mueller, concocted the age of the Rig Veda to be 1200 B.C., with the stipulation it was written by nomadic Aryans (riding on horseback, presumably with a mobile library). Actually, the Rig Veda was compiled well before 3000 B.C. Contrary to popular belief, Gautam Buddha lived during 1887–1807 B.C., and the short but remarkable life’s mission of Adi Shankaracharya was accomplished between 509 and 477 B.C. The first known mathematician and astronomer from India, Aryabhatta, was born in 2765 B.C., and the Sulvasutras, heralding the discipline of geometric algebra, were completed before his birth. But in the occidental “scholarship,” Aryabhatta’s year of birth was changed to 476 C.E. with the misreading of his epoch-making Aryabhatteeum. These were not accidental errors, but were the result of a carefully planned alteration of manuscript copies. Notice that the four Vedas preceded the Sulvasutras. Note also none of the Vedangas, the Upangas, the Brahmanas, the Aranyakas, and the Upanishads could possibly have been written later than the second millennium B.C. So much for the objectivity claimed by and attributed to a few Western historians, which has been mindlessly emulated and replicated by a majority of Indian academicians even after the British had ceased to be the rulers of India.

Lakshmikantham and Leela go beyond merely complaining about the “Eurocentric historical indifference” toward the Indian documented treasures. For example, we are told the Gregory-Leibniz series for p/4 was first discovered by Nilkanta and was clearly stated in his Tantra Sangraha (1500 C.E.). The so-called Pythagoras’s Theorem (sixth century B.C.) and its converse was known to the Indian sages of the third millennium B.C. The general principle of trigonometric functions was enunciated in the Surya Siddhanta, preceding even the Sulvasutras period. Brahmagupta (30 B.C.) solved the second order indeterminate equation Nx2 + 1 = y2, and foresaw Newton’s Law of Gravitation. The authors also demonstrate that Bhaskara II (486 C.E.) had the expertise in the area that was re-invented and, of course, systematized as Differential Calculus by Newton and Leibniz in the late 17th century. The Greeks got their plane geometry from India and their language was derived from Sanskrit. Incidentally, the Greeks “themselves had supposed or conjectured, that they had received their intellectual capital, especially in geometry” either from China or from India.

Naturally, the obvious conclusion one reaches is that the beginnings of world culture, as far as astronomy and mathematics are concerned, were not around the Euphrates and the Tigris rivers, but in the Sapta Sindhu of the Indus valley. This is a fact in Sanskrit; it may be fiction in English.

In modern times, it’s not fashionable to pay tributes to the old country while enjoying the riches of the (adopted) new country. But it should be recorded that the universities of Nagarjuna, Nalanda, Takshasila, Tamraparni, Vallabhi, and Vikramasila were internationally reputed and had gracefully functioned for long, but eventually perished hundreds of years before Bologna, Oxford, Paris, and Sorbonne had their days. And when we say “perished,” let it be clear that they were made to perish. Because they were known to have allowed idolatrous worship and had employed Brahmins as permanent faculties, their campus buildings were razed to the ground; all the residents, who dared not put up a fight in any case, killed; and entire book collections, burnt by invading Muslims. This was followed by Christian missionaries from Portugal and Great Britain, who, regardless of their own denominations, destroyed Sanskrit manuscripts by the hundreds, and vehemently continued to spread their religion in that unfortunate land. How could they have not known that their forefathers and their forefathers’ forefathers were the simple-minded, naked hunters roaming in the pastoral forests of Europe, while those very manuscripts were being created and critiqued in India? Ironically, latter-day luminaries such as Carlyle, Emerson, Goethe, Hegel, Lagrange, Schopenhauer, Thoreau, Twain, Voltaire, and Weil, who showered praises on the Indian creativity, belonged to the same Western tradition.

Ideally, in the realm of creativity, intuition, and pure intellect, extraneous issues like racial and regional discrimination should not carry weight. Which is what Lakshmikantham and Leela are acutely cognizant of, as they track down the fountain of global mathematics. That is what the genius of Vyasa must have also impelled his disciples Jeminai, Paila, Sumanthu, and Vaishampayana to observe and to follow, as they joined him in the codification of the gems of Vedic Shakhas and Samhitas. —Bhaiyya Joshi

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