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The Mathematical Marvel that was India

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  • JK
    http://www.indiacurrents.com/news/view_article.html?article_id=faee26bfd75fdd4ce22990835d8901ea THE ORIGIN OF MATHEMATICS by V. Lakshmikantham and S. Leela.
    Message 1 of 1 , Feb 2, 2005
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      THE ORIGIN OF MATHEMATICS by V. Lakshmikantham and S. Leela.
      University Press of America, Inc., Lanham, MD. Hardcover. 92 pages.

      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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