03-03-2005, 08:59 PM
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.
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->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 1534â1500 B.C.) and Chandragupta (327â320 B.C.) of the
Gupta dynasty, by making the former a coeval of Alexander the Great, and by
erasing the latterâs 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 1887â1807
B.C., and the short but remarkable lifeâs 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 âscholarship,â Aryabhattaâs
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
âEurocentric historical indifferenceâ 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 Pythagorasâs 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 Newtonâs 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 âthemselves had supposed or conjectured, that they had received
their intellectual capital, especially in geometryâ 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, itâs 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 âperished,â 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 forefathersâ 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.
âBhaiyya Joshi
<!--QuoteEnd--><!--QuoteEEnd-->
THE ORIGIN OF MATHEMATICS by V. Lakshmikantham and S. Leela. University
Press of America, Inc., Lanham, MD. Hardcover. 92 pages.
www.univpress.com.
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->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 1534â1500 B.C.) and Chandragupta (327â320 B.C.) of the
Gupta dynasty, by making the former a coeval of Alexander the Great, and by
erasing the latterâs 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 1887â1807
B.C., and the short but remarkable lifeâs 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 âscholarship,â Aryabhattaâs
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
âEurocentric historical indifferenceâ 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 Pythagorasâs 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 Newtonâs 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 âthemselves had supposed or conjectured, that they had received
their intellectual capital, especially in geometryâ 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, itâs 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 âperished,â 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 forefathersâ 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.
âBhaiyya Joshi
<!--QuoteEnd--><!--QuoteEEnd-->