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The Indic Mathematical Tradition 6000 BCE To ?
* Vedic Math Seminar & Workshops *
* (www.hssbayarea.org/vedicmath) *

by Dr. Shri Srinivas Padiyar

You think you are not good at math! Do you find math boring?
Or you are a math lover who wants to challenge yourself.
Then this workshop is for you.

What is Vedic Math?

* Vedas are ancient knowledge developed by Hindus
thousands of years ago. Many of this knowledge
is lost. Vedas are core scriptures of Hindus.
Vedic Math is a small part of this vast ocean
of knowledge.
* Vedic Math has a remarkable coherence and simplicity
that makes it easy to understand and adopt in daily
life. Through its amazingly easy methods, complex
problems can often be solved in least amount of time.
* The benefits of using Vedic Mathematics include
more enjoyment of maths, increased flexibility,
creativity and confidence, improved memory,
greater mental agility and so on.

About Dr. Srinivas Padiyar
Dr. Padiyar, a physician by profession, self learned Vedic Math at
the age of fifty. Since then he has given hundreds of lectures and
conducted workshops and seminars. He has written a two volume book
on Vedic Math, "Vedic Maths - Maths with smile". In his mission to
teach Vedic Math, he has appeared on DoorDarshan (India's National
TV Network), has prepared Video Cassettes and VCDs on Vedic Math.
See his detailed biography at

All events listed below are free of charge

Seminar - What is Vedic Math?
Date: July 11th (Sunday), 2004
Time: 5:00 pm - 6:00 pm

Venue: Newark Library
6300 Civic Terrace Ave.
Newark, CA 94560

Contact: Gautam (510) 623-7541

Special Workshop for Teenagers only (Age: 13 - 19)
Registration Required:
Register online at www.hssbayarea.org/vedicmath/reg.html or email
hss_sfo@yahoo.com <mailto:hss_sfo@yahoo.com>

Santa Clara County
Date: July 12th & 13th (Mon & Tue), 2004
Time: 4:30 PM - 6:30 PM

Serra Park
739 The Dalles Ave.
Sunnyvale, CA 94087

Contact: Parag Joshi: 408-735-9032

Alameda County
Date: July 14th & 15th (Wed & Thurs), 2004
Time: 4:30 PM - 6:30 PM

Newark Library
6300 Civic Terrace Ave.
Newark, CA 94560

Contact: Deepika Desai: 510-623-7541

Workshop for Adults and Teenagers
Registration Required
Register online at www.hssbayarea.org/vedicmath/reg.html or email

Santa Clara County
Date: July 12th & 13th (Mon & Tue), 2004
Time: 7:00 PM - 9:00 PM

Serra Park
739 The Dalles Ave.
Sunnyvale, CA 94087
Contact: Parag Joshi: 408-735-9032

Alameda County
Date: July 14th & 15th (Wed & Thurs), 2004
Time: 7:00 PM - 9:00 PM

Newark Library
6300 Civic Terrace Ave.
Newark, CA 94560
Contact: Ramesh Rao: 510-659-8543

Visit www.hssbayarea.org <http://www.hssbayarea.org>.
came via email:

Book <b>'Origin and History of Mathematics'</b> now available


International Foundation For Vedic Science(IFFVS) is honoured to have
published book 'Origin and History of Mathematics' by
V.Lakshmikantham and
J. Vasundhara Devi.

It is a matter of great concern that India's contribution to the
world of science is often underestimated,negated,distorted and
twisted to such an extent that many westerners and their followers in
India have had a tough time believing that Indians could contribute
to the field of original sciences,although they could produce
literature,speculative metaphysics,mysticism and art.The chronology
of Indian history has also been demoted by 1200 years in a planned
way.Thus a great deal of confusion has been created by the so-called
scholars(pseudo-scholars) regarding Indian history and India's
contribution to the modern world of mathematics and Sciences.IFFVS
has been one of the leading organizations in and outside of
India that shows a great concern over inaccurate history of India and
damaging 'orientalist' portrayals of India and India's cultural and
scientific legacy,portrayals that have persisted in educational
curricula despite the scathing critiques levelled by post modern
scholars.IFFVS always aims at making a proper review of India's
contribution to the world civilisation in mathematical and other
sciences, so that (1) the standard western portrayal of civilisation
of India as irrational and 'world negating' may be challenged, (2) a
due and proper role of India in shaping the positive and
scientifically modern civilisation may be acknowledged,(3)
stereotypes,inaccuracies and ommissions may be pointed out and role
of India in the field of math,science and technology may accurately
and authentically be portrayed in educational curricula the world
over and (4) the history of Indians in India may be presented with
Indian chronology and Indian perspective.IFFVS has always been in
favour of promoting the indocentric view of world history and
civilisation which talks about the unified world as one unit and
discards the Eurocentric view of the world that divides the
whole world into many segments and classes.

Prof. V. Lakshmikanthan (a high profile Mathematician from Andra
Pradesh of India and has been head of the Dept. of Mathematics in
various universities of USA since 1965 who also has been founder of
many mathematical Depts in various universities of USA) in the
present study challenges world negating view of India's contribution
to the world of mathematics and indentifies and acknowledges the
Indian element in modern math,science and technology.This
excellent study will help the unbiased scholars to know where the
ideas of western scientists,mathematicians and technocrats have been
derived from Indian sources.The scholars will be forced to think
whether the various branches of mathematics are from
Greek,Babylon,Arab or India.This study will also help dispel
the 'orientalist' idea superimposed by Macaulay and his
successors upon Indians since 1835, resulting in an inferior self-
image on the part of many modern Indians and causing them to look up
to the west for answers.

Price is only $27.00 CDN (inclusive of postal charges) and can be
ordered from:

International Foundation For Vedic Science
67 Clemens Street
London,On N5Y 1H7

Please visit website www.vedascience.com for other publications and
let us know if there are any questions.Thanks

Ashwini Kumar Rajpal
International Foundation For Vedic Science
A non-profit charitable organization
Interesting site
<b>Hinduism & Quantum Physics </b>
<b>Hindu Temple</b>
Take a look at the original Solar Geometry drawing for Mercury, Venus and Earth is as follows:
<img src='http://evolutionoftruth.com/abennett/images/abx-mve.gif' border='0' alt='user posted image' />

A, the Sun
B, Mercury
C, Sqrt distance Venus
D, Venus^.75
E, Venus mean radial orbital distance, 1.866025404.
F, Earth mean radial orbital distance, 2.583305712

Note how the key points of this geometry coincide with the floor plan of this Hindu temple:

<img src='http://evolutionoftruth.com/abennett/images/temple.jpg' border='0' alt='user posted image' />

The outer blue circle has a diameter of 2, the diameter of orbit of Mercury.

The inner blue semicircle has a diameter of 1.866025404, the mean radius of orbit of Venus.

Along the vertical red line are successively delineated Venus^0 (Mercury), Venus^.5 (Geometric average, mean radius of orbits of Mercury and Venus), Venus^.75 (Geometric average, times of orbit of Venus and Mercury), and V^1.0 (mean radius of orbit, Venus).

The green line running from bottom center to the upper right corner of the square touching the blue circle is .5*(sqrt 6 + sqrt 2), 1.931851653 (sqrt of diameter of orbit, Venus).

Also encoded within this floor plan is the mean radial distance of orbit of the Earth
Hi ppl, Namaskaar

I first posted this in the Indian culture section; then discovered it belongs better here. It is about these ancient Indian philosophies that I found while surfing the web:

1. The "Nyaya",
2. The "Purva Mimamsa", and
3. Vaisheshika

These philosophies were written not much later than the Vedas, and they stress the importance of scientific reasoning behind whatever is taught and whatever is believed to be true. According to the Purva Mimamsa, revelation must be proved by reasoning, that it should not be accepted blindly as dogma. And according to Nyaya, obtaining valid knowledge is the only way to obtain release from suffering. The followers of this school took great pains to identify valid sources of knowledge and to distinguish these from mere false opinions.

According to the Nyaya school, there are exactly four sources of knowledge (pramanas): perception, inference, comparison and testimony. Knowledge obtained through each of these can of course still be either valid or invalid, and the Nyaya scholars again went to great pains to identify, in each case, what it took to make knowledge valid, in the process coming up with a number of explanatory schemes.

Vaisheshika philosophy is similar to Nyaya. This is only a brief introduction that I found on this website


I have a strong feeling that these philosophies are not different from how the scientists of today trust the validity of theories(e.g. the Darwin's theory of evolution) and facts(experimentaly proved things). I think all of us should study them in detail.
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Varahamihira, a Great Iranic astronomer

I came across this article quite accidently. The claim of the author is incredible. This seems like another of those articles that are dished out by our psuedo-secularists to delink everything good about India from their Hindu/Indian origins. I felt that members here must be made aware of these brazen attempts at cultural aggression.

Further connections with Iran exist (Upadhye 1933). Davar has an exhaustive description of the Maga "Brahmins" and provides substantial new evidence proving Varahamihira's Iranic origin:

"We shall now review the influence of the Mag Brahmins on India. According to K.N.Sitaram,38 [38. "Iranian Influence on Indian Culture": an article by K.N.Sitaram in the K.R.Cama Institute Journal] the influence of the Mag Brahmins was considerable in the 6th century AD, when the Iranian form of sun-worship was in full swing in India. Sitaram holds that king Harshavardhan (AD 606-648), his father Prabhākarvardhan, his father Ādityavardhan and his father Rājyavardhan were all sun-worshippers and {p.66} descendants of Mag Brahmins. It is also significant that `Prabhākar' and `Āditya' are names of the sun. Sitaram asserts that the famous Indian astronomer Varāhamihir of the 6th century AD was a Mag Brahmin, and that he had referred to his Mag Brahmin ancestors in his works. From his father's name Ādityadās (meaning servant of the sun) and from the fact that Varāhamihir dedicated his great work, the Brihatsamhitā, to Mihir (Mithra or the sun), Sitaram concludes that the astronomer was in some way connected with the Mag Brahmins. In this respect a shrewd argument has been advanced by J.E.Sanjana 39, [39. "Varāhamihir - an Iranian name": an article by J.E.Sanjana in the Dinshah J.Irani Memorial Volume] who invites our attention to a certain verse of a Zarathushtrian scripture, named the Meher Yasht (Yasht X), according to which, while Meher (the sun) advances, he is accompanied by Verethraghna (Vritrahaṇa or Behrām) in the form of a "varāz" (varāha or boar). From this Avestan passage one can see the close connection between Varāha (boar) and Mihir (sun), which words go to form the name of the Hindu astronomer, and thus support the theory that he was a Mag Brahmin." (Davar 1962, p.65-66)

<b>The Magas of Persia were of course subsequently absorbed into Islam as the priestly Sayyid or Syed class. Islam - with its focus on the Kaaba of Mecca, the ancient temple of the Assyrian or Syrian Sun-God Hu-Baal, Bel or Baal - came naturally to the heliolatric Persian Magas, who no doubt regarded Islam as an offshoot of the ancient Iranic Solar religion.</b>
So it is possible that the Three Magi who visited the child Jesus were the of the same Magas, the ancestors of Varahamihira?
History of Indian Science and Technology

This site is operated by infinity foundation (Rajiv Malhotra)..

In one of his recent emails he indicated that the site had not been updated for the last year or so due to lack of resources. There is a new volunteer now. Hence there are some new additions.
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.
<!--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

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,
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

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
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
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Susruta and our heritage. (the 'father' of plastic surgery in India).(Oration)</b>

Indian Journal of Plastic Surgery; 1/1/2003; Chari, P.S.

Code Number: pl03002

Mr. Chairperson, ladies and gentlemen, I am thankful that the President and the Executive Committee of our Association nominated my name for the Susruta Oration for the 37th Annual Conference at Bangalore. We, in this country, regard Susruta as the "Father of Plastic Surgery." Who was Susruta? When and where did he live and work? These questions can only be imperfectly answered like similar questions. In respect of the lives of our ancient worthies. The Susruta Samhita would have us believe that once upon a time a number of sages approached Dhanwantari alias Divodasa, King of Kasi, who received Ayurveda from divine sources--Brahma via Prajapati, the Aswins and Indra. Dhanwantari imparts medical knowledge to these sages, and one of them called Susruta codified his oral instructions. There is no sure ground proving the historicity of Susruta, which literally means "that which is well heard" or "one who has thoroughly learned by heating." It is more likely the anonymously edited manual of a school which had selected Susruta as patron. It is only safe to assert that Susruta was of the race of Viswamitra as represented in the Mahabharata- Anushasan Parva, chapter IV. Divodasa, the preceptor of Susruta, is represented as an incarnation or descendant of Dhanwantari, the first propounder of surgical science. The name of the original work was Shalya Tantra (Skt Sala = surgical instrument). Beyond this meagre genealogy we possess no trustworthy information regarding the life and personality of Susruta.

We have no means of ascertaining what the Samhita was like as originally written by Susruta, the present form is a recession or rather a recession of recessions made by Nagarjuna who opinions identify as the founder of the Madhyamika or Northern School of Buddhist philosophy around the second century B.C. A few quotations from the Vridha (Old) Susruta are all that are preserved of the original Samhita, but their genuineness is of a problematic character, and we are not sure whether they are the production of lesser lights, or of ancient though less renowned commentators, attributed to the master to invest them with greater sanctity and authority. The most renowned commentary on Susruta Samhita is that of Dalhana (12th century A.D.) called Nabanda Samagraha. Other notable commentators were Gayadasa (10th century A.D.) and Candrata (12th century A.D.).

At the time of the Mahabharata which nearly approaches the age of Susruta the number of sects among the followers of the healing art numbered five, which were named Rogaharas (physicians), Shaylyaharas (surgeons), Vishaharas (poision curers), Krityaharas (demon doctors) and Bhisagatharvans (magic doctors). Susruta's Compendium is also mentioned in the Bower Manuscript that was found in 1890 in a ruined Buddhist stupa in Kashgar, on the western outskirts of the Gobi Desert, and translated by A.F.R.Hoernle in 1909 at Calcutta. The medical texts were written in the Pali script of the Gupta period according to palaeographic criterion which gives the beginning of the fifth century A.D. as the latest possible date for the text.

The upshot of these arguments is that in Susruta's text we have a work the kernel of which probably started some centuries B.C. in the form of a text mainly on surgery, but which was then heavily revised and added to in the centuries before 500 A.D. This is the form in which we have received the work in the oldest surviving manuscript today.

Susruta gives us a historical window into a school of professionalized surgical practice almost two millennia ago, and which was in its day, almost certainly the most advanced school of surgery in the world. Many details in the description could only have been written by a practising surgeon and it is certain that elaborate surgical techniques were a reality in Susruta's circle.

The first translation of Susruta Samhita were ordered by the Caliph Mansur (A.D.753-774) who had embassies come from his province of Sind to Baghdad along with Hindu scholars bringing books. The Caliph Harun (A.D.786-808) appointed Hindu physicians to Baghdad hospitals and ordered further translations into Arabic of books on medicine, pharmacology, toxicology, astronomy and other subjects. Alberuni who was a member of the court of Mahmud of Ghazni (A.D.997-1030) mentions the current translation of Caraka although complaining of its incorrectness. The centres of Indian learning in his times were Banaras and Kashmir, both inaccessible to the invading armies of Mahmud. The first European translation of Susruta Samhita was published by Hessler in Latin in the early 19th century. The first complete English translation was done by Kaviraj Kunja Lal Bhishagratna in three volumes in 1907 at Calcutta. New sources have been discovered in Tibetan versions, Tamil sources and Mongol versions of Tibetan translations. Indian medicine has played in Asia, the same role as Greek medicine in the West, for it spread to Indo-China, Tibet, Central Asia, and as far as Japan.

The contributions regarding Plastic Surgery in Susruta Samhita are the following:

1. Rhinoplasty by cheek flap.

2. Classification of mutilated ear lobe defects.

3. 15 techniques for repair of torn ear lobes.

4. Cheek flap for reconstruction of absent ear lobe.

5. Repair of cleft lip.

6. Piercing children's ear lobe with a needle or awl.

7. Suture materials of bark, tendon, hair and silk.

8. Needles of bronze or bone, circular, two finger-breadths wide and straight, triangular bodied, three finger--breadths wide.

9. Classification of burns into four degrees-singeing, blister, superficial and deep.

10. Different methods of dressings with various medicaments.

11. Wine to dull the pain of surgical incisions.

12. 101 types of blunt instruments (yantras) and 20 varieties of sharp instruments. According to Susruta the hand is the most important yantra, for without it no operation could be done.

13. Surgical demonstration of techniques of making incisions, probing, extraction of foreign bodies, cauterization, tooth extraction, scarification, excisions, trocars for draining abscess, saws for amputations on various natural fruits, dead wood, and clay models.

14. A system of anatomical dissection of cadavers.

15. Operations for lithotomy, intestinal sutures, couching for cataract, caesarian section to save a live baby if the mother dies in labour and other surgical procedures are mentioned. Ligaturing of bleeding vessels was not known, the bleeding being checked by pressure, cautery or boiling oil.

16. A code of ethics for teachers as well as students.

There is little historical evidence to show that these practices persisted beyond the time of the composition of Susruta's compendium. A few references to surgery found in Sanskrit literature between the 4th to the 8th century A.D. were collected by P.V. Sharma (1972), but the stereotypical nature of most of these references and the paucity of real detail, suggests that the practice of surgery was rare in this period. There is some evidence, however, that although surgery ceased to be part of the professional practice of the traditional physicians of the vaidya caste, it migrated to surgeons of the "barber surgeon" type. As such, it was no longer supported by the underpinning of Sanskrit literary tradition, so it became harder to find historical data about the practice. D.C. Sircar (1987) discusses some epigraphical evidence for the heritage and migrations of the "Ambastha" caste who appears to have functioned as barber surgeons in South India and later migrated to Bengal.

By the 17th century, foreign visitors began to remark on how surgery was virtually non- existent in India. The French traveller, Travernier for example, reported in 1684 that once when the King of Golconda had a headache and his physician prescribed that blood should be let in four places under his tongue, nobody could be found to do it Col. W.S. Sleeman (1893) in his "Rambles and Recollections of an Indian Officer" observed on the same lack of surgeons.

The famous Indian Rhinoplasty method is often cited as evidence that Susruta's surgery was widely known in India even up to comparatively modern times. The operation took place in March 1793 in Poona. A maratha named Cowasjee who had been a bullock-cart driver with the East India Company Army in the Third Mysore War of 1792 was captured by the forces of Tipu Sultan and had his nose and one hand cut off. (A residual puzzle with this account is that 'Cowasjee' in a Parsi name, not a Maratha one). After an year without a nose, he and four of his colleagues, who had suffered the same fate, submitted themselves to treatment by a man who had a reputation for nose repairs. Unfortunately, we know little of this man, except that he was said in one account to be of the brick-maker's caste and by Cowasjee's commanding officer Lt. Col. Ward as an artist' whose residence was 400 miles distant from Poona. Thomas Cruso and James Findlay, senior British surgeons in the Bombay Presidency, witnessed this operation.

They appear to have prepared a description of what they saw and diagrams of the procedure. The details and an engraving from the painting were published at third hand by Barak Longmates a journalist in 1794 in 'The Gentleman's Magazine and Historical Chronicle (66.4 pp.883, 891 and 892). The key innovation was the transplantation of skin from the site immediately adjacent to the defect, while keeping the graft tissue alive and supplied by blood through a connecting skin bridge. Subsequently, through the publication by Carpue (1816) describing his successful use of the technique this method of nose repair gained popularity amongst British and European surgeons. Personal inquiries by Carpue from Cowasjee's commanding officer Lt. Col. Ward described the understanding in Poona, at the time of the operation, that this artist--surgeon was the only one of his kind in India and that the art was heriditary in the family.

The technique used by Cowasjee's surgeon was similar, but not identical, to that described in Susruta's Compendium. Susruta's version has the skin flap being taken from the cheek; Cowasjee's was taken from the forehead. The Sanskrit text of Susruta's description is brief and does not appear to be detailed enough to be followed without an oral commentary and practical demonstration, although an experienced surgeon might be able to discern the technique even so. It is hard to see how such techniques could have persisted purely textually. Maybe, the Poona operation is indeed an extraordinary survival of a technique from Susruta's time, but in that case it seems to have been transmitted through channels outside the learned practice of traditional Indian physicians.

Ayurvedic literature is preserved almost exclusively in the Sanskrit language, and originally in the form of manuscripts written on birch bark, palm leaves or paper. India has, over the millennia, developed about a dozen different alphabets. The scribe who copied out the manuscripts would use the script that was local to the place of work. So it is quite normal to find Sanskrit medical manuscripts from Kerala in the Malayalam script, while a manuscript of the very same text copied in Bengal would be in the Bengali script. Both manuscripts would still be in the Sanskrit language and would be virtually indistinguishable if read aloud.

No systematic effort has been made to collect together all the known manuscripts of Susruta Samhita, let alone compare them all, try to classify them, to tease apart the historical strata in the texts, weed out scribal errors, and adjust the readings of the texts accordingly. The printed editions are vulgate texts, that is so say, they are books printed on the basis of small number of manuscripts from a local region, normally Bombay or Calcutta. And the decisions about what to print when the manuscripts disagree was made on the basis of general common sense but without the support which historical philology and textual criticism can offer. Criterion for determining what is intrinsic and what is extrinsic to rationalist medicine in the Susruta Samhita is based on the observation that medical science is concerned with specifically four factors: the doctor, the substance used (drug or diet), the nursing attendant and the patient. The qualifications essential to each are also specified. The discussion concerned with these are intrinsic to medical science. By contrast, any topic unconnected with these--howsoever may be their importance in philosophy, religion and traditional morality--are extrinsic to medicine.

Today, Ayurveda is one of the six medical systems that are officially recognized by the Indian Government, the others being allopathy (modern medicine), homeopathy, naturopathy, unani, siddha and yoga therapy. The practitioners of the six systems must compete for patients with each other and with a profusion of practitioners of other medical skills, including itenerant tonic sellers, pharmaceutical representatives, village curers, bone setters, midwives, exorcists, sorcerers, psychics, divines, priests, astrologers, grandmothers, wandering religious mendicants and experts in such maladies as snakebite, hepatitis, infertility and 'sexual weakness'. Indian people talk knowingly or not in the Ayurvedic idiom. Even the illiterate peasant of a remote village knows that yoghurt causes phlegm to accumulate in the chest, and everyone uses simple herbs like vetiver (cus cus) which remove 'heat' from the body and makes life during the hot summers a little more bearable. Ayurvedic thought is part of the conceptual universe of every Indian and has been a part of its collective consciousness since very early times.

Professor Debiprasad Chattopadhyaya in his book "History of Science and Technology in Ancient India Vol.II (1986) quotes Gordon Childe's comment that science and technology only develop during periods of urbanization. He describes two such periods in Ancient India, to which we can add two that developed in the succeeding centuries.

1. First Urbanization : Indus Vally Civilization (about 2300 B.C to 1750 B.C.) Dark Age from : 1750 B.C to about 700 B.C.

2. Second Urbanization : Aryan cities in the upper and middle Ganges plains

3. Third Urbanization : The Industrial Revolution and British colonization

4. Fourth Urbanization : Information Technology Revolution and Global Village.

Archaelogists in the second and third decades of the 20th century dug up the outlines of an imposing civilization with a considerable number of flourishing cities in the Indus River Valley extending into Haryana and Lothal, a sea-port, in Gujarat. The First Urbanization is viewed as resulting from profound socio-economic transformation from the neolithic villages to city life in the full sense. An important trait of city life was the creation of exact and predictive sciences-mathematics and astronomy - for revenue and property, inventories, building cities and calculating the farmer's calendar. The farmers surplus could be taken away for trade and commerce and city activities. We are still in the dark regarding the nature of the ruling class as no written material can be used for the purpose since their script has not been deciphered. On the analogy of the situation in Egypt and Mesopotamia it has been suggested that the administration was controlled by priest- groups who used religion, magic and superstitious beliefs to control the people. The city centres of the First Urbanization came to an end about 1750 B.C. for complex reasons as yet not fully understood. Thereafter followed a thousand years called the Dark Age.

About the eighth or seventh century B.C. Indian history started taking a dramatic turn towards the Second Urbanization. After the conquest by the migrating Indo-Aryans of the indigenous people, tribal groups began to settle in towns. Tribal wars led to the establishment of kings and kingdoms first in the upper Ganges basin, followed by the middle Ganges plains and then gradually throughout the subcontinent. There was a profound intellectual turmoil and thinkers explored various alternative avenues to understand nature. Thus came into being the first Indian scientist with a superb scientific method, which paved the way for the revolutionary move forward from magico-religious medicine to rationalist medicine. His name comes down to us as Uddalaka Aruni of the Gautama clan. He was the first to formulate and apply the essentials of the method of experimental verification. Secondly, he developed in a rudimentary form a promising unified theory of man and nature. Both contributed to the making of the tradition of rationalist medicine in the Indian subcontinent. Its essence consisted of the observation of facts (Skt drstanta) and reasoning or generalizing (Skt. Hetic) based on it.

Without bluntly rejecting the earlier scriptures embodying mythological beliefs and religious injunctions, Uddalaka dismisses all these in favor of a rational search for the ultimate cause of everything in nature recommending direct observation in the real sense. By an experimental demonstration he discovers to his son that which is the finest essence this whole world has that is its soul. That is Reality. That is Atman. That art thou, Svetaketu. (Chandogya Upanishad 13.1 1.4 and 6.3.1-15)

Uddalaka deserves to be placed with Thales of Miletus (640-546B.C.) who is believed by Western scientists to have initiated the spirit of inquiry and the pioneer of scientific observation. The main source of our information regarding Uddalaka Aruni are the Upanishads, particularly one chapter in the Chandogya Upanished exclusively recording his discourse though this needs to be supplemented by some passages from earlier sources like the Satapatha Brahmana (xi, 4.1-9) which mentions him as a man of considerable wisdom, willing to acquire that he himself did not possess from whomsoever possessed it, regardless of caste or status. The early Buddhist literature contains 550 stories called Jatakas which orthodox Buddhists believe to be accounts of Buddha's former births. One of these (Jataka No. 487) bears the name Uddalaka and mentions that he studied in Taxila under a renowned teacher there. He became highly learned and the leader of a group of roving ascetics in quest of knowledge and purity. He seemed to repeatedly point out that the only right method of scientific investigation into the nature of reality is that of inference by way of induction. His basic theme is that of the making (or evolving) of everything in the universe from the primeval matter. From this naturally follows the view that in the ultimate analysis man is nothing but an evolution of it - a view formulated in the text by the oftrepeated formula, "That thou art, Svetaketu." There is no scope in this formula for any divine agency having anything to do with the making of man. The phenomenon called death was understood by him as the return of the body to food, water and heat and therefore ultimately to sat', or primeval matter.

The essential core of medical science took shape already before the time of the Buddha who died around 485 B.C. or shortly after Uddalaka's time. The Caraka Samhita admits that various medical systems were in circulation. Apparently, during the formative period of rationalist medicine, different authorities were groping in different ways for determining the most effective therapeutic principles; various avenues had to be explored for medical science to be standardized.

What was the status of doctors in our early history ? While steps were being taken by the ancient physicians and surgeons to move towards remarkable results, the utmost contempt was shown for them in the legal literature, the Dharmashastras, when the law codes were taking distinct shape in the sixth and fifth century B.C. It was declared that they were so inherently impure that their very presence pollutes a place; food received or given to them was impure, they were not invited for sacrificial ceremonies, in social status they were considered no better than whores, hunters and followers of other despicable professions (Apasthamba 1.6.19; Gautama xvii.7; and Vashistha xiv. 1 - 10, 19). The obvious need of their services to society was acknowledged of course, as was that of the followers of other mean professions. Because the healers were absolutely shorn of respectability it was prescribed that medical practice should better be restricted to the Ambastha caste (Manu X.46-47). According to Manu (X. 116) persons of noble birth are forbidden learning that is different from the learning of the Vedas; medicine, logic and poison-removing being mentioned. The law givers understood that medicine and logic are closely related. Logic was detested for the reason that excessive indulgence in logic encourages heresy or the tendency to question the scriptures. The Dharmashastras have the primary purpose of validating the ideal of the hierarchial society - an ideal of which the priests were the main theoretical custodians. P.V. Kane in his monumental "History of the Dharmashastras" shows that already "dharma" acquired a sense of "the priveleges, duties and obligations of a man, his standard of conduct as a member of the Aryan community, as a member of the caste, as a person in a particular state of life."

In the translation of Kautilya's "Arthashastra" (about 300 B.C) by Professor R. Shama Shastri of Mysore there is chapter on salaries to be paid by the Mauryan Emperor to his employees. The highest salary was 64,000 panas and only the Queen Mother, heir apparent, the Chief Minister, the Commander - in - chief of the Army, the Chief of the Harem, the Emperor's Purohit or spiritual advisor and the family priest were entitled to it, possibly because of their proximity to the Ruler and the fear of assassination. The next salary slab was halved to 32,000 panas for notable government functionaries and subsequently halved over and over again. The physician was placed in the salary slab of 4 panas flanked by the water carrier and the horse-groom. The belief got institutionalized creating formidable difficulties for the progress of medical science. As late as 1836 when the Calcutta Medical College was started, when an Orthodox Hindu got enrolled and actually dissected a cadaver his courage had to be boosted by the booming guns of Fort Williams. If, hardly 170 years back, so much courage was needed to overcome orthodox opposition to dissection and all this under the protection and patronage of a powerful Government, it is not difficult to imagine how much greater courage was required of the ancient surgeons to prescribe a detailed mode of dissection as a necessary precondition for attaining medical proficiency.

Europeans after gaining entry into India built a series of hospitals but to start with, and for two centuries thereafter, these hospitals were solely for Europeans. The first European hospital was founded by the Portuguese Albuquerque in 1510 at Goa. Its management was handed over to the Jesuits who made it one of the best managed hospitals in the world. For the care of the native poor the British built a hospital in South Madras called the Native Infirmary which was named the Stanley Hospital in 1940. The French built a hospital in Pondicherry in 1701 and when the French left India the Government of India upgraded it to JIPMER. In Calcutta a hospital for the native poor was built in 1792, a precursor of the later Medical College Hospital. In Bombay the first Britsh hospital was built in 1676. In 1843 through a munificent donation by Sir Jamshetji Jeejeebehoy the J.J. Hospital started and two years later the Grant Medical College was attached to it. At first no Indians were attached to the teaching faculty. The Gordhandas Sunderdas Medical College and the K.E.M. hospital arose as a counter to British managed hospitals in 1925. The most important condition of the endowment was that all members of the teaching faculties should be well qualified Indians. Dr. Jivraj Mehta was its first dean.

It is commonly believed that proper education in India was started by the British. Mahatma Gandhi in a speech at Chatham House, London, in 1931, October 20 said, "I say without fear of my figures being challenged successfully, that today India is more illiterate than it was fifty or a hundred years ago, because the British administrators when they came to India, instead of taking things as they were, began to root them out. They scratched the soil and began to look at the root and left the root like that, and the beautiful tree perished. The village schools were not good enough for the British administrator, so he came out with his programme. Every school must have so much paraphernalia, buildings and so forth. Well, there were no such schools at all. There are statistics left by British administrations which show that, in places where they have carried out a survey, ancient schools have gone by the board, because they was no recognition for these schools, and the schools established after the European pattern were too expensive for the people."

William Adams in his Report on the State of Education in Bengal and Bihar in 1835 observed that there seemed to exist 100,000 village schools in Bengal and Bihar attached to temples, mosques and dharamsalas. In the Madras Presidency the Governor, Sir Thomas Munro, stated that "every village had a school' and for areas in the Bombay Presidency around 1820 G.L. Prendergast found "that there is hardly a village, great or small, throughout our territories, in which there is not at least one school, and in larger villages more." Dr. G. W. Leitner in 1882 showed that the spread of education in Punjab around 1850 was of the same extent. Despite the politically unsettled times the most unscrupulous chief, the avaricious money lender and even the free - booter vied with the small landowner in making peace with his conscience by founding schools and rewarding the learned. Institutions of higher !earning existed in many districts of Madras Presidency according to the collector's reports. In Malabar, the Samudrin Raja (Zamorin) maintained one old institution as a family trust. Where no colleges existed such learning in the Vedas, Shastras (Law), Astronomy, Ganeet, Ethics etc. were imparted in agraharams or usually at home. The Malabar data mentioned 194 pupils to be studying medicine.

How was all this education actually organized and maintained? The village to an extent had all the semblance of a State; it countrolled revenue and exercised authority within its sphere. Notwithstanding all that has been written about empires - Mauryan, Vijayanagar, Mughal etc. - throughout its history Indian society and polity has basically been organized according to non-centrist concepts. The annual exchequer receipts of the Emperor Jehangir did not amount to more than five percent of the computed revenue of the empire, and that of Aurangzeb, with all his zeal for maximizing such receipts, did not ever exceed 20 percent. In terms of basic expenses, both education and medical care, like the expenses of the local police and the maintenance of irrigation facilities, had primary claims on revenue. It was this revenue that maintained not only higher education but also the system of elementary education. Other recepients of revenue included those employed in administrative, economic and accounting activities; religious and charitable allowances, agraharams, maintenance of religious places, pundits, poets, joshis, medical practitioners and others.

The dispossession of the various categories of revenue assignees started as soon as the British took over de facto control of any area. Through various means like enhanced rates of assessments, revenue assignments, cash or grain allowance for teachers being appropriated to the total state revenue, slashing down of district charges, that is, the amounts traditionally utilized within the districts. The degeneration of education is ascribable to the gradual but general impoverishment of the country, and the means of the manufacturing classes greatly diminished by the introduction of European manufactures.

The neglect and uprooting of Indian education, and its replacement by an alien and rootless system had several consequences for India. To begin with it led to an obliteration of literacy and knowledge of such dimensions that recent attempts at universal literacy and education have been unable to make an appreciable dent in it. Next it destroyed the Indian social balance in which traditionally, persons from all sections of society appear to have been able to receive an optimum schooling which enabled them to participate openly and appropriately in the social and cultural life of their locality. And most importantly, till today, it has kept most educated Indians not only ignorant of the society they live in, the culture which sustains this society, but yet more tragically for over a century it has induced a lack of confidence and loss of bearing amongst the people of India in general.

Dr. Farouk E. Udwadia noted in his book "Man and Medicine," medicine does not change in an isolated milieu or as an isolated phenomenon. It was merely a part of the change that altered the whole fabric of human society; and each aspect of life and living influenced the other.

How does one acquire learning? In the seventh century A.D. Adi Sankaracharya said, " One fifth is the inherent qualities of the student; one fifth is by discussion and study together with his fellow - students. One fifth by a teacher interested to teach; one fifth by his own hard work and efforts; and one fifth by experience.

The present scenario in teaching hospitals in bleak. All departments are understaffed and the government's policy is to downsize the number of salaried faculty. The best talent is no longer attracted by the offered salaries. The majority opt for private practice and the problem is to acquire experience, judgment and updating of knowledge and skills. Holding workshops and C.M.E.s are not enough. We need to evolve a more dynamic medical education by harnessing the methods of modern information technology.

Recent decades have seen an explosion in the knowledge base in surgery. The development of sophisticated operative techniques has demanded subspecialization in surgical training. Individual faculty members carry this a step further when they become "superspecialists" with practices confined to anatomically circumscribed targets. This trend towards tunnel vision undermines the clinical practice setting. This phenomenon is ironic. Scientific progress has refined the surgeon's armamentarium - but only if properly recruited. Specialists have lost their common educational moorings, so too have they lost their ability to communicate and to strengthen each other's role in patient care.

Professor K. Mohandas, Director of Sri Chitra Tirunal Institute of Medical Sciences, in an address at the Annual Conference of Vice- Chancellors at Chandigarh in December, 2001 outlined a program of action through an information technology enabled flexible education program. This program may be implemented in a phased manner with the following objectives:

1. To ensure quality, relevance and uniformity of standards in training and evaluation.

2. To encourage evidence- based medical practices and the use of appropriate technology which are proven, essential and cost-effective.

3. To enable a flexible training program allowing not only quick incorporation of the latest advances, but also one that will facilitate learning at one's own pace and place. Most of the training for specialization can be done at the practitioner's place of work or home, thus reducing prolonged absence from professional responsibilities and facilitating conscious learning and updating of knowledge, techniques and technology.

The proposal should ultimately lead to individualization of medical education and training so that the illeffects of regimented education can be minimized both in quality and quantity. Moreover, the fruits of advances in health sciences would become more easily available to patients across a wider socioeconomic spectrum.

Plan of Action

Phase I

1. Establish internet facilities in all the medical colleges and make it accessible to the students and teachers.

2. Encourage students to gather information from the Internet to supplement those from standard textbooks. Small discussion groups mentored by teachers may then discuss all the information, with the teacher lending his/her experience to clarify doubts, assess the credibility of the information and helping to adapt it to the local/regional realities. The whole process should be aimed at synthesizing and assimilating information so that its application becomes clear and practicable.

3. The Health Science Universities and the medical faculties of traditional universities may set up egroups (discussion groups) within and among themselves so that knowledge, information, experience and problems may be shared and discussed in a wider circle.

This phase should be completed in about 24 months, at the end of which all training institutions will be net worked to optimize information acquisition, dissemination and assimilation, both from the point of view of expanding the knowledge base as well as its most effective application.

Phase II

Aim to establish the necessary infrastructure to utilize the benefits and advances in information technology. With a national nodal agency entrusted to complete infrastructural development and coordinating the resultant multi media network, the phase should in five years ensure that the national health sciences network will be able to adopt, absorb and adapt to the rapid technological developments that continuously repave the information highway.

At the end of this phase the following objectives must have been achieved

1. A National Nodal Agency that coordinates the functioning of health science network.

2. Regional or state agencies responsible for network operations within the region/state and operating in tandem with the national co-ordinator.

3. A reorganized undergraduate curriculum that maximizes learning and optimizes practical application of existing and emerging clinical and research information, using the tools of information technology.

4. Online retrieval of information from a national main frame computer. Knowledge and information from all institutions must also be made available to this central storage facility.

5. Video conferencing facilities, if not in every teaching institution, at least in well dispersed and strategically located centers so that geographical distances will not prove to be major impediment.

6. Facility for digital data transmission of texts, biological signals (ECG, EEG, EMG etc) and images-not necessarily restricted to teaching institutions, but also accessible and available from reputed hospitals, research institutions and even individual practitioners.

Phase III

This phase which should ideally be completed in 10 years should usher in an era of flexible learning and training at the postgraduate level with facilities for continuous updating of knowledge and skills, as well as evaluation and recertification of the competency of medical teachers and practitioners at optimal intervals.

More specifically

1. Acquisition of knowledge and skills for specialist practice and their evaluation at a pace affordable and feasable for the aspirants. The curriculum and training programs must be so designed as to enable the candidates to undergo the training without having to leave their place of practice or work for long periods, and the number of candidates need not have to be restricted as in the existing educational systems.

2. An accreditation system for hospitals which can serve as training centres so that trainees can choose a hospital not too far and not too different from their patient population, epidemiological composition and disease burden.

3. Public health programs integrated into Clinical practice so that the new paradigm of health care delivery system that would hopefully emerge from the reorganized education and training programs, based on flexibility, relevance and feasibility, will have prevention of diseases and promotion of health as the first priority.

The Government of India and the State Governments, in association with the Medical Council of India should adopt the implementation of technology enabled medical education as an urgent priority. It should form part of the new National Health Policy. Perhaps the first step may be the identification of an agency to work out the detailed action plan in a time-bound manner and this could be done by the Union Ministry of Health following a round of consultations with the State Governments, the Ministry of Human Resources Development and the Medical Council of India.

Our heritage of Indian Medicine stretches over 5000 years, from the period of the First Urbanization to the era of the global village. That medical science is not merely a branch of technical knowledge, but that it has an important ethical aspect, have been emphasized in both Susruta and Charka Samhitas as well as in various medical codes of ethics upto the present times. Zoroastrianism, the first monothestic religion in the world, in its scripture, Avesta embodied the tenets of its priest physicians or Magi in the three words-humata, hukata, havarasta-which means "good thoughts," "good words" "good deeds". The same three words are the Tata crest adopted by Jamshetji Tata.

"The difficulty lies not in the new ideas, but in escaping the old ones, which ramify into every corner of our minds."

J. M. Keynes


(1.) Alberuni's India. An account of India about A.D. 1030. In: Sachau, Edward C, editors. Delhi - Jullundur - Lucknow- Bombay: Popular Edition; S. Chand & Co; 1964.

(2.) Bhishagratna, Kaviraj Kunja Lal. An English translation of the Susruta Samhita. Based on Orginal Sanskrit Text in three volumes. K. L. Bhishagratna Calcutta, No. 10, Kasi Ghose's Lane. 1907

(3.) Bower, Hamilton. The Bower Manuscript translated by A.G.R. Hoernle. Oxford: The Bodlean Library; 1909.

(4.) Calders Ritchie. Medicine and Man. George Allen and Unrwin. London: 1958.

(5.) Chattopadhyaya, Debiprasad: History of Science and Technology in Ancient India. Calcutta: Firma Klm Pvt Ltd; Vol 11.1986.

(6.) Da Bartolomeo, Fra Paulino. On Education of Children in India. Voyages to the East Indies. Book 11. Rome: 1796.

(7.) Dharampal. The Beautiful Tree: Indigenous Indian Education in the Eighteenth Century. New Delhi: Biblia Impex Pvt. Ltd; 1983.

(8.) Flexner, Abraham. Medical Education in the United States and Canada. New York City: The Carnegie Foundation; 1910.

(9.) HH Bhagvat Sinh Jee, Maharaja of Gondal. A Short History of Aryan Medical Sciences. 2nd edn. Shree Bhagvat Sinh Jee. Gondal: Electric Printing Press; 1927.

(10.) Jaggi OP. A Concise History of Science. Chandigarh,Delhi: Atma Ram & Sons; 1974.

(11.) Jolly, Julius. Indian Medicine translated from German by C.G. Kashikar. Poona: 1951.

(12.) Kane PV. History of the Dharmshastras. Poona: Bhandarkar Oriental Institute; 1946.

(13.) Sastri, Shama R. Arthashastra of Kautilya.3rd edn. Mysore: Mysore University Press; 1929.

(14.) Sigerist HE. History of Medine 11. Early Greek, Hindu and Persian Medicine. New York: Oxford University Press; 1961.

(15.) Singhal GD, Tripathi SN, Chatuvedi GN. Fundamental and Plastic Surgery Considerations in Ancient Indian Surgery based on Chapters 1-27 of Sutra-Sthana of Susruta Samhita. Varanasi: Singhal Publications; 1981.

(16.) Sri Sankara carya. Viveka cudami translated by Swami Madhavananda. Calcutta: Advaita Ashram (Publication Department); 1989.

(17.) Svoboda, Robert E. Ayurveda: Life, Health and Longevity New Delhi: Penguin Books (India) Ltd; 1993.

(18.) Udwadia FE. Man and Medicine. New Delhi: Oxford University Press; 2000.

(19.) Wujastyk, Dominik. The Roots of Ayurveda. London New York Toronto New Delhi: Penguin Books; 1998.

(20.) Zimmer, Henry R. The Science of Hindu Medicine. Vadodara: Good Companions Publishers; 2000.

P. S. Chari

Department of Plastic Surgery, Postgraduate Institute of Medical Education and Research, Chandigarh160012, India.

Delivered on 30th November 2002 at APSICON 2002, Bangalore, India

COPYRIGHT 2003 Medknow Publications<!--QuoteEnd--><!--QuoteEEnd-->
From "The Financial Express" dated March 25 2005

<b>India finds 50 lakh manuscripts and counting</b>

NEW DELHI, MARCH 24: People at the National Mission for Manuscripts are a surprised lot. When they began a survey to map and document ancient scriptures lying neglected and unseen in numerous pockets of the country they followed an estimate that India had nearly 10 to 20 lakh of them.

The figure they found out after their pilot survey in three states, had shot up to a staggering 50 lakh manuscripts, making India the largest storehouse of the `records of yore' in the world. And the count is not the final tally, says Sudha Gopalakrishnan, director of the mission.

Seven lakh of these are just from the three states-UP, Bihar and Orissa, where the mission surveys were held. And of the interesting volumes that they came across include a voluminous copy of the Mahabharata weighing a quintal and a metre long copy of Quran.

The mission, established in 2003 by the centre under the Ministry of Culture to attend to the unkempt manuscripts across the country, plans to embark on a hunt for the ancient volumes in states such as Rajasthan and Gujarat.

The last year's search in three states - 30 districts of Orissa, 13 districts of Uttar Pradesh and 10 districts of Bihar was carried out through a well-defined strategy involving around 2700 people. "We involved students and teachers in our drive to find the scriptures. They then searched the villages in the districts-in libraries, temples, monasteries and Madrassas for the texts," says Gitanjali, co-ordinator of the survey.

From Orissa itself, around 17,857 repositories were found, most of them containing texts of the 'tantric' thought. From Unnao in up about 25,000 manuscripts were procured.

The 50 lakh also includes manuscripts that were digitized and documented such as the 500 manuscripts of the 6000 stored at the Iqbal library in Srinagar and 85 manuscripts of 1,000 Kudiyattam manuscripts from Kerala.

The mission has also identified 3,500 manuscripts from the Orissa state museum, 4,000 vaishnavite manuscripts from Majuli islands in Assam and 6,500 manuscripts from Tamil Nadu about Siddha stream of medicine, digitisation of which began from January 15 this year, according to a report prepared by the mission.

Yet another project of the mission is to embark on preservation of manuscripts with natural ingredients and considering the climatic conditions of the area of preservation.

There are references on preservation of scriptures in ancient and medieval literature such as Ashokan edicts, Kautilya's Arthashastra, puranas, Dasabodhas and the medieval saint literature, Shreenand Bapat, an indology lecturer at Tilak Maharashtra Vidyapeeth says in a paper that he compiled on preserving ancient scriptures.

Saroj V Bhate, honorary secretary of Bhandarkar Oriental Research Institute (BORI) in Pune, says the institute is planning to coach around 30 people in indigenous methods of conservation.

"One of the reasons for bringing the manuscripts from Mumbai to Pune in 1971 was because the climate here is dry. There need not be much done to preserve the documents, except for treatment with tobacco powder and camphor. But that is not the case with the areas in the coastal belt, where humidity is more," Bhate says.

Sudha Gopalakrishnan says they had organised an exhibition and seminar where different regions across the country had exhibited their specific method of preservation. These would be compiled into reference texts and would be used for preservation works in future, she says.
J<b>antar Mantar Observatory</b>

<b>Jantar Mantar - astronomical observatories Maharajah Jai Singh II of Jaipur </b>
Very interesting topic... interested people can view my presentation on the subject organized by DESI(DESI is doing lot of similar work...explore http://www.desiumd.org) in the following link...


Excellent powerpoint presentation on the subject, Vinod. I've saved a copy on my hard-drive. Please check you PM.
There was a thread that I initiated in BR,during the days when political correctness had not run amuck there and I was still tolerated. Iwilll resurrect someof my posts from there since there is a virtual goldmine of information in one place. The URL is


<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->I will try to reconstruct this thread from what i have saved,Kaushal

posted by Gganesh

I came across this great link that provides an index of Ancient Indian Mathematicians. It basically made me want to read more. I did a google search and came up with a few more useful links. I would greatly appreciate any relevant input.

History Topics: Index of Ancient Indian mathematics

Astronomy and Mathematics in Ancient India

Indian Mathematicians


Vigyan: A website of Indian Science and Technology

History of Mathematics in India

Equations and Symbols



Member # 138

posted 15 August 2002 10:37 AM
The use of concise mathematical symbolism (<,>,=,*,(), inf., sup.,the integral sign, the derivative sign, the sigma sign etc is a relatively recent revolution in mathematics, When calculus was invented by Newton and Leibniz independently, they used different notations. Newton used dots on top of the quantity and called them fluxions, while Leibniz used the 'd' notation. Unfortunately when all the major advancements in science and mathematics were happening in Europe in the 17th and 18th century, India was stagnant, caught in interminable wars and conquests.

Ironically it was the Indian place value notation that triggered the advance in Europe. Prior to this it was common to express all problems in wordy sentences and verse.

As to the value of PI (cannot be expressed as a fraction) it is impossible to calculate it without the use of some variant of the 'method of exhaustion'. In this particular instance it was a matter of using increasingly larger number of isosceles triangles( forming an n sided polygon) within the circle. This is the germ of the method of series expansions. The ancient Indians were well aware of this technique and used it for several trigonometric calculations. The felicity with which Indians did series expansions extended to Ramanujam. He was the incomparable master and there may be none like him on the face of this earth again.

Again there is no claim that the Indians did everything. For example there is no evidence that the Indians were familiar with the representation of complex numbers and complex variables or advanced topics such as the calculus of variations.

The ancient vedic indians were interested in very practical aspects of mathematics, namely the positions of the stars, developing a panchanga (calendar), ordinary mathematics for everyday use, measurements, such as that of land and weights etc.. There is no evidence that they were familiar with the science of mechanics for instance, which developed in Europe in the 18th century after Newton.


posted 15 August 2002 11:32 AM

a History of PI (does not give details)




The Beautiful Tree

Subhash Kak

Sulekha Columns, May 22, 2001

As a young boy raised in small towns of Jammu and Kashmir, I often came across people who could not read or write. The school books said that literacy in all of India was low, perhaps 30 percent or so, and this was despite the introduction of the British education system more than 100 years earlier. The books implied that before the arrival of the British the country was practically illiterate. This thought was very depressing. Perhaps I shouldn't have believed the story of India's near total illiteracy in the 18th century so readily. India was rich 250 years ago when the British started knocking at the door for a share of its trade. Paul Kennedy, in his highly regarded book, The Rise and Fall of the Great Powers : Economic Change and Military Conflict from 1500 to 2000 estimates that in 1750 India's share of the world trade was nearly 25 percent.

To understand this figure of 25 percent, consider that this is USA's present share of the world trade, while India's share is now only about half a percent. India was obviously a very prosperous country then, and this wealth must have been mirrored in the state of society, including the literacy of the general population.

Unfortunately, education in medieval India is not a subject that has been well researched. But thanks to the pioneering book, The Beautiful Tree by Dharampal, we now have an idea of it before the coming of the British. The book uses British documents from the early 1800s to make the case that education was fairly universal at that time. Each village had a school attached to its temple and mosque and the children of all communities attended these schools.

W. Adam, writing in 1835, estimated that there were 100,000 schools in Bengal, one school for about 500 boys. He also described the local medical system that included inoculation against small-pox. Sir Thomas Munro (1826), writing about schools in Madras, found similar statistics. The education system in the Punjab during the Ranjit Singh kingdom was equally extensive.

These figures suggest that the literary rate could have approached 50 percent at that time. From that figure to the low teens by the time the British consolidated their power in India must have been a period of continuing disaster.

Amongst Dharampal's documents is a note from a Minute of Dissent by Sir Nair showing how the British education policy led to the illiteratization of India: "Efforts were made by the Government to confine higher education and secondary education, leading to higher education, to boys in affluent circumstances... Rules were made calculated to restrict the diffusion of education generally and among the poorer boys in particular... Fees were raised to a degree, which, considering the circumstances of the classes that resort to schools, were abnormal. When it was objected that minimum fee would be a great hardship to poor students, the answer was such students had no business to receive that kind of education... Primary education for the masses, and higher education for the higher classes are

discouraged for political reasons."

According to Dr Leitner, an English college principal at Lahore, "By the actions of the British the true education of the Punjab was crippled, checked and is nearly destroyed; opportunities for its healthy revival and development were either neglected or perverted."

Dharampal's sources appear unimpeachable and the only conclusion is that 250 years ago the Indian basic education system was functional. Indeed, it may have been more universal than what existed in Europe at that time.

One might, with hindsight, complain that the curriculum in the pathshalas was not satisfactory. Dharampal's book lists the texts used and they appear to have provided excellent training in mathematics, literature, and philosophy. Perhaps the curriculum could have had more of sciences and history. I think the school curriculum was not all that bad in itself. Judging by the standards of its times, it did a good job of providing basic education.

What was missing was a system of colleges to provide post-school education. After the destruction of ancient universities like Taxila and Nalanda, nothing emerged to fill that role. Without institutions of higher learning, the Indian ruling classes did not possess the tools to deal with the challenges ushered in by rapid scientific and technological growth.

The phrase ‘the beautiful tree’ was used by Mahatma Gandhi in a speech in England to describe traditional Indian education. Gandhi claimed that this tree had been destroyed by the British. Dharampal's book provides the data in support of Gandhi's charge.

The Macaulayite education system, put in place by the British, almost succeeded in erasing the collective Indian memory of vital, progressive scientific, industrial and social processes. But not all records of the earlier history were lost. Dharampal has authored another important book, Indian Science and Technology in Eighteenth Century: Some Contemporary European Accounts which describes the vitality of Indian technology 250 years ago in several areas.

It is not just colonialist ideas that are responsible for the loss of cultural history. The need to pick and choose in today's information age is also leading to an erosion of cultural memory. The scholar and mathematician C. Muses from Canada did his bit to counter it by writing about Ramchundra (born 1821 in Panipat), a brilliant Indian mathematician, whose book on Maxima and Minima was promoted by the prominent mathematician Augustus de Morgan in London in 1859. Muses's work appeared in the respected journal The Mathematical Intelligencer in 1998. Ramchundra had been completely forgotten until Muses chanced across a rare copy of his book.

Muses called me over a year ago, just before he died, to tell me how he got interested in India. He said that he wanted to make sense of why Indians had not developed science, as colonialist and Marxist historians have long alleged. But the deeper he got into the original source materials, he found an outstanding scientific tradition that had been misrepresented by historians who were either biased or plain incompetent.

Although Muses did not so speculate, one might ask if de Morgan's own fundamental work on symbolic logic owed in part to the Indian school of Navya Nyaya. De Morgan, in his introduction to Ramchundra's work, indicates that he knew of the Indian tradition of logic, "There exists in India, under circumstances which prove a very high antiquity, a philosophical language (Sanskrit) which is one of the wonders of the world, and which is a near collateral of the Greek, if not its parent form. From those who wrote in this language we derive our system of arithmetic, and the algebra which is the most powerful instrument of modern analysis. In this language we find a system of logic and metaphysics."

Finally, there is the loss of memory taking place due to the carelessness with which we are preserving our heritage. This is a process of permanent loss, although on a few lucky occasions long-forgotten documents are found. One example of this latter event is the recovery of the lost notebooks of Srinivasa Ramanujan (1887-1920), who may have been the greatest mathematical genius of all time. Ramanujan had been called a second Newton in his own lifetime, yet the full magnitude of his achievements was appreciated only when his [lost] notebooks, full of unpublished results, were discovered in the eighties.

You can read a fine biography of Ramanjuan by Robert Kanigel titled The Man Who Knew Infinity. I also recommend Ramanujan: Letters and Commentary, edited by Bruce Berndt and Robert Rankin.

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Posted: 18 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  



Statistician C.R. Rao to Receive
National Medal of Science
ALEXANDRIA, VA - Statistician and American Statistical Association (ASA) member C.R. Rao, Eberly Professor Emeritus of Statistics and Director of the Center for Multivariate Analysis at Pennsylvania State University, will be honored at the White House with the National Medal of Science on May 29, 2002.

Rao earned his PhD and ScD at Cambridge University, and has received 27 honorary doctoral degrees from colleges and universities across the world. He has over fifty years of experience, largely in academics. Rao joined the ASA in 1970 and was honored two years later with election to Fellow of the American Statistical Association "for outstanding and prolific contributions … and for his devoted statistical teaching and service." In 1989, Rao was awarded the Samuel S. Wilks Medal for outstanding contributions to statistics. He also served as president to five other statistical societies and has been elected Fellow of numerous other organizations.

Rao has spent his entire career promoting statistics and their usefulness in society. "If there is a problem to be solved, seek statistical advice instead of appointing a committee of experts. Statistics can throw more light than the collective wisdom of the articulate few," said Rao.

The National Medal of Science honors individuals for pioneering scientific research that has enhanced our basic understanding of life and the world around us. The National Science Foundation administers the award established by Congress in 1959 for individuals "deserving of special recognition by reason of their outstanding contributions to knowledge in the physical, biological, mathematical, or engineering sciences." Visit www.nsf.gov/nsb/awards/nms for more information about the National Medal of Science.

For additional information on the American Statistical Association or Dr. Rao, please contact Megan Kruse or Jeanene Harris at the ASA by calling (703) 684-1221, emailing publicaffairs@amstat.org, or visiting the ASA Web site at www.amstat.org.

About Prof. C. R. Rao


C. R. Rao, one of this century's foremost statisticians, entered statistics quite by chance and went on to become a household name in the field. He is currently at Penn State as Eberly Professor of Statistics and Director of the Center for Multivariate Analysis

C. R. Rao, who was born in India, received his education in statistics at the Indian Statistical Institute (ISI), Calcutta, which has the distinction of being among the first ones to be founded for the study of statistics in the world.

The first result in statistics to bear C. R. Rao's name was proven by him at the young age of 25; he became a professor at 28 and went on to make many more fundamental contributions to statistical theory and it's applications.

From the young age of 28, he headed and developed the Research and Training Section of the ISI, and went on to become Secretary and Director of the ISI, from which he retired as Jawaharlal Nehru Professor in 1984.

His contributions to statistics have been recognized by his election as a Fellow of the Royal Society, UK; as a Member of the National Academy of Sciences, USA, as one of the eleven Life Fellows of King's College, Cambridge, UK and the conferring of 19 honorary doctorates by universities all over the world.

The Government of India awarded him the Padma Bhushan, a high civilian award and made him its sixth National Professor, in recognition of his contribution to the cause of furthering knowledge.

In 1988, the Times of India ranked him among the TOP TEN Scientists of Modern India, along with Nobel Laureates C. V. Raman, S. Chandrasekhar and H. Khorana and mathematical genius, S. Ramanujan.

C. R. Rao's research has influenced not only statistics, but also the physical, social and natural sciences and engineering.His students work in universities and research institutions all over the world, and several of them have gone on to become world leaders of research in their areas of specialization.

He is an inspiring role model for statisticians as well as students from all disciplines. This book is an ideal gift for scientists and researchers as well as for high school and college students.

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Posted: 18 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  


More on Ramchundra



Raina, Dhruv, ‘Mathematical foundations of a cultural project or Ramchandra’s treatise "Through the unsentimentalised light of mathematics"’, Historia mathematica 19 (1992), 371-384
The 19th century witnessed a number of projects of cultural rapprochement between the knowledge traditions of East and West. In his Treatise on the problems of maxima and minima, the Indian polymath Ramchundra tried to render elementary calculus amenable to an Indian audience in the indigenous mathematical idiom. The "vocation of failure" of the book is discussed within the context of encounter and the pedagogy of mathematics.


34. Ramchundra. TREATISE ON PROBLEMS OF MAXIMA AND MINIMA SOLVED BY ALGEBRA London 1859 Wm. H. Allen. 8vo., 185pp., 8 plate, original cloth. Owner signed and owner bookplate (Edward Ryley) . Good, cloth faded, cover and spine ends worn, one tiny chip in spine cloth. $235.00


My own lecture, entitled ‘Multiculturalism in history: voices in 19th century mathematics education east and west’, was on the history of interaction between European and Indian mathematics education in the 19th century, discussing the contributions in particular of Henry Colebrooke, Yesudas Ramchundra, and Mary Everest Boole

Note I am only reproducing my own posts since otherwise the custodians at BR may choose in their infinite wisdom to zap this arcihve forever
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->you have to go to a reputed University library (maybe IIM, Ahmedabad has one i dont know) and look for magazines (such as Ganita )and books. I have been told IIT, Bombay has an outstanding library

The original Sanskrit texts have been published i believe by Munshiram Manoharlal & Motilal Banarsidas. Here are a list of publishers


It is very difficult to find original sanskrit texts in the US and we have to order from Delhi, so i would be grateful if you could post any sources which you have found useful in your search. I have been looking for a book on the Apastamba Sulava Sutra with original verses.

I will be happy to help you search , in case you have a slow internet connection.


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Joined: 31 Dec 1969
Posts: 481

Posted: 22 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  


A good place to start are some of these articles;


References for Bhaskara I


Biography in Dictionary of Scientific Biography (New York 1970-1990).

K Shankar Shukla, Bhaskara I, Bhaskara I and his works II. Maha-Bhaskariya (Sanskrit) (Lucknow, 1960).
K Shankar Shukla, Bhaskara I, Bhaskara I and his works III. Laghu-Bhaskariya (Sanskrit) (Lucknow, 1963).

R C Gupta, Bhaskara I's approximation to sine, Indian J. History Sci. 2 (1967), 121-136.
R C Gupta, On derivation of Bhaskara I's formula for the sine, Ganita Bharati 8 (1-4) (1986), 39-41.
T Hayashi, A note on Bhaskara I's rational approximation to sine, Historia Sci. No. 42 (1991), 45-48.
P K Majumdar, A rationale of Bhaskara I's method for solving ax ± c = by, Indian J. Hist. Sci. 13 (1) (1978), 11-17.
P K Majumdar, A rationale of Bhatta Govinda's method for solving the equation ax - c = by and a comparative study of the determination of "Mati" as given by Bhaskara I and Bhatta Govinda, Indian J. Hist. Sci. 18 (2) (1983), 200-205.
A Mukhopadhyay and M R Adhikari, A step towards incommensurability of and Bhaskara I : An episode of the sixth century AD, Indian J. Hist. Sci. 33 (2) (1998), 119-129.
A Mukhopadhyay and M R Adhikari, The concept of cyclic quadrilaterals: its origin and development in India (from the age of Sulba Sutras to Bhaskara I, Indian J. Hist. Sci. 32 (1) (1997), 53-68.
K S Shukla, Hindu mathematics in the seventh century as found in Bhaskara I's commentary on the Aryabhatiya, Ganita 22 (1) (1971), 115-130.
K S Shukla, Hindu mathematics in the seventh century as found in Bhaskara I's commentary on the Aryabhatiya II, Ganita 22 (2) (1971), 61-78.
K S Shukla, Hindu mathematics in the seventh century as found in Bhaskara I's commentary on the Aryabhatiya III, Ganita 23 (1) (1972), 57-79
K S Shukla, Hindu mathematics in the seventh century as found in Bhaskara I's commentary on the Aryabhatiya IV, Ganita 23 (2) (1972), 41-50.
I I Zaidullina, Bhaskara I and his work (Russian), Istor. Metodol. Estestv. Nauk No. 36 (1989), 45-49.

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Posted: 22 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  



References for The Indian Sulbasutras

B Datta, The science of the Sulba (Calcutta, 1932).
G G Joseph, The crest of the peacock (London, 1991).

R C Gupta, New Indian values of from the Manava sulba sutra, Centaurus 31 (2) (1988), 114-125.
R C Gupta, Baudhayana's value of 2, Math. Education 6 (1972), B77-B79.
S C Kak, Three old Indian values of , Indian J. Hist. Sci. 32 (4) (1997), 307-314.
R P Kulkarni, The value of known to Sulbasutrakaras, Indian J. Hist. Sci. 13 (1) (1978), 32-41.
G Kumari, Some significant results of algebra of pre-Aryabhata era, Math. Ed. (Siwan) 14 (1) (1980), B5-B13.
A Mukhopadhyay and M R Adhikari, The concept of cyclic quadrilaterals : its origin and development in India (from the age of Sulba Sutras to Bhaskara I, Indian J. Hist. Sci. 32 (1) (1997), 53-68.
A E Raik and V N Ilin, A reconstruction of the solution of certain problems from the Apastamba Sulbasutra of Apastamba (Russian), in A P Juskevic, S S Demidov, F A Medvedev and E I Slavutin, Studies in the history of mathematics 19 "Nauka" (Moscow, 1974), 220-222; 302.


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Posted: 22 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  


Dharmapal's Bha_rata: eCourse




For the un-initiated, Dharampal is a Gandhian - Historian who has
researched and brought to the notice of the public at large many new
insights and levels of thinking that were neither professed nor
popularised by the mainstream historians. His books on Eighteenth
Century Indian Science and Technology, Pre-British Indian Education
System, Panchayat System in the pre-Colonial era and others all have
brought about a new method of looking at the past of this country
and at the archival material available with the various archives,
museums and libraries on India.

It has been his quest to understand the meaning and life of ordinary
people of this country, their methods of organising their lives and
the tools and means they adopt in doing so, their customs and
culture and their aspirations, he has travelled a vast research
journey mostly alone and documenting scraps of material which
incidentally has opened a huge body of knowledge for the rest of the
world. He maintains, that it is the need to convince himself of the
meaning behind the events in history and ascertain and validate the
facts that has driven him in his work. That some of them have been
published and the publications has inspired many individuals and
launched institutions is a consequence he probably did not predict
or prepare for.


The eCourse - DHARAMPAL'S INDIA would highlight his views, work and
interpretation of historical events. Though by no means this would
claim to be comprehensive, we have designed this course to be an
introduction and orientation to his larger works.

SAMANVAYA has had the privilege of working with Dharampalji for over
2 years now.

The course will be limited to few people who are inclined towards
further learning / work based on this understanding. The course
would consist of short capsule of materials selected by people who
have worked with Dharampalji; these would be mailed across followed
by a discussion on the same.

If you are interested to register, please mail samanvaya@vsnl.com
with a note on yourself and why you are interested. The course will
be for a duration of 3 weeks on-line starting late September. <!--QuoteEnd--><!--QuoteEEnd-->
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Posted: 27 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  



ECIT Sourcebook on Indic Contributions in Math and Science

This sourcebook will consist primarily of reprinted articles on Indic contributions in math and science, as well as several new essays to contextualize these works. It will bring together the works of top scholars which are currently scattered thoughout disparate journals, and will thus make them far more accessible to the average reader.

There are two main reasons why this sourcebook is being assembled. First, it is our hope that by highlighting the work of ancient and medieval Indian scientists we might challenge the stereotype that Indian thought is "mystical" and "irrational". Secondly, by pointing out the numerous achievements of Indian scientists, we hope to show that India had a scientific "renaissance" that was at least as important as the European renaissance which followed it, and which, indeed, is deeply indebted to it.

Currently, the following table of contents is proposed for this volume:

1. Editors' Introduction (Subhash Kak)

Section 1: Mathematics

2. D. Gray, 2000. Indic Mathematics etc.

3. Joseph, George Ghevarughese. 1987. "Foundations of Eurocentrism in Mathematics". In Race & Class 28.3, pp. 13-28.

4. A. Seidenberg, 1978. The origin of Mathematics. Archive for History of Exact Sciences 18.4, pp. 301-42.

5. Frits Staal, 1965. Euclid and Panini. Philosophy East and West 15.2, pp. 99-116.

6. Subhash Kak, 2000. Indian binary numbers and the Katapayadi notation. ABORI, 81.

7. Subhash Kak, 1990. The sign for zero. Mankind Quarterly, 30, pp. 199-204.

8. C.-O. Selenius, 1975. Rationale of the chakravala process of Jayadeva and Bhaskara II. Historia Mathematica, 2, pp. 167-184.

9. K.V. Sarma, 1972. Anticipation of modern mathematical discoveries by Kerala astronomers. In A History of the Kerala School of Hindu Astronomy. Hoshiarpur: Vishveshvaranand Institute.

Section 2: Science, General

10. Staal, Frits. 1995. "The Sanskrit of Science". In Journal of Indian Philosophy 23, pp. 73-127.

11. Subbarayappa, B. V. 1970. "India's Contributions to the History of Science". In Lokesh Chandra, et al., eds. India's Contribution to World Thought and Culture. Madras: Vivekananda Rock Memorial Committee, pp. 47-66.

12. Saroja Bhate and Subhash Kak, 1993. Panini's grammar and computer science. ABORI, 72, pp. 79-94.

Section 3: Astronomy

13. Subhash Kak, 1992. The astronomy of the Vedic altars and the Rgveda. Mankind Quarterly, 33, pp. 43-55.

14. Subhash Kak, 1995. The astronomy of the age of geometric altars. Quarterly Journal of the Royal Astronomical Society, 36, pp. 385-395.

15. Subhash Kak, 1996. Knowledge of planets in the third millennium BC. Quarterly Journal of the Royal Astronomical Society, 37, pp. 709-715.

16. Subhash Kak, 1998. Early theories on the distance to the sun. Indian Journal of History of Science, 33, pp. 93-100.

17. B.N. Narahari Achar, 1998. Enigma of the five-year yuga of Vedanga Jyotisa, Indian Journal of History of Science, 33, pp. 101-109.

18. B.N. Narahari Achar, 2000. On the astronomical basis of the date of Satapatha Brahmana, Indian Journal of History of Science, 35, pp. 1-19.

19. B.L. van der Waerden, 1980. Two treatises on Indian astronomy, Journal for History of Astronomy 11, pp.50-58.

20. K. Ramasubramanian, M.D. Srinivas, M.S. Sriram, 1994. Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion. Current Science, 66, pp. 784-790.

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Posted: 27 Aug 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  



A Brief Discussion on the Contributions of India
"The first nation (to have cultivated science) is India. This is a powerful nation having a large population, and a rich kingdom (possession). India is known for the wisdom of its people. Over many centuries, all the kings of the past have recognized the ability of the Indians in all branches of knowledge," wrote Sa`id al?Andalusi, a leading natural philosopher of the eleventh century Muslim Spain (Salem and Kumar, 1991, p. 11). The emphasis in the above quotation is not on India being "the first nation to cultivate science." It is on the fact that the European scholars, as late as the eleventh-century, thought India as a leader in science and technology. This is in contrast with the modern common perception about India in the Western minds or with the colonial period.

Poetry in Science: As early as 2600 B.C., the Egyptian monarch Khufu erected a great "house of writings," thus inaugurating a tradition that, by the time of Rameses II (ca. 1300 B.C.), yielded a collection numbering at least 20,000 papyrus scrolls, each protected in a cloth or leather cover. During the 300 year period, between the sack of Thebes by the Assyrians and the invasion of Alexander the Great's armies in 332 B.C., practically all of Egypt's libraries were turned to ash and dust. We know, of course, that this great loss was soon compensated-and afterward repeated-by the great library at Alexandria. This was not typical of only Egypt. Similar decimation of the written words occurred elsewhere in China, Europe, and the Middle East. The Qin dynasty in China, the Reformation in Europe, and Kublai Khan invasion of the Middle East remind us clearly and concretely: the written words are fragile.

While the textual riches of Alexandria, China, and Rome were being put to the flame, a wholly different tradition of scientific expression was brought to a peak in India, in a manner that would prove enormously more resilient to the vicissitudes of time and adversity. This was the oral, poetic tradition of Indian thought, whose greatest purveyor in astronomy and mathematics was Aryabhata I (b. 476 A.D.). }Aryabhata I, by almost any account, was the equal in Indian astronomy to what Cladius Ptolemy became to the tradition of Greek science in Islam and late medieval Europe.

Aryabhata I composed a most remarkable work in Sanskrit known as the Aryabhatiya. Its text consists of a mere 121 stanzas, each with several lines in varying metre and rhyme scheme. The whole is divided into a brief introduction (ten verses), followed by three major parts, one on mathematics (Ganita, 33 verses), one on time reckoning and planetary models (Kalakriya, 25 verses), and one on the mathematics of the sphere and its applicability to astronomical calculation (Gola, 50 verses).

There are no numbers anywhere in the composition. Nor are there figures, drawings, or equations. The Aryabhatiya expresses the highly sophisticated mathematics of sine functions, volumetric determinations, calculation of celestial latitudes and motions, and much more, in the form of a poetic code. This code, invented by Aryabhata I (though others like it had existed earlier on) and delineated in the introductory section, uses an alphabetical system of numerical notation. Specific values are assigned to specific letters and letter combinations, such that any value can be expressed in words and recited through the given metric scheme.

Use of a poetic code did mean, however, that transmission of this most valuable text could be achieved orally. This means through memorization and spoken transfer, or more accurately, by this particular text becoming a part of living memory among succeeding generations of scholars. This occurred during much of the medieval era, when many famous libraries and teaching centers were destroyed in India, as elsewhere, by foreign conquest and civil strife. However, many books were reproduced later on from the oral tradition

The image brought to us by the history of Aryabhata I's seminal work is indeed striking: at the very moment when Ptolemy's, Hipparchus', Eudoxus' and Euclid's books darkened the Alexandrian sky with textual ash, the Aryabhatiya was being passed and preserved through the most transient yet durable medium, the spoken and memorized word in the hearts of the Indians.

Mathematics: The present place?value notation system (base 10), used to represent numbers, is Indian in origin. The Mayas (base 20) and the Babylonians (base 60) used place?value systems as well, although their systems were different from that of the Indians. The role of place-value notation is quite important in mathematics and computers. For example, the extreme difficulty of performing mathematical operations in the absence of a place?value notation system caused Greek mathematics and astronomy to suffer. Nicholas Copernicus (A.D. 1473?1543) was forced to use the Hindu numerals for their ingenuity (Rosen, 1978, p. 27): "This [Hindu] numeral notation certainly surpasses every other, whether Greek or Latin, in lending itself to computations with exceptional speed. For this reason I have accepted [it]." Copernicus, in his book, On the Revolutions, used Hindu?numerals for his computations while advocating the heliocentric model of the solar system.

Trigonometry deals with specific functions of angles and their applications to calculations in geometry. It unites the disciplines of arithmetic, algebra, geometry, and astronomy. The Alexandrian Hipparchus (ca. 150 B.C.) and Ptolemy (ca. A.D. 100--170) helped to lay the foundations of trigonometry. With the work of Aryabhata I (ca. A.D. 500) in India, trigonometry began to assume its modern form. For example, consider a circle of unit radius, so that the length of an arc of the circle is a measure of the angle it subtends at the center of the circle. In order to facilitate calculations in geometry, the Greeks tabulated values of the chords of different arcs of a circle. This method was replaced by Indian mathematicians with another system that used the half chord of an arc, known today as the "sine" of an angle.

The origin of the word "sine" in trigonometry can be traced to the Sanskrit language. The Sanskrit word for the chord of an arc comes from an analogy with a "bow string," which is called "samasta?jya." The half?chord of the arc was called "jya?ardha," later shortened to "jya." The Arabs borrowed the concept from India and chose a similarly word "jaib" for the mathematical operation, which linguistically means a "lace fold or pocket" used in clothes.

This Arabic word was literally translated into Latin and called "sinus," meaning curved surface or fold. This Latin word was later metamorphosed into "sine" or "sin" in the English language. (Joseph, 1991; Kumar, 1994) Such etymological knowledge can be found in some dictionaries and encyclopedias but, ironically, only rarely in trigonometry books.

When the Arabs borrowed a concept from the Indians, they usually attributed the source correctly, especially in their early medieval literature. They often kept the same or similar pronunciation for many words, as shown by the previous example. In other instances, they translated the Sanskrit word into Arabic.

For example, the Sanskrit word for zero (a Hindu concept) is sunya, which translates literally into the Arabic word sifr. When the Europeans learned of it, they called it cipher or zephirum in Latin. This was transformed eventually as zero in English.

Natural Sciences: Regarding the earth's motion in his heliocentric model, Aryabhata I, some thousand years before Copernicus, suggested that the earth might be in axial rotation, with the heavens at rest, so that the apparent motion of the stars would be an illusion. In order to explain the apparent motion of the sun, Aryabhata I used the elegant analogy of a boat in a river: "As a man in a boat going forward sees a stationary object moving backward, just so at Lanka (Sri?Lanka) a man sees the stationary asterisms (stars) moving backward in a straight line." (Clark, 1930, Gola 9) The interpretation is that a person standing on the equator of the earth (Sri?Lanka) that rotates toward the east would see the stars (asterisms) moving in a westward direction. Aryabhata I's hypothesis of the earth's rotational motion is clearly explained by the analogy of the boatman as given above. He incorporated the concept of relative motion, many centuries before its more formal discussion by the noted Parisian scholar Nicholas Oresme in the fourteenth century. (Toulmin and Goodfield, 1961).

The ancient Indians realized the common connections between plants, animals and humans. They also realized the role of plants in medicine and the role of animals in the preservation of nature. In view of the importance of trees for humans, unnecessary cutting of a tree was against social and religious codes in India. Asoka (2nd century B.C.), a king in India known for his Maurya?empire and propagation of Buddhism, defined a strict law against the demolition of trees. Similarly, protection of animals led to the movement of vegetarianism. The Hindus went to the extent of worshiping both life forms; Animals and plants are revered along with gods. It is a curious fact that the Hindu concept of transmigration of souls was a common belief among the Greek philosophers and not the Greek society. Some connections between the Greek philosophers and Indian philosophy and the possibility of such interactions will also be explored.

Kanada wrote a book, Vaisesika?Sutra, in which he proposed that matter is made up of small particles, called parmanu (atoms). Kanada's description is based on the impossibility of infinite division of matter: "parmanu is not visible; the non?perception of atoms disappears when they mass together to form a combination of three double?atoms, a combination which does assume visibility." Cyril Bailey compared the Indian description of atoms with the Greek description, and wrote: "It is interesting to realize that an early date Indian philosophers had arrived at an atomic explanation of the universe. The doctrines of this school were expounded by Vaicesika Sutra [VaiÑesika?Sãtra] and interpreted by the aphorisms of Kanada . . . .Kanada works out the idea of their combinations in a detailed system, which reminds us at once of the Pythagoreans and in some respect of modern science, holding that two atoms combined in a binary compound and three of these binaries in a triad which would be a size to be perceptible to the sense." (Bailey 1928, p. 64)

As this section amply demonstrates that India made substantial contributions to science and technology in the ancient and medieval period. However, such contributions are not in the mainstream knowledge in the absence of its inclusion in the academic curricula. This project is a modest effort to bridge such gaps.

Salient Features
Most writings related to Indian scientific contributions are written in specialized or obscure journals on Indology. Most articles are written in isolation with little or no connection/comparison with the western science or with other contemporary cultures. In the absence of a cross-cultural study, it is unlikely that such knowledge will ever be assimilated into the mainstream knowledge of science. For this reason, I plan to write my articles/modules with a cross-cultural emphasis. Such a study will not be in conflict with the mainstream science; it will fill the gaps in our understanding of science. I also plan to publish my articles in the mainstream journals/magazines (examples: Science as Culture, The Physics Teacher, Journal of College Science Teaching, or American Educational Research Journal)

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Joined: 31 Dec 1969
Posts: 481

Posted: 02 Sep 2002    Post subject: Re: Ancient (and recent) Indian Mathematics  


Kerala School of mathematics

For more on the Kerala School of mathematics, see 'Science and Technology in Ancient india',published by Vijnan Bharati, Mumbai, pp.56.Prominent among the Kerala School were;

Madhava (1340-1425 ce)
Neelakantha Somayaji (1445-1545 ce)
Jyeshtadeva (1520 ce)
Putumana Somayaji (circa 1730)
Raja Sankara Varma

Cross posted from Indiancivilizations

I would like to add contribution of Kerala to Calculus-
On the page 111 of the research paper "The Sanskrit of Science" by Dr.
Frits Stal (Journal of Indian Philosophy, vol. 23, p.73-127, March 1995),
it was mentioned, " The fact remains that Leibnitz, Madhava , Newton,
Nilakantha and others made the same discoveries, the Indians even
Madhava and Nilakantha were from Kerala.
N. R. Joshi.

If you had to put your finger on why Indian mathematics did not become the engine of engineering and then the economy that their european counterparts became, what would be the reason.

In order for any academic field of endeavor to flourish at an advanced level, there must be peace and relative prosperity in the land and such endeavors must be supported by the state. A good example is the Indian Institute of Science and its successor institutes the IIT's which are churning out good work at a steady rate today. It is AlBiruni who remarked that Ghazni's marauding raids had left all of northwest India in ruin and bereft of the presence of savants in the sciences and mathematics. He specifically makes mention of the fact that many have fled to states beyond the reach of his master. It is no coincidence that Ujjain which was a center of scientific activity during pre-Islamic times ceased to be a center after the medieval era. In 1304 CE Alla ud din in one of his many jihads completely destroyed Ujjain, the center of Indian scholarship. North India never recovered from this as from the earlier destruction of Nalanda by Bakhtyar Khalji in 1198 CE, which destroyed Buddhist scholarship.

The center of gravity of Indian scholarship slowly shifted southwards until the 18th century when the British delivered the coup de grace of English based education, which inflicted the double whammy of lack of continuity as well as cutting of the vast majority of Indians from access to any educational institution.

But the spirit of Indian Mathematics could not be extinguished. It came back with a roar in the person of Ramanujam, the greatest number theorist in all of human history.


The achievements early Hindu science are hardly known in an objective form. They are either being neglected due to the efforts of the leftist Anti-Hindu academics from the West and India or exaggerated by uneducated Hindus. One of the great Hindu theories of which we get some limited glimpses are the ideas on sound propagation which are discussed at length in the mImAsa text of shabara svAmin. In short they include the following idea for the transmission of sound:
1) nAda or sound is a property of vAyu. 2) The sound movements are constituted by a series of air movements of the nature of a current termed vAyusantAna. 3) The sound causes the vAyu paramANus to successively undergo saMyoga vibhAga that s conjunctions and disjunctions resulting in spreading of the original impact as sound.

The vaisheShika scholars like prashastpAda and the later shrIdhara introduced the concept of the sound wave. He explicity compares sound to the waves in water. They posited that at anytime sound forms a circle and spreads as circles or spherical shells from the source: yathA jalavIchyA tad avyavahite deshe vIchyantaram upajAyate tato.apanyat tato.apayaditpanena krameNa vIchi santAno bhavati tatha krameNa shabda santAno bhavati /

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