Research Into Indic Mathematicians

[Guest]

There are some typos , the Suri name is spelled Sun

[Guest]

There is one quality which the Arabs and the Arabized savants from central asia exhibited that by and large the occidental mathematicians have not, even till today. They have given credit to the Hindu for the things they learned from us, which the occident has rarely done. The Arab books have said repeatedly that they learned most of algebra and astronomy from the Hind and the Sindhind (Siddhanta). Saad al Andalusi was equally effusive when he asserted categorically that the Hind were far ahead of the rest of the world in certain fields. Such an acknowledgment has been very rare from the countries of Europe, after they began colonizing us in the 18th century and it was almost absent after the discovery of sanskrit. It was official policy of the Vatican to take credit for discoveries made in lands colonized by powers that were under the control of the Vatican. The calculus is a case in point . where the circumstantial evidence of wholesale theft in related field as such as Astronomy, navigation, the making of the calendar, etc, etc. is very strong.

There is an obstinacy among the occidentals to refuse to recognize even well accepted facts such as the number system as being a hindu discovery , even when faced with the evidence. A good case is a childrens book on Counting by Denise scmandt Besserat

[Bodhi]

^

<!--QuoteBegin-Kaushal+Mar 6 2009, 02:06 PM-->QUOTE(Kaushal @ Mar 6 2009, 02:06 PM)<!--QuoteEBegin-->There are some typos , the <b>Suri </b>name is spelled <b>Sun</b>
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<!--emo&--><img src='style_emoticons/<#EMO_DIR#>/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo--> and both are congenitally related!

[Hauma Hamiddha]

Kaushal - You may want to add the name of vaTeshvara of the lATa country to the list. I am currently caught up with some issues and do not have the time to say too much more right now on this interesting topic. However, if you want an electronic copy of vaTeshvara's works on spherical geometry and astronomy drop me a mail and I will try to get for you.

[Guest]

<!--QuoteBegin-Hauma Hamiddha+Mar 8 2009, 08:49 AM-->QUOTE(Hauma Hamiddha @ Mar 8 2009, 08:49 AM)<!--QuoteEBegin-->Kaushal - You may want to add the name of vaTeshvara of the lATa country to the list. I am currently caught up with some issues and do not have the time to say too much more right now on this interesting topic. However, if you want an electronic copy of vaTeshvara's works on spherical geometry and astronomy drop me a mail and I will try to get for you.
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Good point, i dont know how i missed him. i would certainly appreciate a copy of the same

[Guest]

This is an excerpt from a forthcoming monograph under construction titled TIME AND THE CALENDAR IN INDIA A HISTORICAL PERSPECTIVE " - a tentative title

Pl. see the remarks on the propensity of the Occidental to ignore or downgrade the indic contribution


CHAPTER I INTRODUCTION

In order to understand the Indic approach to the challenges faced by the human , one must understand the cosmology and the calendar of the Hindu. The calendar and the cosmos have always played a large part in the consciousness or weltanschuung of the Hindu and he spent a large portion of his observational powers in deciphering the universe around him. In this he was not alone, as we know now that other ancient civilizations, such as the Babylonian, the Egyptian and the Chinese had similar interests and a curiosity about the heavens. But the answers the Indic came up with were quite prescient for his time and the resulting numbers were far more accurate than the European world realized or knew, even millennia after the Indic discovered these periodicities. The extraordinary allergy that the Occidentals, with a few notable exceptions, have exhibited to the serious and scholarly study of the Indic mathematical tradition, and when they have done so, the vehemence with which they have denied the value of these traditions, is astonishing to say the least. In those instances where they recognized their value, they have tried their best to assert that it was plagiarized from the Greeks and later the Babylonians. When such a stance became more and more difficult to sustain, they maintained that it was not autochthonous to the subcontinent but brought in from elsewhere by the largely mythic people called the Aryans. The consistency with which the Occidental denied the Indic contributions is exemplified in the writings of various Indologists such as Whitney , Bentley , Moriz Winternitz Albrecht Weber , W W Rouse Ball, G R Kaye, Thibaut and continues on till today in the works of David Pingree . As we have emphasized, there were exceptions such as Brennand, Playfair, Colebrooke, Sewell, and Bailly.


 


THE RELUCTANCE OF INDOLOGISTS IN THE OCCIDENT TO ACKNOWLEDGE THE VEDIC EPISTEME


The resulting illiteracy on the part of the western scholar on matters pertaining to India was lethal to the understanding of their own history and leaves Occidental historians, the task of explaining why there was no progress in Europe between the time of the Greek contribution to the mathematical sciences and the flowering of the renaissance resulting in the Keplerian paradigm shift, a period exceeding 1600 years. We are compelled to remark that the sudden explosion of knowledge that took place during the renaissance, occurred shortly after the Jesuits sent 70 scholars to Malabar in the 1500’s . When it came to reconciling himself with the obvious depth of knowledge of the ancient Indic, the occidental had no hesitation in coming to the conclusion that the Indic had borrowed everything from Greece. But he is more than reluctant to accept that a massive transfer of knowledge took place from India to Europe, even though the evidence is far more compelling. We will remark in passing that there is a palpable difference in the manner in which the Occidental views the transmittal of knowledge, depending on the directon in which the transmittal is alleged to have transpired.

DIFFERING STANDARDS OF CLAIMS FOR TRANSMISSION OF KNOWLEDGE
In fact no study of this kind would be complete without a reference to the differing standards by which Occidentalists have concluded whether a particular discipline was imported or exported out of the Occident. We quote C K Raju
“However, we have also seen that the standard of evidence is not uniform, but varies with the claim being made. The standard of evidence required for an acceptable claim of transmission of knowledge from East to West, is different from the standards of evidence required for a similar claim of transmission of knowledge from West to East. Thus there is always the possibility that similar things could have been discovered independently, and that western historians are still arguing about this, even in so obvious a case as that of Copernicus. Finally we have seen that this racist double standard of evidence is not an incidental error, but is backed by centuries of racist tradition, religious exhortations by Popes, and by legal interpretations authoritatively handed down by, say the US Supreme Court.”
Priority and the possibility of contact always establish a socially acceptable case for transmission from West to East, but priority and definite contact never seems to establish an acceptable case for transmission from East to West, for there is always the possibility, that similar things could have been discovered independently.

“Hence to establish transmission we propose to adopt a legal standard of evidence, good enough to hang a person for murder. Briefly we propose that the case for any must be established on the grounds of
1. Motivation,
2. opportunity,
3. Circumstantial evidence and
4. Documentary evidence.
The importance of epistemological continuity has been repeatedly stressed above; any such claim must also take into account epistemological issues”
Examples abound, especially when it comes to areas such as Mathematics, Astronomy and Linguistics and the discovery of the origin of scripts. In particular we cite the instance of David Pingree’s PhD thesis titled “Materials for the Transmission of Greek astrology to India”. Notice he does not ask whether such a transmittal ever happened. That is a given, a hypothesis that need not be proven. This is another example of a circular argument. Assume the answer that there was a transmittal, in the initial hypotheses, merely because there was probable contact however, tenuous that may be, and then claim that it is an incontrovertible fact.
The conventional wisdom in the West was that the Jesuits were sent to convert the Indics to the Christian faith and as a byproduct teach them the finer points of the occidental civilization. In reality it turns out, they were sent to learn a whole host of topics such as navigation, mathematical techniques including trigonometry, and the Indian approach to calendrical astronomy. In short the Jesuits embarked on a systematic study of the Indic episteme, since it was obvious that the Indics had made considerable advances, which the Jesuits were quick to realize were far in advance of their own . We are in the process of chronicling the study of those individuals who in turn studied India or studied subjects in which the Indics had great proficiency, beginning with ancient Babylon to the British, primarily to understand the role that India and the Indic episteme played in the renaissance of Europe. While there is nothing here that can be regarded as being morally reprehensible, one wonders why there was the extreme reluctance to admit that they learned from others too. In this one has to concede that the Arab scholar during the heyday of Islam observed a higher degree of ethics than his brethren in the Occident, because he never exhibited the slightest hesitation in attributing to the Indic the episteme that he had learned from him.

Typical of the stance of the Occidental is the attitude of the late Professor David Pingree who occupied the only faculty position that I am aware of on the History of mathematics in the western world at Brown University. On the one hand, Professor David Pingree, spent most of his entire professional career studying Indian texts and manuscripts. He compiled and catalogued a comprehensive bibliography of all materials available on the computational sciences in India. The work was so voluminous, that the net result was a 4 volume compendium which he appropriately termed the Census of the exact sciences. Yet he kept insisting that India lacked the astronomical tradition necessary for the development of these techniques. To those who defend Prof Pingree, I have a simple question to ask. Why did Prof Pingree spend his precious time cataloging the census of the exact science in India, especially when he was vociferously proclaiming that India did not have an Astronomical tradition? He hints at the answer to this, by saying that historians have had to rely on disparate and often desperate sources to decipher what the Greeks knew. In other words, he makes the assumption that the Greeks had a rich tradition in astronomy despite the paucity of materials attesting to such a tradition, whereas the Indics, who had a voluminous literature on the topic, should be decreed as having no tradition in astronomy. The obvious non-sequitor inherent in such a stance, seems to escape the notice of most people, and even if it does not, the attitude seems to be to let this massive misrepresentation continue as long as it is not challenged It is unfortunate that such blatantly racist views go unchallenged, especially by the people most affected by this massive lie..

We view the study of history and philosophy of science as central to the understanding of any civilization and its ethos. And hence we make no apology for the emphasis on science, and especially on Astronomy in our own studies of the Indic peoples. Such an emphasis has been lacking in the past partly because major advances in the sciences, that have the potential to be of use in the study of history, have occurred only recently in the last 100 years and partly also because it has been difficult to find individuals who have proficiency In more than one discipline, such as Astronomy and Archaeology.

The Ancient Vedics seemed to have an obsession for precision as well as a fascination for large numbers. They also subscribed to the notion that the planet earth and the solar system were of immense antiquity without a beginning, in contrast to the creationist theories propounded by many in the Occident till recently. A combination such as this makes an excellent prerequisite for time keeping and for devising a useful and practical calendar. So, they turned to the sky and began to decipher the meaning behind the various cycles and periodicities that they observed, in order to help them plan their activities, such as the planting of their crops. In general it has to be admitted that the Indic approach to the measurement and calibration of time and the calendar, has been extraordinarily thorough, and if precision were the sole criterion it is obvious they had an inordinate respect for the importance of such precision. Let us see how they went about developing a calendar that would convey a lot of information merely by knowing the day of the month, after constant observation of the sky both during the day and the night over centuries. The result was a highly efficient and accurate calendar. The added bonus of such a system is the usefulness of the recordings of ancient astronomy to decipher the age at which various events took place, and the development of methods now known collectively as Archaeo-astronomy. In this chapter we will give a rather brief introduction to Indic astronomy, and in subsequent chapters we will come back to the historical development of the key ideas behind calendrical astronomy
The basic information the ancients used for purposes of time keeping were the motions of the sun and the moon relative to the earth. So far nothing unusual, as did all the other ancients. The cycles they used including the day, the week, the fortnight, and the month are shown in Table 1.
TABLE 1 CYCLES OF TIME IN ANCIENT INDIA

60 ghatikas (or 30 muhurtas or 8 praharas) in a 24-hour period (ahoratra)
15 tithi in a paksha or a fortnight, 15th is Poornima or amavasya
The Lunar Month (2 pakshas in a month), shukla waxing and krishna waning
The Sidereal Year(Nirayana) , the Tropical Year,the Anomalistic Year
The six seasons of a year (each season comprises 60 days )
60 year Jovian cycle/ 360 year ‘divine cycle
2700 year cycle of the Sapta Rishi or the Ursa Major
25,800 year cycle of the asterisms called the Great Year or the precession cycle
432,000 year cycle called a yuga (= duration of Kaliyuga)
4,320,000 year cycle known as the Maha Yuga
Kalpa, the cycle consisting of 4.32*10**9 years


We will give a brief history of Indic astronomy in the next chapter, to put the astronomical discoveries in the proper context within the larger canvas of Indic history. Contrary to the conventional wisdom of occidental versions of the Indic narrative, as exemplified by the writings of David Pingree, India had a very strong and consistent tradition of scholarship in the so called exact sciences of antiquity (as Neugebauer called them) such as astronomy and mathematics. The list of famous astronomers and mathematicians is staggering both in the quantity, and in the quality of the contributions, as well as the time span over which it occurred. We list in Table 15 in the appendix, significant contributers to the episteme. That such a list would include such a large number of individuals who made significant contributions, was certainly a revelation for me.

INDIAN COSMOLOGY AND TIMELINES OF HISTORY

We give a introduction to the Indic concept of Time and the cosmological time frames of the Yugas. There are some who feel that the reference to a Mahayuga going back 4,320,000 years, is without foundation, since we do not have recorded history going back that far and the more appropriate measure to us is a time scale that is consonant with the start of river valley civilizations . There is a suspicion that somewhere along the historical past, there was confusion in the interpretation of the various definitions of the year, which has resulted in such long periods being assigned to the Yugas such as Kaliyuga. We will discuss later the relevance of the divine year which is mentioned as being comprised of 360 tropical years. For example the duration of a Kaliyuga in Divine years is a more manageable 1200 years and the entire Mahayuga is 12000 years which is of the same time scale as the beginning of river valley civilizations, if we assume that there was a confusion regarding the interpretation of the year. We will discuss this later. In my view, it is the attempt of the ancient Indic to describe geologic time scales associated wth the beginning of recorded hstory that causes confusion and has invited the ridicule of some in the occident such as Thomas Babingtin Macaulay and has prompted him to chatracterize the entire literature of India as being worthless. ..

[Guest]

Pingree claims that the only extant copies of the Paitamaha Siddhanta are those that were incorporated in the Vishnu Dharmottara Purana. Has anybody seen this purana and is it available in printed copy. To whom can the Paitamaha siddhanta be attributed.


The contents of the monograph on the calendar ( Time and the calendar in India 1
A historical perspective ) as presently envisioned include the following


1
Table of Contents 2
Chapter I Introduction 6
The reluctance of Indologists in the occident to acknowledge the vedic episteme 7
Differing standards of Claims for transmission of knowledge 7
Table 1 Cycles of Time in ancient india 9
Indian Cosmology and Timelines OF History 9
the Celestial Sphere 10
Heliocentric vs Geocentric Paradigms 10
Figure 1 The concept of the Celestial sphere 10
Figure 2. The celestial sphere showing the ecliptic, its inclination to the celestial equator and the coordinates right ascenson, declination 11
ecliptic क्रांतिवृत (Kranthivruth) 12
Figure 3. The Ptolemaic Armillary sphere 12
Figure 4 The path the Sun traverses through the CONSTELLATIONS OF the Zodiac 13
The coordinates of the Celestial sphere 13
Figure 5 and 6 The celestial Sphere indicating the Solstices and the Equinoxes 14
equinox वसंत संपत (Vasanth Sampat) Vernal equinox 15
precession of the Equinoxes 15
Table 2 16
Solstice 16
synopsis of equatorial coordinate system 17
Figure 7 Zenith and altitude 17
The Year 18
Table 3 Difference between the Sidereal and Tropical Year 19
Hindu calendar - Year numbering 19
Table 4 SUMMARY of various Measures of a year 20
Table 5 Planetary Revolutions in Mahayuga of 4,320,000 years 20
The Month 21
Table 6 Measures of a month 21
Figure 8. 22
Table 7 The names of the solar months( Sauramaas) are as follows 23
Table 8 Months of the lunisolar calendar 23
The elements of the Panchangam,,, 24
Table 9 The 5 elements of the Panchanga 24
The Tithi 25
Week days ( Vaara) 25
Table 10 Days of the Week 26
Table 11 The Days of of the Indian Lunar Synodic Month 28
The Nakshatra and the key role it plays in Ancient Indian Astronomy 29
Nakshatra and The Precession of the equinoxes 30
Table 12 The Indian Nakshatra 31
Table 13 Values for the Lunar sidereal orbit and the Lunar Synodic orbit 32
Karana 32
Yoga 33
Table 14 Comparison of some astronomical constants 34
How old is the universe, Kalachakra and the Yuga concept, Hindu cosmological time frames 35
Table 15 a day in Brahma’s life of 1 Kalpa 35
Table 16 How old is the universe 36
When and where were the 12 signs of the zodiac first mentioned 37
Figure 8. The shift of the vernal equinox through different Nakshatras over 6 millennia 37

Chapter II History of the Calendar in India 40 undr construction
Appendix A Glossary 41
Appendix C Pictorial Vignettes 68
Appendix D Vedic Epistemology 70
The Vedic Paradigm for the development of Knowledge 70
Appendix e Index of Indic Savants in the computational sciences from antiquity 77
References 80
Appendix f Select Bibliography 81
Abbreviations 84
Primary and other Sources in the Indic Sciences of antiquity 86
Primary Sources 86
Other Sources 89
Bibliography Kosambi’s catalogue of Primary Source Material 99
Kosambi’s Chronological Outline. 103
Sources of Sanskrit Manuscripts In India 105
Appendix G Astronomical Observatories in India 114
Stone Observatories of Jai Singh 114
The old Madras Observatory 114
Calcutta 115
Lucknow 115
Thiruvananthapuram 115
Pune 115
Calcutta 116
Indian Astronomy in the early 20th Century 117
Hyderabad 117
Kodaikanal 118
Hyderabad 119
NainiTal 119
Mount Abu 120
Appendix H Resources for Sanskrit Manuscripts outside India 121
Appendix I proposed Chronology 127

For the small universe of people interested in topics such as these, what would you like to see included in such a book. ( I cannot say i would be able to satisfy every desire ) but i am curious as to what people are curious about

[dhu]

http://ckraju.net/blog/

“Newton was an honest theologian. For fifty years he diligently researched all the manipulations which entirely transformed the Bible. Brought up virtually as an orphan, and living unmarried, he had no confidante to turn to. Afraid of the backlash, he understandably hid his work: an 8-volume history of the church.

What is inexcusable is the way Newton’s 50-year effort remained hidden even after his death. Suppressed for over 250 years! It is Western historians I accuse of utter dishonesty, not Newton. If they could knowingly hide Newton’s lifework for so long, and continue trying to keep it hidden as Whiteside more recently did, nothing that Western historians say should be trusted or accepted on faith. For several centuries, European historians were mainly priests, writing in times of intense religious fanaticism, so their mindset was that of missionaries, out to glorify themselves and belittle others by any means possible, and without any regard for the facts.

Of course, Newton did not invent the calculus, but neither does he claim credit for it. (It is Western historians who credit him for it.) Newton acknowledges a whole series of earlier mathematicians, including Cavalieri. Newton claims credit mainly for having made the calculus rigorous .

Newton’s claim to rigour was wrong, even by Western standards of proof, and his more discerning contemporaries like Berkeley were well aware of it. However, Newton’s attempt at “rigour” socialised the imported calculus, and made it socially acceptable in the West. (Descartes and Galileo had earlier rejected it.)

It is interesting to see the effect this had on his physics. Hoping to make calculus rigorous, Newton made time metaphysical. (“Absolute, true, and mathematical time” which flows on “without regard to anything external” is obviously a metaphysical notion, in fact, a religious one.) As pointed out in my expository paper (”Time:What is it that it can be Measured?” in Science and Education , 2005) this was a step backward from Newton’s predecessor, Barrow, who had called Augustine a “quack” for evading a clear physical definition of time. Barrow himself tried to supply such a definition, later corrected by Poincaré.

The failure to define time properly led to the failure of Newtonian physics, and its replacement by Poincaré’s special theory of relativity. (The speed of light is postulated a constant, just to be able to measure time.)

Newton, in the course of his priority dispute with Leibniz, over calculus, did claim credit for the sine series, and we know that this was factually false, for the sine series was known in India from a couple of centuries earlier.

However, this claim too has to be put in the context of the prevailing Doctrine of Christian Discovery: according to which only Christians could be regarded as discoverers. The church decreed that ownership of a piece of land must go to the first Christian to spot it. (Hence, the claim that Columbus “discovered” America, or that Vasco da Gama “discovered” India.) The people already living on the land did not matter, and the church encouraged their killing on a mass scale, where possible, as actually happened on three continents. This doctrine was made into a law by the US supreme court, and that is where the current US law on land-ownership vis-a-vis the “Red Indians” stands.

So, the point is this. Despite the horrendous historical injustice involved, it would be completely incorrect to say that anyone who owns a piece of land in the US today is a thief. It is not a matter of personal dishonesty, at all, but a matter of systematic appropriation.

The same thing applies to what I have said about Newton. His claim to the sine series was part of a systematic process of intellectual appropriation during the centuries of extreme religious fanaticism in Europe: it was not a matter of personal dishonesty. Copernicus did nothing different, nor did Clavius, Tycho Brahe; in fact, these three directly knew the sources from which they were appropriating.”

http://ckraju.net/blog/?p=30

[Bodhi]

Kaushal wrote the below elsewhere. Pasting it here, since he provided some interesting data:

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->In all fairness DR. Susheeelan, I have to say one thing about the Arab
savants. It was a very rare occurrence that the Arabs and other savants
would claim credit for something they did not do . They consistently
called the number system they propagated as Hindsa. At the Bayt al
Hikmah in baghdad (House of wisdom)the had a translation house as well
as many well known scientists under Haroun AL Rashid. At Toledo in
Moorish Spain they had the worlds greatest library at the time when
it was reconquered by Spain in 1085. But the creative spark died
outbecause consrvative elements in Islam took over from the MUtazili( do
a google on this)

I quote from my forthcoming book
Anno Domini Nostri Iesu (Jesu) Christi ("In the Year of the Lord Jesus
Christ") 1268 in a little village called Cambridge north west of
London, a group of workmen began constructing structures to house what
would become in time one of the great learning centers of Europe and the
world. But in 1268 Europe was largely a backwater. It would be well over
300 years before Cambridge could boast a world renowned scientist on its
roster. The writings of the ancient Greeks were largely lost, and it
was only after Toledo and its world famous library was reconquered from
the Moorish rulers of Andalusia and Southern Spain in 1085 CE that
Europe was able to make strides in the various branches of knowledge
thanks to the large number of Arab documents that now fell into the
hands of the Spaniards at one of the greatest libraries of the middle
ages. For example, Ptolemy’s Almagest (from the Arabic Al Majisti
) was translated into Latin from Arabic reputedly by a Gerard of Cremona
in 1175 CE. This was the sole text in Astronomy for the majority of the
people in Europe during the ensuing centuries, till the 17th century.

But throughout history, and especially thanks to the Arabs, the work of
the Hindus was increasingly available to the Europeans. In 1068 CE Said
Al-Andalusi, as far as we are aware, the first historian of Science and
as his name indicates from Moorish Spain, wrote Kitab Tabaqut al-Umam in
Arabic(Book of Categories of Nations, Livres des Categorie des Nations).
The book was translated into French in 1835 by Regis Blachere and
into English by Alok Kumar in 1992. The text was produced in Spain in
the 11th century in which Said was reported to have made the observation
that only eight nations were interested in and comprehended Science .
These eight people were the Hindus, the Persians, the Chaldeans, the
Jews, the Greeks, the Romans , the Egyptians, and the Arabs. In this
list, he placed the Hindus at the head because ‘Les Indous,
entre tout les nations, a traverse le siècle et depuis
l’antiquité, furent la source de la sagesse, de la justice et
de la modération. Ils furent un peuple, donne de vertus
pondératrices, créature de pensées sublimes,
d’apologues universel d’inventions rares et de traits
d’esprit remarquables’,
“Among all nations, during the course of centuries and since
antiquity the Indics were the source of wisdom, justice and moderation.
We credit the Indic nation and its people with excellent intellect,
exalted ideas, universal maxims, rare inventions and wonderful talents.
They are indeed gifted with a trait characterized by a remarkable spirit

Said al Andalusi goes on to say “To their credit, the Indics have
made great strides in the study of numbers and of geometry. They have
acquired immense information and reached the zenith in their knowledge
of the movements of the stars (astronomy) and the secrets of the skies
(astrology) as well as other mathematical studies. After all that, they
have surpassed all the other peoples in their knowledge of medical
science and the strengths of various drugs, the characteristics of
compounds and the peculiarities of substances. "<!--QuoteEnd--><!--QuoteEEnd-->

Kaushal, Good luck with your new book!

I have a small comment about this aspect, of Moslems in general and Arabs in particular being honest about giving credit to Hindus (and others) for their inventions.

For this, one has to look deeper in the moslem psychology. For a musalman, even more for an arab, the Supreme Knowledge, the ilm-haqIqI, was after all relealed only to one of theirs. All other human knowledge, in moslem psychology, is mundane and bears no comparision to the Revealed Knowledge, therefore giving its credit to others is no big deal. In his 'Problem with Secularism, 2007' Elst has written a very informative essay on the psychological aspects of the alleged Arab intellectual generosity of giving due credit to others.

[acharya]

1. Bibhutibhusan Datta, 1929, The Hindu Contribution to Mathematics, Allahabad
2. Umesh Mishra, 1936, Physical Theory of Sound and its origin in Indian Thought, Allahabad
3. P.C. Ray, 1902, History of Hindu Chemistry, 2 Vols Calcutta
4. R.C. Datta, 1877, Materia Medica of the Hindus, Calcutta.
5. Dhirendranath Mookerjee, 1921, pp. ‘Notes on Indian Astronomy’, Journal of the Department of Letters, Vol. V, pp. 277-302.
6. Ekendranath Ghosh, 1929, ‘Was the Equation of Time Known to the Vedic Sages?’ IHQ, Vol.V, pp.136-37
7. B.B. Datta, 1932, The Science of Sulva- A Study in Early Hindu Geometry. Calcutta
8. G. Thibaut, 1875, ‘On the Sulva-sutra’ JASB pp. 227-275

[Husky]

Moorish civilisation and even the science of "islam's" golden age were frequently (largely?) pioneered by non-religious kaffiris of muslim birth. There's a lot of writers who wrote on this, including McCabe IIRC. Umm, look over Ali Sina and/or Ibn Warraq and/or Anwar Sheikh - one or perhaps all of these covered the so-called "islamic golden age" and how it was not islamic, with reference to first-hand quotes and historians I think.
Was it the Australian Atheist site in my sig that also covered the same? Not sure anymore.

[HareKrishna]

<!--QuoteBegin-Husky+Oct 11 2009, 04:19 PM-->QUOTE(Husky @ Oct 11 2009, 04:19 PM)<!--QuoteEBegin-->Moorish civilisation and even the science of "islam's" golden age were frequently (largely?) pioneered by non-religious kaffiris of muslim birth. There's a lot of writers who wrote on this, including McCabe IIRC. Umm, look over Ali Sina and/or Ibn Warraq and/or Anwar Sheikh - one or perhaps all of these covered the so-called "islamic golden age" and how it was not islamic, with reference to first-hand quotes and historians I think.
Was it the Australian Atheist site in my sig that also covered the same? Not sure anymore.
[right][snapback]101882[/snapback][/right]
<!--QuoteEnd--><!--QuoteEEnd-->
Some point the superiority of islamism over christianism on the fact that islam,including Mohamed ,suported science(Mohamed is quoted to say:you should search science as far as China'and'the scientists are the best in front of God'or something like this),while christianism was against science(considered waste of time).
Even if many scientists was non-muslims ,islamism not only tolerate but even suported science .

[Husky]

<!--QuoteBegin-HareKrishna+Oct 11 2009, 06:42 PM-->QUOTE(HareKrishna @ Oct 11 2009, 06:42 PM)<!--QuoteEBegin-->Mohamed is quoted to say:you should search science as far as China'and'the scientists are the best in front of God'or something like this[right][snapback]101887[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->There are online Korans I think, possibly even translations. Any link to the verse? I don't remember reading that (then again, IIRC I quit midway through reading the koran; it's only the babble that I read in full)


<b>ADDED:</b> Is the blue bit in the following related?
www.hraicjk.org/muslim_spain_and_islamic_science.html
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Muslim Spain and Islamic Science
(From "A Golden Era?" Chapter7, "The Wrath of Allah" plus new material)</b>

[...]

Islam and Knowledge

Muslim modernists have tried to argue that one verse out of eight in the Qur'an states that man must search for knowledge. However the Arabic word used is "ilm" which refers to "religious knowledge" rather than knowledge of the real world. Even today, a number of Western scientists compartmentalize the two types of knowledge - one compartment for rational knowledge from Monday to Friday and one for the supernatural on Sunday. Thus, Averroes (Ibn Rushd, 1126-1198) argued that "cultivation of science should be totally independent of the Muslim creed."'0

In the fourteenth century Islamic fundamentalists finally succeeded against secular knowledge. "But then the dark night of ignorance, ... the flood of misdirected scholarship [theology], enveloped the glimmer (of truth)." ~ Since that time science and technology have retrogressed in the Islamic world. Examples abound: for example, Ibn Rushd was tolerated in Muslim Spain by Kaliph Abu Yaqub but when the latter died in 1184, the new Kaliph, Abu Yusuf prohibited the study of science and logic. Ibn Rushd's "Commentaries on Aristotle" wherein he opposed "revealed" and unverifiable truths and supported rational truths proved by science were condemned by both Islam and the Christian Church. Ibn Rushd and other students of philosophy were exiled from Cordova and most of his books were burnt.

Omar Khayyam was a Persian poet, mathematician and astronomer. His works were considered skeptical, irreverent and sacrilegious by the ulama and had to be passed around covertly.

Another great Muslim thinker was Ibn Sina (Avicenna, 980-1037). He had a profound knowledge of many subjects, he had memorized the Qur'an at the age of ten and was a doctor at seventeen. His great work on medicine, "Al-Qanum" remained the textbook for many centuries. But he was an independent spirit: if he thought a glass of wine would prove to be a pick-me-up he would have one regardless of what was written in the Qur'an. On several occasions he had his books banned and had to flee persecution. A contemporary Islamic fundamentalist, Imam Al-Ghazzali 12 called him an infidel and even today fundamentalists attack him. Witness this quote from the Saudi- financed "Islamic World Review

"The story of famous Muslim scientists of the Middle Ages such as Al Kindi, AI-Farabi, Ibn-al-Haytham and Ibn Sina shows that, aside from being Muslims, there seems to have been nothing Islamic about them or their achievements. On the contrary, their lives were distinctly unIslamic. Their achievements in medicine, chemistry, physics, mathematics and philosophy were a natural and logical extension of Greek thought." 13

Al-Kindi was a rationalist who had his library confiscated and, at the age of sixty, was subjected to fifty lashes.

Al-Farabi "depended on pure reason, not Shariah, for discriminating between good and bad." 14By order of the Emir he was hit on the head with his book a number of times and consequently he lost his sight.<!--QuoteEnd--><!--QuoteEEnd-->

[HareKrishna]

<!--QuoteBegin-Husky+Oct 11 2009, 06:53 PM-->QUOTE(Husky @ Oct 11 2009, 06:53 PM)<!--QuoteEBegin-->Any link to the verse?
<!--QuoteEnd--><!--QuoteEEnd-->
i read it some years ago in a book about world religions at the chapter about islam.
so i dont remember if it was in koran or hadīth.

[ramana]

X-posted from BRF....

<!--QuoteBegin-"Neela"+-->QUOTE("Neela")<!--QuoteEBegin--><!--QuoteBegin--><div class='quotetop'>QUOTE<!--QuoteEBegin-->X-post from Maths thread<!--QuoteEnd--><!--QuoteEEnd-->

Gentlemen,

I often engage in writing mails myself on issues supporting India. But here is something that I need Mathematicians/Maths fans to do.

Prof.Marcus du Sautoy is doing some great service in the United Kingdom popularizing Maths. He comes often on radio and TV. And in general a very open person. He recently aired a programme called Story of Maths where he traces the origins of Mathematics.
His home page is here: http://people.maths.ox.ac.uk/~dusautoy/


As far as I know, he is the first person to have acknowledged the works of Kerala School of Mathematicians in public domain in the West
See here:
http://www.telegraph.co.uk/education/31368...the-answer.html

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->It therefore came as a huge shock to me to discover recently that a school of Indian mathematicians in Kerala in south India arrived at this formula several centuries earlier. It should, in fact, be called the Madhava formula, in honour of the Hindu scholar who first hit upon it.

π was not the only great mathematical discovery made in India. Negative numbers and zero – concepts that in Europe, as late as the 14th century, were viewed with huge suspicion – were being conjured with on the subcontinent as early as the seventh century. <!--QuoteEnd--><!--QuoteEEnd-->


<b>It is important that we use this guy and pass on more details to him.
So someone eqipped with a good idea of Indian Maths/Astronomy books like Surya Siddhanta, Panchange etc should contact him and let him know the details.</b>

Cheers

<!--QuoteEnd--></div><!--QuoteEEnd-->

[acharya]

India's Scientific and Cultural Heritage
Prof. N. S. Ramaswamy*
THHE long march of Man from nomadic an existence 10,000 years ago to the current level of civilization has been achieved by the contribution of sages, saints, scholars, scientists and philosophers in different parts of the world. We are indebted to all of them, who in their life time struggled and contributed for the welfare of man, animals and nature. In general, India contributed in the spiritual, cultural and philosophical sectors, while westerners contributed in science and technology for -the materialistic progress. Each country has a unique genius. Indians are indebted to the West for the modem technology, like instant communication, computers, rapid modes of travel, innovation in production, etc. India contributed largely to the inner world of Man. In certain cases, Indian sages discovered scientific truths long before westerners did. Mankind should be grateful to both ancient wisdom of India and the modern scientists and technologists of the West.
Many scholars think that it is India's century, whereby India's ancient thought and wisdom would be useful to solve the myriad problems afflicting mankind and to improve quality of life. Therefore, we propose to give a glimpse of India's scientific and cultural heritage so that Indians would get a better appreciation of our contributions, which will enable them to spread India's ancient wisdom not only to Indians but also to rest of the world.
Information given in this article has been taken from a variety of sources - both Indian and foreign. I express my gratitude to them. The number being large, I am not giving their names, for which I apologize. Voluminous books by eminent scholars are now available in Sanskrit, English and some regional languages.
I must express my profound gratitude to Dr. N. Gopalakrishnan, Honorary Director, Indian Institute of Scientific Heritage. The world owes a great deal to this great son of India, who has dedicated his life to spread the messages contained in our ancient thought and wisdom through his writings and lectures in India and abroad. I have taken a lot of material from his publications, for which I thank him.
Swami Vivekananda and Sri Aurobindo as well as many foreign scholars and Indologists believe that this is India's century, when the whole world would come to India to seek solutions to the problems confronted by mankind.
India's ancient thought and wisdom has covered most areas of human endeavor -science, technology, economics, psychology, law, governance, health, education, culture, philosophy, mysticism, cosmology, astronomy, astrology, linguistics, logic, music, dance, Yoga, meditation, environment, ecology, architecture etc: Sages and scholars made hundreds of discoveries in these areas, largely without any equipments or library, and partly through experiments as in the case of medicine, surgery,metallurgy, etc. They led virtuous lives and meditated with a prayerful heart. Many of these discoveries perhaps came to them as revelation, intuition and imagination. There is nothing supernatural about their powers. These saints and sages were selfless souls, who were only interested in the welfare of man, animal and nature. They led a simple life, desiring nothing for themselves. Most of them had family also. They had lofty ideals and worthy goals. Their discoveries prove that man is capable of unraveling the mysteries of the cosmos and nature, using then- inherent powers and following the principles laid down in India's spiritual literature. Such knowledge is known as Para Vidya, or higher knowledge^ as distinct from Apara Vidya or secular and materialistic knowledge obtained through the senses and using .equipments wherever necessary.
In spite of such a head start of 3000 years, India looks to the West in scientific and technological fields. Our Education system ought to be given enough resources and autonomy to carry out research as well as to document and disseminate India's ancient knowledge and wisdom. Our rich temples ought to fund such studies. Tirupati, Sabarimala and Guruvayoor temples should establish study centres. Educational institutions, under the management and control of religious Mutts, can help such pursuits.
We have compiled information on India's Scientific Heritage. Indians discovered profound and marvelous concepts, such as, counting, numbering system, zero, decimals, place value, infinity, Pythagoras theorem, gravitation, spherical shape of earth, planetary movements, diameter of the earth and atmosphere, speed of light, age of the Universe, time, metallurgy, atom and hundreds of such scientific truths, re-discovered later by western scientists using equipments. Sankara postulated the Advaita philosophy.
Indians gave a plausible explanation for the inequality and inequity in creation and suffering,by postulating the Law of Order, Law and Effect and Law of Rebirth. Ayu now being accepted by the West as method, since medicines are organic, was done by Sushrutha. Indians gave s arguments in favor of vegetarianisn western scholars were vegetarians, i Bernard Shaw, Shakespeare, Russell, and thousands of others. Our saints a had discovered the mysteries of nati before western scientists did. Mai discoveries of our sages are now attri Newton, Galileo, Kelvin, Copernicus, Pj etc. A list of discoveries by bur sages corresponding finding by the West will a later issue. A large number of wesl Emerson, Maxrmieller, Isherwood, Oppenheimer, Einstein, Mathew Arnol Frawley, Will Durant, Toynbee, Basham, Lin yu Tang, Walters - were in by Indian philosophers — Vivekana Abhedananda, Prabhupada and Ram Yogananda, Mahesh Yogi and Deepak Osho, Dayananda and Ravi Shankar ai others. These philosophers instilled in Indian thinking among US scholars. Y meditation have become popular there. C are also helping. They have to be hell facilities to learn more on Indian heril to spread Indian wisdom.
What is the advantage of knowing ancients had discovered these truths ear the west? The main objective is to Bharath, Most of us do not know anythii ^ India's past glory. We should blame o that, even after 60 years of independem is no attempt on the part of the Establisl educate the young about our ancient gloi hidden energy would then emerge and them to conduct research so that the contribute to the progress of our nati should adopt whatever is good in the the East as well as our own ancient and concepts, provided they are scientific rational. Superstitions should be abolished. Nothing should be accepted in blind belief. Experience is the key test of any statement. Even the concept of God should be proved by experience. Ramakrishna said that he saw God. Knowledge is of various kinds — Prathyaksha (manifested, visible), Anumana (inference) and Pramana (authority of great people). When we cannot see or infer, we should accept statements of those who are knowledgeable and have had experience. It is in that spirit we accept Einstein and Sankaracharya.
With the same attitude, we should take the postulatidn of our sages as valid. The younger generation of Indians do need to know much about ancient Indian discoveries in the field of Science, Astronomy, Mathematics, Metallurgy, etc. Fortunately, there are still hundreds of scholars, who are struggling, without support and recognition, to keep alive our heritage and prayerfully waiting for support their studies and documentation. Our corporate world should come forward. Though there is no profit in such investigations they will be the beneficiaries of a stable and united India. Understanding ancient thought and culture would help to strengthen our bonds to keep India as a nation state. The Corporate sector should introduce Indian Heritage as part of their HRD programmes. Rich temples in the south, like Tirupati, Guruvayur and Sabarimala ought to start Sanskrit colleges to study Vedas and show their relevance to current situations and problems. •
India's Scientific and Cultural Heritage — II*
Prof. N. S. Ramaswamy

I
N the earlier part of this article we have thanked Dr. N.Gopalakrishnan, Honorary Director of Scientific Heritage for his dedication to ancient India's thought and wisdom.
We give below Dr. N. Gopalakrishnan's writings in the Heritage Publications Series-66.

We have also listed a few discoveries of Indians, said to have been discovered by Westerners much later. We are thankful to him for permitting the reproduction. We are sure our compilation and pleas would awaken India.


No, Subject Discovered by Year
1 Discovery and Use of Zero Pingalacharya 200 B.C.
2 Loans and Interests Vishnusmruthi 100 BC
3 Charging Interest Vishnu Smruthi 100 B.C.
4 Pythagorus Theorem Boudhayana 700 BC
5 Binomial Theorem Pingalacharya 200 BC
6 Geometry in Sulbasutra-II Boudhayana 700 BC
7 Rules of Bodies in Motion Aryabhata - I 499 AD
8 Arc and Chord Aryabhata-I 499 AD
9 Circle - Value of Phy Aryabhata - I 499 AD
9- A Circle - Value of Phy Bhaskaracharya - I 628 AD
10 Triangles Aryabhata - I 499 AD
1 1 Rotation of Earth - II Aryabhata - I 499 AD
1 2 Eclipse-I Aryabhata - I 499 AD
1 3 Four Quadrants of Earth Aryabhata - I 499 AD
14 Nrushiyojanam Aryabhata - I 499 AD
15 Day Diameter Panchasiddhantika 4 505 AD
16 Meridian and Time Varahamihira
17 Knowledge on Infinity Bhaskaracharya - II Brahmaguptha 1148 AD ' 600 AD
18 Use of Ratio and Proportion Bhaskaracharya - I 628 AD
1 9 Use of Fractions Bhaskaracharya - I 628 AD
20 Partnership and Shares Bhaskaracharya I 628 AD

21 Progression of the Type
I sq + 2 sq + 3 sq + 4 sq . Bhaskaracharya I 628 AD
22 Progression of Type 1 cu+2 cu+3 cu+4 cu Bhaskaracharya I 628 AD
23 Triangles - (Quiz) Bhaskara I 628 AD
24 Rotation of Earth-I Brahmagupta 629 AD
25 Place Values-J Vyasa Bhashya to Yoga Sutra 650 AD
26 Parallax-H Lallacharya 700 AD
27 Parallax-HI Lallacharya 700 AD
28 Apogee, Perigee and Orbit of Earth Lallacharya 700 AD
29 Appearance of Circumference of Earth Lallacharya 700 AD
30 Shape of Earth Lallacharya 700 AD
3J Globe Varahamihira 505 AD
32 Meridian and Time Bhaskara I 628 AD
33 Eclipse - II Lallacharya 700 AD
34 Eclipse-II Lallacharya 700 AD
35 Angular Dimensions Vateswara 880 AD
36 Horizon Vateswara 880 AD
37 Astronomical Definitions Vateswara 880 AD
38 Equator Vateswara 880 AD
39 6 o* Clock Circle Vateswara 880 AD
40 Circle of Diurnal Motion Vateswara 880 AD
41 Day Radius Vateswara 880 AD
42 Ecliptic Vateswara 880 AD
43 Setting Point of Ecliptic Vateswara 880 AD
44 Rising — Setting Line Vateswara 880 AD
45 Day Radius and Earthsine Vateswara 880 AD
46 Sun's Prime Vertical Vateswara 880 AD
47 Progression of the Type En+En Sq + En Cu Sreedharacharya 900 AD
48 First Degree Indeterminate Equation Sreedharacharya 900 AD
49 Newton Gauss (1670 AD) Vateswara 904 AD
50 First Order Equation - II Sreedharacharya 990 AD
51 Equations of Higher Order - I Sreedharacharya 990 AD
52 Permutations and Combination - I Sridharacharya 990 AD
53 Interest Calculation Sridharacharya 990 AD
54 Meeting place of the two surfaces Aryabhata I 499 AD
55 Meridian Sankaranarayana I 950 AD

56 Eclipse - I Sarikaranarayana 950 AD

57 Knowledge on Infinity Brahmaguptha Bhaskaracharya II 600 AD 1148 AD

58 Calculations with Zero Sripati 1039 AD

59 Permutations and Combination - II Bhaskaracharya 1114 AD

60 First Order Equation - I Bhaskaracharya II 1114 AD

61 Equations of Higher Order - II Bhaskaracharya II 1114 AD

62 Area of Circle and Sphere Bhaskaracharya 1114 AD

63 Polygonal Bhaskara II 1114 AD

64 Lenth of ARC - Chord Bhaskara II 1114 AD

65 Arc and Arrow Bhaskara II 1114 AD

66 Volumes of4 Cones Bhaskara II 1 1 14 AD

67 Gravity Bhaskara II 1114 AD

68 Use of Average Values Bhaskaracharya II 1 150 AD

69 Gregory's (1632 AD) Madhava 1350 AD

70 De-Molvre's (1650 AD) Approximation Madhavacharya 1350 AD

71 Lhuiler's (1782 AD) Formula Madhavacharya 1360 AD

72 Lebnitz (1673 AD) Power series Puthumana Somayaji 1440 AD

73 Newton's Infinite GP Convergent Series Nilakanta 1444 AD

74 Taylor (1685 AD) Series of Sine and' Cosine Nilakanta 1444 AD

75 Somayaji's Theorems Puthumana Somayaji 1450 AD

76 ARC and Chord Puthumana Somayaji 1450 AD

77 Sine, Cosine Radius and ARC Puthumana Somayaji 1450 AD

78 Newton's (1660 AD) Power Series Puthumana Somayaji 1450 AD

79 Velocity of Planets per day Puthumana Somayaji 1450 AD

80 Place Values - 11 Sankaracharya -

8 1 Tycho Brahe Reduction of Ecliptic Achyuta Pisharoti -

82 Parallax - I Lallacharya -

Many scientific inventions that are attributed to foreigners have actually been discovered by our ancient masters of science. Given below are the discoveries and the names of the ancient Indians and western scientists, as given by Dr. N. Gopalakrishnan in the HPS-66.
1 BHQUDHAYANA - 700 BC
Pythagoras Theorem Pythagorus - 500 BC Proof of Pythagorus Theorem Euclid - 300 BC
2 SUSRUTHA - 700 BC
Cataract Operation Joseph Lister - 1600 AD Lithotomy Marios Santos - 600 AD Plastic Surgery Joseph Constantine -1814 AD Nose Surgery Gasparo Tag cozzi - 1600 AD

1 BHQUDHAYANA - 700 BC
Pythagoras Theorem Pythagorus - 500 BC Proof of Pythagorus Theorem Euclid - 300 BC
2 SUSRUTHA - 700 BC
Cataract Operation Joseph Lister - 1600 AD Lithotomy Marios Santos - 600 AD Plastic Surgery Joseph Constantine -1814 AD Nose Surgery Gasparo Tag cozzi - 1600 AD

3 GOUTHAMA - 300 BC
Evolution Theory Wave Nature of Sound Darvin - 1800 AD Hyghen - 1700 AD
4 KANAADA - 300 BC
Atomic Theory Dalton - 1893 AD'
5 CHARAKA - 300 BC Blood Circulation Micro Organism ' Hrarvey - 1656 AD Lewis Pasture -1822 AD
6 ARYABHATTA - I 476 AD
Spherical Shape of Earth Revolution of Earth Apogee Sine & Cosine Diameter of Earth Value for Pye Square Root Determination Galileo - 1564 AD Kepler- 1571 AD Kepler DeMolvre's i Copernicus-1473 AD Lindemann - 1882 AD Cantanew 1546 AD
7 VARAHAMIHIRA - 505 AD
Comets Haley - 1656 AD
8 BRAHMAGUPTA - 628 AD
Style's Equation +ve Integral Sterling Formula Newton Sterling Interpolation Equation for Area for Cyclic Quadrilateral Equation for Radius of Cyclic Quadrilateral Intermediate Equation of Second Degree Style - 1600 AD DeMolvre's - 1667 AD Sterling - 1642 AD Newton/Sterling
W. Shell - 1619 AD Lhuiler - 1782 AD Langrange - 1560 AD
9 LALLACHARYA - 748 AD
Perigee Kepler
10 GOVINDASWAMIN - 800 AD
Newton Gauss Forward Interpolation Formula Newton/Gauss
11 VATESWARA - 860 AD
Newton Gauss Backward Interpolation Formula Newton / Gauss 1640
12 BHASKARA - II - 1114 AD
Gravity Cyclic Method Newton Galois - 1600 AD

Inverse Cyclic. Method Differential Calculus Toilers Theorem • Theory of Continued Fraction Pellian Equation Euler - 1600 AD Newton Rolle - 1646 AD Sanderson Deoron Pale - 1660 AD
13 MADHAVA - 1350 AD
Taylor Sine Cosine Series Lebnitz Series Gregories Series for Arc Lebnitz Infinite Taylor - 1685 AD Lebnitz - 1642 AD Gregory Lebnitz
14 PARAMESWARA - 1360 AD
Lhuiler formula Lhuiler - 1782 AD
15 NILAKANTA - 1440 AD
Infinite GP Series Lebnitz Power Series Newton Lebnitz
16 SAYANA - 1400 AD
Velocity of Light Newton - 1642 AD
17 PUTHUMANA SOMAYAAJI - 1440 AD
DeMolvre's Infinite Series DeMolvre's
18 ACHYUTHA PISHAROTI - 1530 AD
Tycho-Brahe Reduction Tycho Brahe - 1546 AD

-

[asritha1]

[quote name='Viren' date='08 August 2007 - 01:12 AM' timestamp='1186515274' post='71940']

Kaushal:

Have you checked this?

http://www.daivajna.org/daivajna/asp/home.asp



From the dieties/temple they pray to, seems like they are/have close links to Gaud Saraswats.

[/quote]



Really awesome.unbelievable you referred excellent thing here.Thanks for this.No more words to express my feeling.Thanks a lot...

[ravicv]

I've always been surprised that most Indians are ignorant of the fact that Aryabhatta is considered by many to be one of the Father's of Cryptography as we know it today, apart from laying the basis for calculus, and his various other achievements. The Aryabhatta Remainder Theorem (ART) is directly relevant to Public Key Cryptography, and the Aryabhatta algorithm is currently employed in cryptography. The following paper has a simple description of the ART:



http://security.nknu.edu.tw/publications/2005SCIS.pdf



See:



http://www.springerlink.com/index/66777251J5617T31.pdf



for a formal reference. The annual RSA security conference in 2006 (San Jose) had Aryabhatta's contributions as it's main theme:



http://www.rsaconference.com/about-rsa-c...e-1995.htm



Further interesting and readable information on Aryabhatta's contributions to cryptography may be found at:



http://arxiv.org/ftp/cs/papers/0604/0604012.pdf



http://arxiv4.library.cornell.edu/ftp/ar...2.3409.pdf

[Guest]

[url="http://sites.google.com/site/itihasabharati/scientific-contributions"]India’s Scientific Contribution to Europe and other World Civilizations[/url]

[acharya]

http://www.chowk.com/articles/hindu-math...odbhoy.htm



Hindu Mathematics – How Original Was It?

Pervez Hoodbhoy June 15, 2009

Tags: Mathematics , history , science , India

“Mathematics In India�? by Kim Plofker, Princeton University Press, Jan 2009, 394pp, £28.95, Reviewed for Nature by Pervez Hoodbhoy, Department of Physics, Quaid-e-Azam University, Islamabad, Pakistan.





In a world finely divided on issues of culture, politics, religion, and race, it is



a relief to know one thing that stands above them – mathematics. The diversity among today’s mathematicians shows that it scarcely matters who invents new concepts or proves new theorems; cold logic is immune to the prejudices of arbitrary whim and historical accident. And yet, over the ages, many were the ways by which different families of the homosapien species distilled the essence of the cosmos to capture the magic of numbers.



“Mathematics in India�? by Kim Plofker, a German professor specializing in the history of mathematics, shows just how different one of these ways was and how culture and mathematical development can be intimately connected. This carefully researched chronicle of the principal contributions made by a great human civilization covers the earliest days of Indian history through the beginning of the modern period. Somewhat regrettably, it stops short of the period of the legendary mathematician, Ramanujan (b. 1897) whose name still appears in published papers.



Plofker’s book fulfils an important need in a world where mathematical historiography has been largely shaped by the dominance of the Greco-Christian world view and the Enlightenment period. Too little has been written on the mathematical contributions of other cultures. One reason for neglecting Indian mathematics was Eurocentrism – British colonial historians in India generally paid little attention and assumed that the natives had been too preoccupied with spiritual matters to make significant contributions in the exact sciences. Another reason is that many ancient Indian mathematical texts have long been extinct. Often the only indication that they once existed comes from scholars referring to the work of predecessors from an earlier age.

As Plofker wryly notes, two historians of Indian mathematics recently published articles in the same edited volume wherein the estimates of their subject’s origins differed by about two thousand years.



Nevertheless, Sanskrit texts that survived the ravages of time reveal a rich tradition of Indian mathematical discoveries for well over 2500 years. In the Early Vedic period (600-1200 BC), a decimal system of numbers had already been established in India together with rules for arithmetic operations, (ganita) and geometry (rekha-ganita). These rules were encoded into a complex system of chants, prayers, hymns, curses, charms, and other religious rituals. For example, acclamations of praise to the air, sky, times of day or heavenly bodies were expressed in powers of ten that went to a trillion and more. Cryptic phrases called sutras contained arithmetic rules for activities such as laying out a temple building or for arranging a sequence of sacrificial fires.



As in other agricultural civilizations, Indian mathematics probably emerged in response to real needs such as measuring land areas and keeping track of financial transactions, incomes and taxation. A rigid caste and class hierarchy reserved the mystery of numbers for elite Brahmins. High status was accorded to the custodians of jealously guarded secrets. There was immense fascination with large numbers. Thus it is said that the young prince Buddha successfully competed for the hand of beautiful princess Gopa – he could recite a number table that included names for the powers of ten going up beyond the 20th decimal place, in addition to outshining his virile and handsome rivals in the martial arts.



The desire to preserve power also meant that the mathematically knowledgeable did not strive to make its communication easier. Modern mathematicians, used to simple tabular expressions, will find quite perplexing the rhythmic chant of the famous Aryabhata (5th century AD): makhi-bhakhi-phakhi-dhaki-nakhi-nakhi-nakhi-hasjha-skaki-kisga-sghaki-kighva-ghaki…(225-224-222-219-215-210-205-199-191,…). This chant, containing values of sine differences (in arc minutes), would be memorized by aspiring mathematicians in much the same way as verses of the Gita.



The book details the impressive achievements of Indian mathematicians: Aryabhatta, Brahmagupta, Mahavira, Bhaskara, Madhava…until the Sanskrit tradition finally became irrelevant with invasion of modern mathematics from Europe in the 19th century. Among prominent Indian achievements is discovery of the solution to indeterminate equations and the development of infinite series for trigonometric quantities.

Discovered by the Kerala school (14th century) of Madhava, these series build upon the work of Bhaskara-II. By an ingenious computation of a circle’s circumference by polygonization, Madhava was able to arrive at a numerical value of pi correct to the 11th decimal place. Indeed, a few significant developments preceded those in Europe. Intrigued by rules he discovered in an unnamed Sanskrit text, Reuben Burrow, a British mathematician posted in Bengal as an instructor in the engineers corps, wrote a paper in 1790 entitled: “A Proof that the Hindoos had the Binomial Theorem�?.



But how Indian was early Indian mathematics? Did it evolve in parallel or did it absorb ideas and knowledge from elsewhere? Cultural pride creates its own versions of truth. In a recently re-invigorated India, many wish to believe that that all worthwhile mathematics originated in ancient India. But this book may not please them. Plofker is not ready to certify that the concept of zero was an Indian invention; it could well have been conveyed by Chinese Buddhist pilgrims. Nor is she willing to believe that differential and integral calculus was anticipated in India ahead of Leibnitz and Newton.



The chapter “Exchanges with the Islamic World�? is of particular significance. The Muslim conquest of India brought with it the Islamic mathematical tradition. Built upon the foundation of Greek mathematics, Muslims had made important advances between the 9th and 13th centuries. Greco-Islamic and Indian mathematics were structured quite differently with the former emphasizing proof and the latter result. Probably because of Islamic influence, Indian ideas of the nature of mathematical proof moved in the direction of greater rigour.



The book carefully separates fact from hyperbole, copiously quoting formulae. This makes it heavy reading in many places, and one wishes that it had been interspersed with vignettes and light anecdotes. It is more of a research monograph than a popular book. But that is the price that scholarship often exacts.



From this book one understands in fine detail how the early development of Indian mathematics was influenced by the need to build temples of specific proportions, astrological imperatives, etc. It could be argued that Islamic mathematics also had a religious motivation: the need to know precise times for the 5-times daily prayers, the direction of the Qibla, etc.



But, all said and done, mathematics is mathematics. The bottom line is that a quadratic equation solved by whoever and by whatever means has to give exactly the same solutions.

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