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Research Into Indic Mathematicians
He is referring to the work o f the Aryabhata group at the unversity of Exeter by Dennis Almeida and George Geverghese (also at University of Manchester)... I refer to their work in my Indology and Indologists .some excerpts

Mateo Riccii an Italian Jesuit Missionary who with Michael Ruggieri opened the door to China for evangelization but more importantly from the perspective of determining the means by which knowledge was transmitted to Europe, acted as the transmitter of such knowledge from the east to the West. Born in Macarena on October 6, 1552. Went on to study law at Rome. Where in 1572 he joined the society of Jesus (SJ)…. He studied mathematics and geography under Clavius at the Roman college between 1572 and 1576 and in 1577 left for the indies via Lisbon. He arrived in Goa in 1578 where he taught at the college until 1582 and went on to China to establish the Catholic church there. But it is the 4 years he spent in Goa and Malabar that interests us.
The Portuguese if we recall had a large presence in Cochin (until the protestant Dutch closed down the Cochin College in 1670. So Ricci was sent to Cochin and remained in touch with the Dean of the Collegio Romano. He explicitly acknowledges that he was trying to learn the intricacies of the Indian calendrical systems from Brahmanas. ( See for instance , Ricci (1609)
The task of preparing the Panchangas (literally the five parts) which were more than a calendar and would properly be referred to as a almanac,, was the provenance of the Jyotishi pundit who was well versed in the Calendrical algorithms to devise the proper almanac for his community. Each community (for example farmers) had differing needs for their almanac and hence the need for a Jyotishi Pundit. Today this is done with Calendrical software with the help of the ephemeris published by the Government of India annually. The standard treatises used then were the Laghu Bhaskariya and in Kerala the karanapadhati.
So, it is clear that Matthew Ricci was trying to contact the appropriate Brahmanas, as he explicitly stated that he was trying to do, and it appears unlikely that he did not succeed in imbibing these techniques from them.

The Aryabhata Group at the University of Exeter in the UK “Transmission of the Calculus from Kerala to Europe”, published in Proceedings of thje International symposium and Colloquium on the 1500th Anniversary of the Aryabhatiyum, Kerala Sastra Sahitya Parishat,2002.
Ricci (1609) et les remaniements de sa traduction latine (1615)’, in: Académie des Inscriptions & Belles-Lettres. Comptes rendus des séances de l'année 2003, janvier-mars, 2003, 61-84.

see also Prof. K. Ramasubramanian, Department of Humanities and Social Sciences , published a paper on `Indian Perspective on the Ontological status of Theory, in Bulletin of Kerala Mathematics Association, Vol.3, No.1, 2006. He also contributed an article entitled `Algorithms in Indian.

Astronomy', to the book "Contributions to the History of Indian Mathematics , Ed. Gerard, G. Emch, R. Sridharan and M. D. Srinivas and published by Hindustan Book Agency, New Delhi, 2005.

"Sherlock Holmes in Babylon" ed by Marlow Anderson, Victor katz, Robin wilson, Published by Mathematical association of america article on the so called Gregory series . see especially the paper by Ranjan Roy comparing the contributions of Leibnitz ,Gregory,Newton and Nilakanta somayaji.

An interesting piece of Nilakantha's work is the derivation of Leibniz-Gregory series:


Nilakantha's derivation the of above series is all the more interesting because it used the geometrical definition of π as the ratio of circumference and diameter of a circle.

Many thanks.

And I see from a search on IF that there are several posts about this in the forums. Sorry for asking first and then searching later.

Bodhi, in case you get to read this: don't trouble yourself about my request. Next to Kaushal's material above, there's some posts by member Geet in the "The Indic Mathematical Tradition 6000 BCE To ?" forum which has news links. So I'm set.

The tree in my blog expands or zooms when you click on it. Here the tree is not readable, because you cannot zoom on it.

related to 12.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Although of little importance as a research mathematician, William Jones is well known to historians of mathematics since he corresponded with many 17th century mathematicians, including Newton. He was, however, elected a Fellow of the Royal Society in 1711. Jones then served on the Royal Society committee set up in 1712 to decide who had invented the infinitesimal calculus, Newton or Leibniz . We should now describe how Jones came to be considered an important Newton supporter in the dispute. (The Royal Society made sure that only strong Newton supporters served on their committee!)

Through lecturing in the coffee houses, Jones came in contact with leading scientists of the day such as Brook Taylor and Roger Cotes. John Collins, famed for his correspondence with a wide range of scientists, had died in 1683 and in 1708 Jones acquired his mathematical papers. These included transcripts of Newton's manuscripts, letters and results obtained with the method of infinite series which Newton had discovered in about 1664. Newton had written up these results in De analysi but they had not been published. With assistance from Newton himself, Jones produced Analysis per quantitatum series, fluxiones, ac differentia in 1711 although it should be noted that this first edition of 1711 did not record either Newton's name nor that of Jones. As an appendix to this work Jones added Newton's Tractatus de quadratura curvarum which was a shortened version of the work on analytical calculus which Newton had written in 1691. The second edition of Analysis per quantitatum published in 1723 did contain a preface written by Jones. Another contribution made by Jones towards publishing Newton's work relates to the Methods fluxionum, written by Newton in 1671. Newton had tried to get it printed over a period of five years but finally gave up in 1676 when Cambridge University Press rejected it. Jones made a copy of the original Latin, giving it the title Artis analyticae specimina sive geometria analytic and it was this version which was eventually published. In 1731 Jones published Discourses of the Natural Philosophy of the Elements.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Jones' first wife died and he remarried several years later to Mary Nix on 17 April 1731. She was 25 years old and Jones was 56 at the time of their marriage. They had three children, two of whom survived to adulthood: Mary born in 1736 and William <b>{Grand father of AIT}</b> born 10 years later. On his death Jones left a large collection of manuscripts and correspondence which it appears he had intended to publish as a major piece of work. There are many notes and copied parts of original manuscripts to which he had access. Wallis writes in [2]:-

His collection of some 15,000 books was considered to be the most valuable mathematical library in England and was bequeathed to George Parker, the second earl of Macclesfield. His papers were not in the bequest; nevertheless many are at Shirburn, where they have remained (1995) with access extremely restricted. Almost the only permitted publication has been those papers contained in the two-volume Rigaud Correspondence. Among Jones's manuscripts was another projected mathematical book, which his son, Sir William, had intended, but failed, to publish. {Why? Isnt it obvious why?}
Book Review in Pioneer, 25 Sept., 2007

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->What's new in Kerala school revelation

NS Rajaram

<b>The Universal History of Numbers, 3 volumes, Georges Ifrah, Penguin, $25 </b>

<b>Finally it all came to pass as though across the ages and the civilisations, the human mind had tried all the possible solutions to the problem of writing numbers, before universally adopting the one which seemed the most abstract, the most perfected and the most effective of all."</b> In these memorable words, the French-Moroccan scholar <b>Georges Ifrah</b>, the author of the monumental but somewhat flawed book, The Universal History of Numbers, <b>sums up the many false starts by many civilisations until the Indians hit upon a method of doing arithmetic, which surpassed and supplanted all others -- one without which science, technology and everything else that we take for granted would be impossible. </b>This was the positional or the place value number system. It is without a doubt the greatest mathematical discovery ever made, and arguably India's greatest secular contribution to civilisation.

<b>The recent publicity over the use of infinite series by Kerala mathematicians several centuries before Newton and Gregory has failed to note that it is not a new discovery. CT Rajagopal and K Mukunda Mura wrote about it in 1944.</b> While the rediscovery of India's contribution to calculus is certainly welcome, it should not obscure other important contributions to mathematics coming from India. <b>Of these none is more important than the modern number system.</b>

This brings us back to George Ifrah's book mentioned at the beginning. <b>It tells the story of humanity's 3,000-year struggle to solve the most basic and yet the most important mathematical problem of all -- counting. The first two volumes recount the tortuous history of the long search that culminated in the discovery in India of the 'modern' system and its westward diffusion through the Arabs. From our viewpoint, the second volume is the most interesting. </b>The third volume, on the evolution of modern computers, is not on the same level as the first two.

While not without limitations, especially with regard to alphabetical writing, The Universal History is fascinating to read. <b>It shows that the term 'Arabic numerals' is a misnomer; the Arabs always called them 'Hindi' numerals. What is remarkable is the relatively unimportant role played by the Greeks. They were poor at arithmetic and came nowhere near matching the Indians. Babylonians, a thousand years before them, were more creative, and the Maya of pre-Colombian America far surpassed them in both computation and astronomy. So, the Greek Miracle is a modern European fantasy.</b>

<b>The discovery of the positional number system is a defining event in history, like man's discovery of fire. It changed the terms of human existence. While the invention of writing by several civilisations was also of momentous consequence, no writing system ever attained the universality and the perfection of the positional number system. </b>Today, in the age of computers and the information revolution, <b>computer code has all but replaced writing and even pictures. This would have been impossible without the Indian number system, which is virtually the universal alphabet as well.</b>

<b>What makes the positional system perfect is the synthesis of three simple yet profound ideas:</b> Zero as a numerical symbol; zero having 'nothing' as its value; and, zero as a position in a number string. <b>Other civilisations, including the Babylonian and the Maya, discovered one or other feature but failed to achieve the grand synthesis that gave us the modern system.</b>

<b>The synthesis was possible because of the Indians' capacity for abstract thought: They saw numbers not as visual aids to counting, but as abstract symbols. While other number systems, like the Roman numerals, expressed numbers visually, Indians early broke free of this shackle and saw numbers as pure symbols with values.</b>

<b>The economy and precision of the positional system has made all others obsolete. Some systems could be marvels of ingenuity, but led to incredible complexities. </b>The Egyptian hieroglyphic system needed 27 symbols to write a number like 7659. <b>Another indispensable feature of the Indian system is its uniqueness. Once written, it has a single value no matter who reads it.</b> This was not always the case with other systems. In one Maya example, the same signs can be read as either 4399 or 4879. It was even worse in the Babylonian system, where a particular number string can have a value ranging from 1538 to a fraction less than one! So, a team of scribes had to be on hand to crosscheck numbers for accuracy as well as interpretation.

The zero was usually indicated by a blank space until first a dot and then the modern symbol came to be used. <b>It was more than 500 years before the Indian system made it to Europe. Leonardo of Pisa, better known as Fibonacci, is credited with being the first to use it in Europe.</b> It may be said that until the 15th century India was ahead of Europe in mathematics, but it began to fall behind in the 16th and the 17th century.

<b>A question for historians of science is why this decline came about. Arab scholar Alberuni claims that the Islamic invasions drove Indian science away from great centres like Ujjain to places further south where the hands of invaders did not reach until much later. It is probably no coincidence that the last great school of mathematics to flourish happened to be in Kerala, the southern-most State.</b>

Modern India has not produced historians of science of the first rank.<b> Following an ideological rather than a scientific approach, Indian historical writings generally tend to be imitative and derivative.</b> No wonder the most significant work on the Sulbasutras -- 'Vedic mathematics' -- was done by American mathematician A Seidenberg.

One expects the younger generation of Indian historians to study India's scientific heritage as earnestly as Ifrah has done.
-- The reviewer is currently working on a cultural history based on the evolution of writing and mathematics


Kaushal I hope you can benefit from this above book in your studies!
from 24:
<!--QuoteBegin-Bodhi+Sep 15 2007, 03:13 PM-->QUOTE(Bodhi @ Sep 15 2007, 03:13 PM)<!--QuoteEBegin-->Jones' first wife died and he remarried several years later to Mary Nix on 17 April 1731. She was 25 years old and Jones was 56 at the time of their marriage. They had three children, two of whom survived to adulthood: Mary born in 1736 and William <b>{Grand father of AIT}</b> born 10 years later.

so in 1746 when our william jones was born, then father william jones was 71 years old (died 3 years down) and mother was 40? Does it happen? Fathering at the age of 71?

Anyway even if it happens, I think I have discovered the root cause of the birth of AIT at last!!! <!--emo&Big Grin--><img src='style_emoticons/<#EMO_DIR#>/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo--> <!--emo&Big Grin--><img src='style_emoticons/<#EMO_DIR#>/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The child's risk of developing the <b>devastating mental illness</b>, which is a group of psychotic disorders marked by <b>delusionary thinking, hallucinations</b> and bizarre physical behavior; rises dramatically and steadily as the age of the father increases.

26.6% of the schizophrenia cases could be attributed to the father's age.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The Romans did start using the Calendar that we call ‘Julian’ in 45 BCE or 709 AUC, although they would not understand either of these counters. <b>The calendar was actually devised by the Egyptian astronomer Sosgenes</b> (on whom there is no Wiki page, nor any other web page), but named for the boss, as was the Napoleonic Code.

Critical evidence to fix the native place of Āryabhata-I
K. Chandra Hari

An attempt has been made to know the native place of the great Indian astronomer Āryabhata. Opinion is divided between Kusumapura and Kerala, and with the identity of Aśmaka in dispute, the scope of the inquiry is limited to the pursuance of legends in Kerala and some efforts to understand the place of the astronomer from his work Āryabhatīyam. Here the study is focused on Āryabhatīyam and relying on Āryabhata’s two distinctive signatures that we see, viz. (1) Latitude of Ujjayinī being given as at 1/16 of the Earth’s circumference north of Laňka. (2) Earth’s diameter being 1050 yojanas or circumference 3299 yojanas using his accurate value of π = 3.1416. It is demonstrated here that the place Āryabhata had been at 10°51′N, 75°45′E. It is further explained that the latitude derived based on the equatorial circumference given by Āryabhata marks the spot where the coastline of Kerala cuts the Hindu prime meridian, i.e. Ponnāni, a major Arab trade centre since ancient times.


K. Chandra Hari is in the Institute of Reservoir Studies, Oil and Natural Gas
Commission, Ahmedabad 380 005, India.

chandra_hari18 at yahoo dot com
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Want to know more about the following?
- Did the calculus begin in India?
- Did the Indian infinite series really amount to the calculus?
- Was this connected to the work of Newton and Leibniz?
- What is the evidence for the transmission of the calculus from India to Europe?
- Did Western historians systematically falsify history over centuries?
- Why is math difficult to learn today? What can be done to remedy this?
- Is any of this relevant to present-day mathematics?
- Is multicultural mathematics really mathematics?


<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Here is a greatly simplified account of the book for the layperson.

Part I: The Nature of Mathematical Proof
Part II: The Calculus in India
Part III: The Transmission of the Calculus to Europe
Part IV: The Contemporary Relevance of the Revised History

Part I: The Nature of Mathematical Proof

The Indian work on the infinite series has been known for nearly a couple of centuries. However, under the onslaught of the Western narrative of the history of science, this was regarded as somehow suspect. It has often been claimed that the Indian series lacked proof. Hence tis book begins with a re-examination of the history and philosophy of what constitutes mathematical proof. The results are surprising.

First, history was falsified at Toledo in the 12th c. CE. After burning books for some 750 years,  the church turned towards books, to catch up with the Arabs, and financed the mass translations of Arabic books at the library of Toledo. However, during the Crusades it was galling for the church to admit learning from the hated Islamic enemy. So history was Hellenized by indiscriminately attributing all secular knowledge in those Arabic books to Greeks. (Euclid was one of the fictions constructed during this process.)

Secondly, the philosophy of mathematics too was changed. During the Inquisition anything (or person) to survive had to be theologically correct. Therefore, the philosophy of mathematics, and the understanding of mathematical proof was modified to bring it in line with the prevailing Christian theology (and especially the valuation of metaphysics over physics). A key idea here was the alleged universality and certainty of (a metaphysical notion of) mathematical proof.

However, formal mathematical proof depends upon logic, but there are an infinity of possible logics to choose from. If logic is decided culturally it is not universal, for Buddhists and Jains for instance have different logics. On the other hand, if the logic underlying proof is decided empirically, why shouldn't the empirical have a place in mathematical proof? (Incidentally, logic decided empirically need not be 2-valued, as natural language or quantum mechanics informs us.)

Part II: The Calculus in India

Next the book provides the first full account of the development of Indian infinite series over a thousand year period,  without appealing to formalism but instead explaining the proofs as given by the people who used the series. The development of these series is related to the bases of wealth in India: agriculture and overseas trade requiring navigation. The successful practice of agriculture in India required a good calendar, which could determine the monsoon or rainy season.  Recalibration of this calendar, and navigation both required knowledge of the shape and size of the earth, and means of determining latitude and longitude. A navigational instrument that has long been known is described---the new feature being the accuracy with which it can be used to measure of angles, thus providing also the instrumental basis of precise angle measurements.

Part III: The Transmission of the Calculus to Europe

Since the Indian infinite series precedes the appearance of the same series in Europe, and since the two were in contact, the onus of proof actually ought to be on those who claim that these identical series were independently rediscovered in Europe, when Europe had barely learnt to add and subtract without the abacus. This is especially the case since so must of post-Hellenic history, since Copernicus, depends upon this claim of independent rediscovery. Nevertheless, the third part of the  book takes up (a) the rules of evidence by which one can discriminate between transmission and independent rediscovery, and (b) how these rules of evidence can be applied to the case of the calculus.

The key motivation was the European navigation problem which required accurate trigonometric values, and an accurate calendar, for its solution. The agency was that of the missionaries who were present in Cochin, since 1500, and patronised by the same Raja who patronised the then-most-active people working on the Indian infinite series. The Jesuits took over the Cochin college in 1550 and started translating local knowledge and sending back these translations to Europe on the Toledo model. They were strongly motivated to learn about trigonometry and the calendar given the great practical importance of the European navigational problem, for the solution of which huge prized had been declared by various European governments. (That problem arose because Europeans did not know enough trigonometry to determine the size of the globe.)  The Jesuits had access to all literature they needed, because of their proximity to it, the support of the king, and also the full support of the local community of Syrian Christians until 1600.

There is ample circumstantial evidence that this very knowledge starts subsequently appearing in Europe, but its non-Christian origins could hardly be acknowledged in the days of the Inquisition, either by those high up in the hierarchy (like Clavius, Tycho Brahe, Kepler etc.) or by those who were threatened by it (like Mercator, Newton, etc.)

Part IV: The Contemporary Relevance of the Revised History

Why is math regarded as a difficult subject to learn? It is the theologification of mathematics that has made it hard to learn. It is impossible to teach numbers in a formally correct way without first teaching set theory, and this cannot be taught to children. Similarly, today it is taught that a point is not the dot that one sees on a paper, but something mysteriously different, leaving the child befuddled. So the way to make math teaching easy is to de-theologify math.  According to sunyavada, it is the dot on the piece of paper that is real, and the abstraction of a point which is erroneous and empty. This would also be in line with the developments in computer technology, which demand a better account of what can and what cannot be represented, because computers simply cannot pretend to understand something that they don't. 

The problem with infinities did not end with the formalisation of the real number system and limits, using sets, and the formalisation of set theory in the 1930's. The formulation of physics using differential equations assumes that physical quantities are differentiable, hence continuous on classical analysis. However, discontinuities and associated infinities continue to arise in physics, as in shock waves and the renormalization problem of quantum field theory. This shows that the calculus has not yet found a satisfactory formulation. How are these infinities to be handled? Either the number system must be changed further to allow infinities and infinitesimals, or the notion of non-representable must be accepted, as in computer arithmetic.
Sometime back there was interest in the Kerala school of mathematics

Article link

The Transmission of Scientific Knowledge from Tamizhagam to Europe
<!--QuoteBegin-Bodhi+Oct 29 2007, 04:58 PM-->QUOTE(Bodhi @ Oct 29 2007, 04:58 PM)<!--QuoteEBegin-->Critical evidence to fix the native place of Āryabhata-I
K. Chandra Hari

An attempt has been made to know the native place of the great Indian astronomer Āryabhata. Opinion is divided between Kusumapura and Kerala, and with the identity of Aśmaka in dispute, the scope of the inquiry is limited to the pursuance of legends in Kerala and some efforts to understand the place of the astronomer from his work Āryabhatīyam. Here the study is focused on Āryabhatīyam and relying on Āryabhata’s two distinctive signatures that we see, viz. (1) Latitude of Ujjayinī being given as at 1/16 of the Earth’s circumference north of Laňka. (2) Earth’s diameter being 1050 yojanas or circumference 3299 yojanas using his accurate value of π = 3.1416. It is demonstrated here that the place Āryabhata had been at 10°51′N, 75°45′E. It is further explained that the latitude derived based on the equatorial circumference given by Āryabhata marks the spot where the coastline of Kerala cuts the Hindu prime meridian, i.e. Ponnāni, a major Arab trade centre since ancient times.


K. Chandra Hari is in the Institute of Reservoir Studies, Oil and Natural Gas
Commission, Ahmedabad 380 005, India.

chandra_hari18 at yahoo dot com

Follow-up article in Current Science by Sri K. Chandra Hari


It's time to herald the Arabic science that prefigured Darwin and Newton

In this era of intolerance and cultural tension, the west needs to appreciate the fertile scholarship that flowered with Islam

Jim Al-Khalili
Wednesday January 30, 2008
The Guardian

Watching the daily news stories of never-ending troubles, hardship, misery and violence across the Arab world and central Asia, it is not surprising that many in the west view the culture of these countries as backward, and their religion as at best conservative and often as violent and extremist.

I am on a mission to dismiss a crude and inaccurate historical hegemony and present the positive face of Islam. It has never been more timely or more resonant to explore the extent to which western cultural and scientific thought is indebted to the work, a thousand years ago, of Arab and Muslim thinkers.

Article continues
What is remarkable, for instance, is that for over 700 years the international language of science was Arabic (which is why I describe it as "Arabic science"). More surprising, maybe, is the fact that one of the most fertile periods of scholarship and scientific progress in history would not have taken place without the spread of Islam across the Middle East, Persia, north Africa and Spain. I have no religious or political axe to grind. As the son of a Protestant Christian mother and a Shia Muslim father, I have nevertheless ended up without a religious bone in my body. However, having spent a happy and comfortable childhood in Iraq in the 60s and 70s, I confess to strong nostalgic motives for my fascination in the history of Arabic science.

If there is anything I truly believe, it is that progress through reason and rationality is a good thing - knowledge and enlightenment are always better than ignorance. I proudly share my worldview with one of the greatest rulers the Islamic world has ever seen: the ninth-century Abbasid caliph of Baghdad, Abu Ja'far Abdullah al-Ma'mun. Many in the west will know something of Ma'mun's more illustrious father, Harun al-Rashid, the caliph who is a central character in so many of the stories of the Arabian Nights. But it was Ma'mun, who came to power in AD813, who was to truly launch the golden age of Arabic science. His lifelong thirst for knowledge was such an obsession that he was to create in Baghdad the greatest centre of learning the world has ever seen, known throughout history simply as Bayt al-Hikma: the House of Wisdom.

We read in most accounts of the history of science that the contribution of the ancient Greeks would not be matched until the European Renaissance and the arrival of the likes of Copernicus and Galileo in the 16th century. The 1,000-year period sandwiched between the two is dismissed as the dark ages. But the scientists and philosophers whom Ma'mun brought together, and whom he entrusted with his dreams of scholarship and wisdom, sparked a period of scientific achievement that was just as important as the Greeks or Renaissance, and we cannot simply project the European dark ages on to the rest of the world.

Of course some Islamic scholars are well known in the west. The Persian philosopher Avicenna - born in AD980 - is famous as the greatest physician of the middle ages. His Canon of Medicine was to remain the standard medical text in the Islamic world and across Europe until the 17th century, a period of more than 600 years. But Avicenna was also undoubtedly the greatest philosopher of Islam and one of the most important of all time. Avicenna's work stands as the pinnacle of medieval philosophy.

But Avicenna was not the greatest scientist in Islam. For he did not have the encyclopedic mind or make the breadth of impact across so many fields as a less famous Persian who seems to have lived in his shadow: Abu Rayhan al-Biruni. Not only did Biruni make significant breakthroughs as a brilliant philosopher, mathematician and astronomer, but he also left his mark as a theologian, encyclopedist, linguist, historian, geographer, pharmacist and physician. He is also considered to be the father of geology and anthropology. The only other figure in history whose legacy rivals the scope of his scholarship would be Leonardo da Vinci. And yet Biruni is hardly known in the western world.

Many of the achievements of Arabic science often come as a surprise. For instance, while no one can doubt the genius of Copernicus and his heliocentric model of the solar system in heralding the age of modern astronomy, it is not commonly known that he relied on work carried out by Arab astronomers many centuries earlier. Many of his diagrams and calculations were taken from manuscripts of the 14th-century Syrian astronomer Ibn al-Shatir. Why is he never mentioned in our textbooks? Likewise, we are taught that English physician William Harvey was the first to correctly describe blood circulation in 1616. He was not. The first to give the correct description was the 13th-century Andalucian physician Ibn al-Nafees.

And we are reliably informed at school that Newton is the undisputed father of modern optics. School science books abound with his famous experiments with lenses and prisms, his study of the nature of light and its reflection, and the refraction and decomposition of light into the colours of the rainbow. But Newton stood on the shoulders of a giant who lived 700 years earlier. For without doubt one of the greatest of the Abbasid scientists was the Iraqi Ibn al-Haytham (born in AD965), who is regarded as the world's first physicist and as the father of the modern scientific method - long before Renaissance scholars such as Bacon and Descartes.

But what surprises many even more is that a ninth-century Iraqi zoologist by the name of al-Jahith developed a rudimentary theory of natural selection a thousand years before Darwin. In his Book of Animals, Jahith speculates on how environmental factors can affect the characteristics of species, forcing them to adapt and then pass on those new traits to future generations.

Clearly, the scientific revolution of the Abbasids would not have taken place if not for Islam - in contrast to the spread of Christianity over the preceding centuries, which had nothing like the same effect in stimulating and encouraging original scientific thinking. The brand of Islam between the beginning of the ninth and the end of the 11th century was one that promoted a spirit of free thinking, tolerance and rationalism. The comfortable compatibility between science and religion in medieval Baghdad contrasts starkly with the contradictions and conflict between rational science and many religious faiths in the world today.

The golden age of Arabic science slowed down after the 11th century. Many have speculated on the reason for this. Some blame the Mongols' destruction of Baghdad in 1258, others the change in attitude in Islamic theology towards science, and the lasting damage inflicted by religious conservatism upon the spirit of intellectual inquiry. But the real reason was simply the gradual fragmentation of the Abbasid empire and the indifference shown by weaker rulers towards science.

Why should this matter today? I would argue that, at a time of increased cultural and religious tensions , misunderstandings and intolerance, the west needs to see the Islamic world through new eyes. And, possibly more important, the Islamic world needs to see itself through new eyes and take pride in its rich and impressive heritage.

· Jim Al-Khalili is a professor of physics at the University of Surrey; he is the 2007 recipient of the Royal Society's Michael Faraday Prize and delivers the Faraday lecture at the Royal Society in London tonight


The contributions of Arab scientists to civilization is undeniable. As other people have pointed out, they used Greek, Assyrian and Indian science, but this is not a surprise. Science is always based on previous work.

I don't agree with Jim, however, that the Arab contribution is unknown in the west. I confess, however, that I might think so because my mother tongue is Spanish, and we were always told at school how important the Arabs had been in the formation of our language, our world and our science. Nonetheless, every English history of science I've read, the Arabs always had a prominent role to play.

It is also disputable that the European Middle Ages were just "Dark Ages". They were years of great technological innovation and not everything was just Aristotelian scholastics (Roger Bacon and William of Ockham are not Modern thinkers).

WML says that "Christian architecture took centuries to catch up with the more advanced classic civilisation it tore down". I disagree.

Hagia Sofia is a Xtian building. It has withstand a 7.5 earthquake, something that no pagan Roman or Greek building could ever do. Greek engineering was very primitive. They couldn't build domes or bridges, which is something the Romans "invented". Romanic and Gothic cathedrals did not abandon Roman principles, but "twisted" them for their own purposes. Gothic cathedrals could reach heights that no Roman architecture could think of. Architecture was not brought back to life by Bruneleschi. It never died.

The Middle Ages did not tear down classical civilisation, they reused it, and abused it as a means of justification.

One interesting bit of the article is this:

"And, possibly more important, the Islamic world needs to see itself through new eyes and take pride in its rich and impressive heritage."

The Muslims I know are proud of their heritage, but they tend to be secular and well educated. What they tell me about their countries tends to be quite depressing. Unfortunately, this is not a Muslim privilege. The understanding of science by the genreal public in Latin America is appalling. The contributions of LA to science have been minimal (Edinburgh University has got more Nobel Prizes than the whole of LA). The widespread mistrut of science among large parts of the population in the US and Western Europe is also disheartening. Nonetheless, science keeps advancing and nowadays one can find good sceintists in the four corners of the world (LA, Africa, Asia, especially, and even Muslim countries like Iran, for what I know).

I will complete Jim's phrase thus:

"the World needs to see itself through new eyes and take pride in its rich and impressive heritage."

Mujokan, great posts.


January 30, 2008 10:49 AM

The claim of the Arab science is false because Arabs only translated both Greek and Indian scientific achievements.
For example Arabic numbers are all Indian numbers, including the concept of Zero. It was introduced in the Arab world when the Khalifa of Baghdad invited two Indian mathematicians to bring Surya Siddhanta written by AryaBhatta in 4th century to Baghdad and then that book was translated into Arabic. Al-Beruni accompanied Sultan Mahmood's invading army to India in 8th century and collected all available books on science and medicines and translated those into Arabic even claiming authorship, but he was just a plagiarist. Similarly Iban Batuta from Morroco travelled to India on 13th century once again to collect all available scientific and mathematical discoveries. However, Arabs do not acknowledge that.<span style='color:blue'>
When Indian mathematics were translated into Latin by the Italian traders then only Europeans have since 14th century the modern mathematics.
The notable Indian inventions were: (a) Number system and arithmatic, square root; (b) Algebra, theory of equation, quadratic equation, square root, imaginary number, logarithm;© Astronomy, planetary system, movement of the earth around the sun,distance of moon from earth and sun from earth, age of the universe, gravity; (d)medicine, system of medicines developed to a very advance level.</span>

Due to the Muslim invasion, Indian universities ( in Taxila, Ujjain, Nalanda, Vikramshila, and in several other places were all destroyed; scholars were killed, books were destroyed too. Only those that had survived were taken to Persia or Arab countries by the Arab scholars who used to follow the invaders.

India is unfortunate that it was occupied by the British, who had so far refused to acknowledge the contributions made by India; however both Germans and Russians did acknowledged that.

Thus, Arabs must acknowledge their debt to India rather claiming what was not invented or discovered by any Arabs at all, but by either Greeks or Indians.

January 30, 2008 10:55 AM

To those of us interested in mathmatics, there is no doubt of the value Islam played in preserving - and improving - the traditions of the Indian, Chinese, Greeks and others; and more widely some of the interest ancient Muslim scholars played in the physical sciences.

I strongly do *not* agree with the assertion modern European science began with Copernicus and Galileo in the 16th century. If I were to pick a starting point (and there is no single starting point) I would suggest Leonardo Fibonacci (of the famous sequence of the same name) of Pisa, who was 12th century. Note that he travelled the Islamic lands and brought the Islamic-preserved (and improved) mathmatics to Europe.

An incisive read is The Chronological List of Mathematicians

In it one can clearly see the peak of the Arabian period, rougly 800-1100 AD. One can also see numerous Asiatic, Arabic, and Western names in the period 1100-1600.

However, ancient academics - or the lack of them - are of ZERO merit in terms of modern culture. Pacific Islanders or Sub-Saharan Africans should not by valued less than Muslims, the Chinese, or Westerners, because they did not have the same academic traditions.

Moreover none of the names mentioned in the article or this post were the ultimate liberators of intellect, the greatest Champion of Reason. That title, if it is given to any single individual, should be awarded to Charles Darwin.

Darwin did not destroy God. He destroyed the one, final, remaining argument for God. It can be argued (and I do) that post-Darwin, religion should more strictly be classified as a mental illness. You are, literally, bonkers if you believe.

Now, if only a few more Muslims, Christians, Jews and Hindus, could *grasp* that, the world would be a happier, and safer, place.

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Mathematics and culture
<img src='http://www.hindu.com/br/2008/02/12/images/2008021250101701.jpg' border='0' alt='user posted image' />

Implications of philosophy and culture for contemporary mathematics

CULTURAL FOUNDATIONS OF MATHEMATICS — The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE: C. K. Raju; Pub. by Center for Studies in Civilizations (CSC) and Pearson Longman, 482, FIE, Patparganj, Delhi-110092. Rs. 1600.

This book is a part of the major project undertaken by the Center for Studies in Civilizations, with Professor D.P. Chattopadhyaya as the Chairman of the Governing Body along with eight other distinguished professors. It is Part IV of Volume X (and the 25th published, of 54 planned parts) in the History of Science, Philosophy and Culture in Indian Civilization.

Science, philosophy and culture (or religion) are an eternal braid. The attempt to assimilate the vast amount of literature that is available on “mathematical proof” on the one hand and the “transmission of the calculus from India to Europe in the 16th c. Christian Era (CE)” on the other, to present a cogent and coherent picture in a volume of 477 pages by the author is a commendable effort.

It is interesting to read passages such as the following: “‘Greek’ notion attached a mystical significance to numbers, so that in 16th century Europe a typical challenge problem to the mathematician was “Is unity a number?” Expected answer, ‘NO’ – unity is not a number! ‘Indian’ notion has no such hang up. A more subtle problem related to the question non-representable (Sunya, both infinitely large and infinitesimally small, later zero).”

‘Math wars’

The author opines that the ‘First Math War’, during the period 10th to 16th century was between the Abacus and Algorismus methods. The advent of calculus is due to Leibniz and Newton, according to the prevalent Western lore. The author states that in the ‘Second Math War’, key results of calculus were in astronomy and mathematics texts of Aryabhata, Bhaskara, Nilakanta, Sankara Variayar, Jyestadeva, and were transmitted from Cochin to Europe by the Jesuit Matteo Ricci. The Indian notion of “Pramana” is different from the European notion of proof, since it permitted the empirical and rounding off procedures. European certitude did not allow the neglect of even the smallest quantity. Dedekind’s 19th century did semi-formalisation of real numbers and this led to the set theory of the 20th century, completing thereby the formalisation of real numbers. Thus, a long time elapsed before calculus was assimilated in India.

The following is a sample of an interesting construct: “Plato clearly thought of mathematics-as-calculation as distinctly below mathematics-as-proof, and this Platonic valuation led to the implicit valuation of pure mathematics and superior to applied mathematics, and to the resulting academic vanity of pure mathematicians, who regarded (and still regard) themselves as superior to applied mathematicians...”

No conflict

“In traditional Indian mathematics, however, there never was such a conflict between “pure” and “applied” mathematics, since the study of mathematics was never an end in itself, but was always directed towards some other practical end. Geometry, in the “sulbasutra”, was not directed to any spiritual end, but to the practical end of constructing a brick structure... Rationale was not valued for its own sake. Hence, rationale was not considered worth recording in many terse (sutra-style) authoritative texts on mathematics, astronomy, and timekeeping. On the other hand, rationale was not absent, but was taught, as is clear, for example, from the very title “Yuktibhasa, or in full form, the GanitaYuktiBhasa,” which means “discourse on rationale in mathematics.”

C. K. Raju misses an opportunity here (or anywhere in this volume) to refer to the notebooks of the 20th century mathematical genius, Srinivasa Ramanujan, whose 3254 entries in his celebrated notebooks did not provide proofs, and the entries were to him, perhaps, sutras, discovered by his untutored mind! “Computers have precipitated a third math war by again greatly enhancing the ability to calculate in a way regarded as epistemically insecure — according to Western metaphysics. The suggested correction is to recognise the distinct epistemic setting of mathematics-as-calculation and teach it accordingly.” This is a sample of a debatable point and several such points have been raised by the author in this treatise.

Finally, it is noteworthy that this commendable effort has been provided in an excellent quality production by the publisher and is recommended for the discerning historians and history-oriented and mathematically inclined readers. It is an essential reference book in libraries the world over.<!--QuoteEnd--><!--QuoteEEnd-->
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Hindu Calculus</b>

K.Ramasubramanian, a professor at the IIT-Bombay, has recently published a book on Hindu calculus, “Ganita Yukti-Bhasa”.  Yukti-Bhasa means rational mathematics. It is the translation of a synonymous work by Madhava of Sangama Grama in Kerala. The book is featured in Pune mirror, a tabloid of the TOI group. (It was not Newton, but Madhava, July 30, 08; p4) “Subsets of calculus existed in the Ganita-Yukti-Bhasa, two centuries before Isaac Newton published his work”.

The following are extracts from the report.

Yukti-Bhasa is a major treatise on Mathematics and astronomy written by Jyeshtadeva of the Kerala School of mathematics in about 1530. The treatise is a consolidation of the discoveries by Madhava Sangamagrama, Nilkantha Somayajee, Parameswara, Jyeshtadeva, Achyuta Panikkar and others of the Kerala School. The book is based on Tantra Sangraha by Nilkantha Somayajee. It was written in Malayalam and was not noticed outside Kerala. Some have argued that it was transmitted to Europe.

The work was unique for its time. It contained proofs and derivations of theorems. This was unusual. Important developments include infinite series expansion of a function, the power series, the Taylor series, the trigonometric series of sine, cosine, tangent and arc tangent, the power series of pi, pi/4, theta the radius, circumference and tests of convergence.

The text is divided into two parts. The first deals with arithmetic, algebra, trigonometry, geometry, logistics, fractions, rule of three, circle and disquisition on R-Sine. The second part deals with astronomy. The planetary theory is similar to that developed by the Danish astronomer, Tycho Brahe.

Madhava Sangamagrama was born as Irinjaatapilly Madhavan Namboodri,.(1350-1425) He was a prominent Hindu mathematician  from Irinjalakuda near Kochi.  He was the founder of the Kerala School of mathematics. He developed infinite series approximations, for a range of trigonometric functions. His discoveries opened the door mathematical analysis.

Nilakantha Somayaji (1444-1544) lived in Tryambakeshwar. He wrote a comprehensive treatise Tantra Sangraha in 1501. He also wrote Aryabhatiya Bhasya and Graha parikrama. (Source wikipedia.)<!--QuoteEnd--><!--QuoteEEnd-->
The Transmission of Scientific Knowledge from Tamizhagam to Europe (15th to 20th centuries)

K. V. Ramakrishna Rao
My list of Indic savants in the computational sciences has now expanded to about 140
Any research into any of these names , will be helpful (some additonal names Parasara, Vashishta, Brahma, Kasyapa)

1. A. Krishnaswami Ayyangar •
2. Acyuta Pisarati (c. 1550 CE-1621 CE)
3. Apastambha, author of Sulva Sutra, circa 2000 BCE
4. Aryabhata (476 CE - 550 CE.)
5. Aryabhata Ia (author of Aryabhata Siddhanta)
6. Aryabhata lb (author of Aryabhattiyum of Kusumapura) Born in Asmaka,, A1b = or not=A1a
7. Aryabhata II ( 9
8. Bakshali Manuscript
9. Baudhayana (fl. 700 B.C.E.)
10. Bhaskara I •
11. Bhadrabahu
12. Bhartrihari, considered to be the father of semantics
13. Bhaskara (1114-c. 1185)
14. Bhaskara 1(629 CE of Vallabhi country)
15. Bhaskara II (Bhaskaracharya son of Maheshwara)
16. Bhattotpala of Kashmir (966 CE)
17. Bhutivesnu son of Devaraja, circa 14th century CE?
18. Bose
19. Brahmadeva •
20. Brahmadeva son of Chandrabuddha 1092 ce
21. Brahmagupta (c. 598-c. 670) , son of Jisnugupta
22. Brihaddeshi •
23. Calyampudi Radhakrishna Rao •
24. Cangadeva (fl. 1205)
25. Chandraprajnapati, ? 5”’ century BCE
26. Chandrasekhara Simha or Chandrasekhar Samanta (are they the same — yes)) 1835 CE
27. D. K. Ray-Chaudhuri •
28. Damodara, son of Parameswara and guru of Nilakantha Somasutvan also
29. Dasaballa (son of Vairochana) 1055 CE
30. Deva (Deva Acharya)
31. Gaargeya
32. Ganesha Daivajna I (1505 CE son of Lakshmi and Kesava))
33. Ganesha Daivajnya II (great grandson of Ganesha Daivajnya 1(1600 CE)
34. Gangadhara
35. Gangesha Upadhyaya •
36. Ghatigopa
37. Govinda Bhatta
38. Govindaswami (c. 800-850)
39. Halayudha (fl. 975)
40. Haridatta (circa 850 CE)
41. Harish-Chandra •
42. Hemachandra Suri (b. 1089)
43. Hemcha n dra
44. Jaganath Pandit (fl. 1700)
45. Jagannatha Samrat •
46. Jayadeva (fl. 1000)
47. Jayant Narlikar •
48. Jyesthadeva of KERALA (circa 1500 CE?)
49. Kamalakara (1616) alt.1610 CE, son of narasimha (belongs to Daivjnya
50. Katyayana , Author of Sulva Sutras
51. Kesava Daivajna
52. Kodandarama (1807-1893) of the Telugu country alternate (1854CE ) son
53. Krishna Daivajna
54. Krisnadesa
55. Kumararajiva
56. Lagadha
57. Lakshmidasa , son of Vachaspati Misra
58. Lakshmidasa Daivajna
59. Lalla son of Bhatta Trivikrama
60. Latadeva , pupil of Aryabhata lb
61. Lokavibhaga (Jaina text)
62. Madhava (son of Virupaksha of the Telugu country)
63. Madhava of Sangramagama in Kerala (1340 to 1425 CE
64. Mahadeva (son of Bandhuka)
65. Mahadeva son of parasurama,
66. Maharajah Sawai Jai Singh
67. Mahavira (Mahaviracharya) (fl. 850)
68. Mahavira , founder of Jainism, author of Surya prajnapati and
69. Mahavira of the Digambara sect
70. Mahendra Sun (1349 CE)
71. Mahendra Sun, pupil of Madana Sun , (1370 CE)
72. Malayagiri, Jam Monk from Gujarat
73. Malikarjuna Sun , 1178 CE, name suggest Telugu country
74. Manava
75. Manjula
76. Manjula (fl. 930)
77. Mathukumalli V. Subbarao •
78. Melpathur Narayana Bhattathiri •
79. Munishvara •
80. Nagesh Daivajnya (son of Shiva Daivajnya) (1619 CE)
81. Narasimha Daivajna (son of Krishna Daivajnya) 1586 CE
82. Narayana Pandit (fl. 1350)
83. Narayana (c. 1500-1575)
84. Narendra Karmarkar •
85. Navin M. Singhi •
86. Nilakantha Somayaji or Nilakantha Somasutvan (1444 CE to 1550 CE) of
87. Nisanku - son of Venkataknishna Sastri (source, sourcebook KVS)
88. Padmanabha son of Narmada (same as Parameswara?)
89. Panduranga swami
90. Panini •
91. Paramesvara (1360-1455 CE) alt.1380 — 1460 CE,a Namputiri of Vataserri in Kerala
92. Patodi
93. Pillai
94. Pingala
95. Prabhakara (pupil of Aryabhata I, 525 CE?
96. Prasanta Chandra Mahalanobis •
97. Prashastidhara (fl. 958)
98. Pruthudakaswami (fl. 850)
99. Putumana Somayaji (c. 1660-1740)
100. Raghunath Raj
101. Raj Chandra Bose •
102. Rajagopal
103. Rama Daivajnya , sonn of Madhusudhana Daivajnya
104. Ramanujam
105. Ranganatha son of Narasimha Daivajnya (1643 CE) . commentary on Surya Siddhanta
106. referred to as son of Padmanabha (1417 CE) are they one and the same
107. S. N. Roy •
108. S. S. Shrikhande •
109. Saamanta Chandrasekhar Simha (see also Chandrasekhar Sinha)
110. Sankara Variyar (1500 — 1600 CE) pupil of Jyeshtadeva
111. Sankara Varman (fl. 1800)
112. Sarvadaman Chowla •
113. Satyendra Nath Bose •
114. Shreeram Shankar Abhyankar •
115. Somaswara circa 11 century CE
116. Sridhara (fl. 900)
117. Sridharacharya
118. Srinivasa Ramanujan •
119. Sripati (son of Nagadeva, 999 CE)
120. Subrahmanyan Chandrasekhar •
121. Suryadeva Yajwan (1191 CE of Gangaikonda Cholapuram in Tamilnadu)
122. The Daivajna Family — The Bernoullis of India
123. Trikkantiyur -
124. Umaswati (fl. 150 B.C.E.)
125. Varahamihira (c. 505-c. 558)
126. Varahamihira (son of Adityadasa)
127. Venkatesh Ketkar
128. Vijayanandi
129. Vijay Kumar Patodi •
130. Virasena •
131. Virasena Acharya
132. Virupaksha Suri of the Telugu country
133. Vishnu Daivajnya (son of Divakara Daivajnya) same as Visvanatha?
134. Visvanatha Daivajna (son of Divakara Daivajna) 1578 CE
135. Yajnavalkya
136. Yallaiya (1482 CE of Skandasomeswara of the Telugu country)
137. Yaska
138. Yatavrisham Acharya
139. Yativrsabha
140. Yavanesvara

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