The Indic Mathematical Tradition 6000 BCE To ?

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http://www.vedamu.org/Mathematics/course.asp
http://www.vedicganita.org/transcendental.htm

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video
<b>This was the Ancient Hindu way of starting fire (earlier to the days of matchbox</b>).
Wooden piece from Arani tree (belonging to the family of Ficus religiosa or Urostigma religiosum, I am not sure) is put for vigourous friction which generates the heat and fire. ...

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Pingala: Inventor of Pascal's triangle 18 centuries before Pascal
<i>The mathematics of poetry -- multicultural mathematics by Dr. Rachel Hall</i>

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An authentic version of history of Indian science
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The Encyclopaedia of Classical Indian Sciences, a book that traces the evolution of different aspects of science, technology and medicine in India, was released here on Monday.

The book, edited by scientist Roddam Narasimha and Helaine Selin, science librarian and faculty associate in Hampshire College, Massachusetts, was released by scientist C.N.R. Rao.

The 492-page book is an attempt to provide an authentic account of natural science, technology and medicine practised by Indians and other South Asians.

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<!--QuoteBegin-Viren+Jan 9 2007, 11:14 AM-->QUOTE(Viren @ Jan 9 2007, 11:14 AM)<!--QuoteEBegin-->An authentic version of history of Indian science
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The 492-page book is an attempt to provide an authentic account of natural science, technology and medicine practised by Indians <b>and other South Asians. </b>

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[right][snapback]62889[/snapback][/right]
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What other south asians? Pakistani? Bongs? The commie newspaper "The muslim" is at it again.

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<span style='color:red'>हड़प्पा एवं सिंधु घाटी सभ्यता से जल संरक्षण सीखें: डा.विष्ट</span>

रोहतक, विशेष संवाददाता। भारतीय पुरातत्व सर्वे के पूर्व निदेशक डा. आरएस विष्ट ने कहा है कि हमें हड़प्पन एवं सिंधु घाटी सभ्यता से जन संरक्षण एवं जल प्रबंधन सीखना चाहिए। यह बात उन्होंने महर्षि दयानंद विश्वविद्यालय के जैव विज्ञान विभाग द्वारा आयोजित जल विषयक कार्यशाला को संबोधित करते हुए कही।

उन्होंने बताया कि प्राचीन हड़प्पन सभ्यता ने जल प्रबंधन के आधुनिक उपायों-जलाशय,जल टंकी, जल वाहिका नहर आदि किए थे। डा. विष्ट ने विशेष रूप से बरसाती पानी के संरक्षण पर जोर दिया। उन्होंने बताया कि हड़प्पन सभ्यता में इस बरत पर विशेष रूप से जोर दिया जाता था कि बरसात के पानी की हर एक बूंद को बचाया जाये। डा. बिष्ट ने हड़प्पन सभ्यता के एक महत्वपूर्ण स्थल-धौलवीर कुच्छ, गुजरात के बारे में दृश्य-श्रव्य प्रस्तुति देते हुए प्राचीन जल संरक्षण उपायों की गाथा व्यक्त की ।
http://www.jagran.com/news/statenews.aspx?...id=6&id=3039002
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Addressing a conference at Maharshi Dayananda University, ex-Director of ASI Dr. R.S.Visht said that the Indus Valley Civilization had championed the usage of rain water harvesting, which we must learn from. He demonstrated using the audio-visual presentation, different water-harvesting arrangement found in the excavations at Dhaulvir site in Gujarat.

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A good book. A research thesis of Ian G Pearce.

Indian Mathematics: Redressing the balance

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Contrary to Euroscentric belief, scholars from India, over a period of some 4500 years, contributed to some of the greatest mathematical achievements in the history of the subject. From the earliest numerate civilisation of the Indus valley, through the scholars of the 5th to 12th centuries who were conversant in arithmetic, algebra, trigonometry, geometry combinatorics and latterly differential calculus, Indian scholars led the world in the field of mathematics. The peak coming between the 14th and 16th centuries in the far South, where scholars were the first to derive infinite series expansions of trigonometric functions.

In addition to mighty contributions to all the principal areas of mathematics, Indian scholars were responsible for the creation, and refinement of the current decimal place value system of numeration, including the number zero, without which higher mathematics would not be possible. The purpose of my project is to highlight the major mathematical contributions of Indian scholars and further to emphasise where neglect has occurred and hence elucidate why the Eurocentric ideal is an injustice and in some cases complete fabrication.
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CONTENTS:

Abstract
Introduction
Early Indian culture - Indus civilisation
Mathematics in the service of religion:
I. Vedas and Vedangas
II. Sulba Sutras
Jainism
The Bakhshali manuscript
Decimal numeration and the place-value system
The Classical period:
I Introduction
II. Aryabhata and his commentators
III. Brahmagupta, and the influence on Arabia
IV. Mathematics over the next 400 years (700AD-1100AD)
V. Bhaskaracharya II
VI. Pell's equation
VII. The end of the Classic period and the state of Indian mathematics abroad by the 12th century
Keralese mathematics:
I. Introduction
II. Mathematicians of Kerala
III. Madhava of Sangamagramma
IV. Possible transmission of Keralese mathematics to Europe
Conclusions
References

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<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Metallurgy in ancient India was advanced</b>
HT Correspondent
Varanasi, January 25
EMINENT METALLURGICAL engineer and former rector of the Banaras Hindu University Prof TR Anatharaman said that ancient India contributed a lot in the field of metallurgy.

He was delivering a lecture on 'Metallurgical Marvels of Ancient India' on the third-day of four-day seminar on 'History of Indian Science and Technology' at Swatantrata Bhawan in BHU here on Thursday.

Prof Anatharaman, also former director of Institute of Technology (IT-BHU) and presently Chancellor of Ashram Atmadeep (Gurgaon) said that recent historical studies and scientific researches have thrown considerable new light on the status of metal extraction and working in Indian sub-continent during the ancient period (1700BC to 1000 AD). 

<b>He said that the world-famous ancient Damascus Swords had its origin in India.</b>

<b>"The Damascus Swords were fabricated from Ultra-high Carbon Steel, known commercially as Wootz, was produced in South India particularly in the state of Andhra Pradesh around 400 BC,"</b> he said.

<b>"Fabrication of the Iron Pillar, seven-ton heavy and seven meter tall at Delhi known for its amazing corrosion resistance despite exposure to the Sun, wind, dust and rain in the open for more than 16 centuries is another metallurgical marvel of ancient India,"</b> he added.

Dr K Krishnan of Archaeology and Ancient History Department at The Maharaja Sayajirao University of Baroda (Vadodara) delivered a lecture on 'Ceramic Technology: Its Beginning and Advancements in The Indian Sub-Continent.' He said that ceramic technology develops with the emergence of the first agricultural communities, designated by the cultural phase 'Neolithic', which had a wide distribution in the sub-continent in space and time."

http://www.hindustantimes.com/news/5922_19...02500030002.htm
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Rajiv Malhotra was mentioned in post #50. I am pasting a section from his Sulekha article <i>How 'Gandhara' became 'Kandahar'</i>
http://www.sulekha.com/blogs/blogdisplay.aspx?cid=4383
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Islamic Scholarship on India</b>

The Arabic, Turkish, and Persian invaders brought their historians to document their conquests of India as great achievements. Many of these historians ended up loving India and wrote excellent accounts of life in India, including about the Gandhara and Sindh regions. Their translations of Indian texts were later retranslated into European languages and hence many of the European Renaissance inputs from Islam were actually Indian contributions traveling via Islam.

Many Muslim scholars showed great respect for Indian society. For instance:
(According to Joseph McCabe, the 'islamic' scholars were secular and many showed atheistic tendencies. That would explain why they showed any respect for Indian society.)

“The Arabic literature identifies numerous ministers, revenue officers, accountants, et cetera, in seventh- and eighth-century Sind as 'brahmans' and these were generally confirmed in their posts by the conquerors. Where these brahmans came from we do not know, but their presence was regarded as beneficial. Many cities had been founded by them and Sind had become 'prosperous and populous' under their guidance.”16

“Of caste divisions very little mention is made. The stereotype social division is in professional classes rather than a ritualized caste-hierarchy: 'priests, warriors, agriculturists, artisans, merchants'.”17

Of all these Muslim scholars, Alberuni left the most detailed accounts of India's civilization. In the introduction to his translation of Alberuni's famous book, Indica, the Arabic scholar Edward Sachau summarizes how India was the source of considerable Arabic culture:18

“The foundations of Arabic literature was laid between AD 750 and 850. It is only the tradition relating to their religion and prophet and poetry that is peculiar to the Arabs; everything else is of foreign descent… Greece, Persia, and India were taxed to help the sterility of the Arab mind… What India has contributed reached Baghdad by two different roads. Part has come directly in translations from the Sanskrit, part has traveled through Eran, having originally been translated from Sanskrit (Pali? Prakrit?) into Persian, and farther from Persian into Arabic. In this way, e.g. the fables of Kalila and Dimna have been communicated to the Arabs, and book on medicine, probably the famous Caraka.”

“As Sindh was under the actual rule of Khalif Mansur (AD 753 - 774), there came embassies from that part of India to Baghdad, and among them scholars, who brought along with them two books, the Brahamsiddhanta to Brahamgupta (Sirhind), and his Khandkhdyaka (Arkanda). With the help of these pandits, Alfazari, perhaps also Yakub ibn Tarik, translated them. Both works have been largely used, and have exercised a great influence. It was on this occasion that the Arabs first became acquainted with a scientific system of astronomy. They learned from Brahamgupta earlier than from Ptolemy."

“Another influx of Hindu learning took place under Harun, AD 786 - 808. The ministerial family Barmak, then at the zenith of their power, had come with the ruling dynasty from Balkh, where an ancestor of theirs had been an official in the Buddhistic temple Naubehar, i.e. nava vihara = the new temple (or monastery). The name Barmak is said to be of Indian descent, meaning paramaka i.e. the superior (abbot of the vihara).”

“Induced by family traditions, they sent scholars to India, there to study medicine and pharmacology. Besides, they engaged Hindu scholars to come to Baghdad, made them the chief physicians of their hospitals, and ordered them to translate from Sanskrit into Arabic books on medicine, pharmacology, toxicology, philosophy, astrology, and other subjects. Still in later centuries Muslim scholars sometimes traveled for the same purposes as the emissaries of the Barmak, e.g. Almuwakkuf not long before Alberuni's time…”

“Many Arab authors took up the subjects communicated to them by the Hindus and worked them out in original compositions, commentaries and extracts. A favorite subject of theirs was Indian mathematics, the knowledge of which became far spread by the publications of Alkindi and many others."

Alberuni leaves no doubt as to the origin of the so-called Arabic system of numbers:

“The numerical signs which we use are derived from the finest forms of the Hindu signs… The Arabs, too, stop with the thousand, which is certainly the most correct and the most natural thing to do... Those, however, who go beyond the thousand in their numeral system are the Hindus, at least in their arithmetical technical terms, which have been either freely invented or derived according to certain etymologies, whilst in others both methods are blended together. They extend the names of the orders of numbers until the 18th order for religious reasons, the mathematicians being assisted by the grammarians with all kinds of etymologies.”

In Islamic Spain, European scholars acknowledged India very positively, as evidenced by an important and rare 11th century book on world science commissioned by the ruler of Spain19. Its author, Said al-Andalusi focused on India as a major center for science, mathematics and culture. Some excerpts:

“The first nation (to have cultivated science) is India. This is a powerful nation having a large population, and a rich kingdom. India is known for the wisdom of its people. Over many centuries, all the kings of the past have recognized the ability of the Indians in all the branches of knowledge.”

“The Indians, as known to all nations for many centuries, are the metal (essence) of wisdom, the source of fairness and objectivity. They are peoples of sublime pensiveness, universal apologues, and useful and rare inventions.”

“To their credit, the Indians 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 [chemistry].”

“Their kings are known for their good moral principles, their wise decisions, and their perfect methods of exercising authority.”

“What has reached us from the work of the Indians in music is the book… [that] contains the fundamentals of modes and the basics in the construction of melodies.”

“That which has reached us from the discoveries of their clear thinking and the marvels of their inventions is the (game) of chess. The Indians have, in the construction of its cells, its double numbers, its symbols and secrets, reached the forefront of knowledge. They have extracted its mysteries from supernatural forces. While the game is being played and its pieces are being maneuvered, there appear the beauty of structure and the greatness of harmony. It demonstrates the manifestation of high intentions and noble deeds, as it provides various forms of warnings from enemies and points out ruses as well as ways to avoid dangers. And in this, there is considerable gain and useful profit.”

Even as late as the 12th century C.E., al-Idrîsî (1100-1166), a geographer and scholar from Spain and Sicily, included the Gandhara region, including Kabul, with India20. The region was famous for the export of its three local products: indigo, cotton, and iron.21<!--QuoteEnd--><!--QuoteEEnd--><!--QuoteBegin-->QUOTE<!--QuoteEBegin-->16 Wink p.150
17 Wink p.151
18 Alberuni (AD 973 - 1048), a Muslim scholar, mathematician and master of Greek and Hindu system astrology, wrote twenty books. In his seminal work, "Indica" (c. 1030 AD) he wrote (“Alberuni's India”, by Edward Sachau. Low Price Publications, New Delhi, 1993. (Reprint). First published 1910 -- translated in 1880s.)
19 In the eleventh-century, an important manuscript titled “The Categories of Nations” was authored in Arabic by Said al-Andalusi, who was a prolific author and in the powerful position of a judge for the king in Muslim Spain. A translation and annotation of this was done S.I. Salem and Alok Kumar and published by University of Texas Press: “Science in the Medieval World”. This is the first English translation of this eleventh-century manuscript. Quotes are from Chapter V: “Science in India”.
20 Ahmad, S. Maqbul, Indian and the Neighbouring Territories in the Kitâb Nuzhat al-Mushtâq Fi` Khtirâq al-`Âfâq of Al-Sharîf al-Idrîsî, E. J. Brill, Leiden, 1960. p. 58.
21 Ahmad. p. 67.<!--QuoteEnd--><!--QuoteEEnd-->Rajiv Malhotra's article also has three or so sections on the genocide of the Hindus in Ancient India (from Afghanistan in the west to the rest in the east).

I came across numerous forums where ignorant islamics took credit for numbers and told the gullible about the glorious islamic civilisation/glorious golden age of islam. Islam reduced Arabic into the pathetic and rigid version of the koran (hailed as sophisticated poetry). By the way, poetry is actually forbidden in islam. So the muslims who wrote poetry and became famous for it, were able to do so in spite of their religion, not because of it.

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My presentation on Indic mathematical Traditions at th e Birla sciecne center in hyderabad, Dec.16,2006

http://indicethos.org/Mathematics/HECMath2.pdf

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Indian-American wins prestigious Abel Prize for mathematics



Press Trust of India

Washington, March 22, 2007

Indian-American mathematician Srinivasa SR Varadhan won the prestigious $850,000 Abel Prize for mathematics this year for his "fundamental contributions to probability theory", it was announced on Thursday.

The 67-year-old professor of New York University's (NYU) Courant Institute of Mathematical Sciences would receive the honour, viewed as equivalent of a Nobel prize, "in particular for creating a unified theory of large deviation", the award committee said.

The six million kronor award was created by the Norway government in 2002 to mark the 200th birth anniversary of great Norwegian mathematician Niels Henrik Abel.

"Varadhan's work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time," said the citation from The Norwegian Academy of Science and Letters, according to a release from the NYU.

He is expected to receive the Abel Prize from King Harald V of Norway in Oslo on May 22.

Professor Varadhan was born in Chennai and received his B Sc honours degree and MA from Madras University. He did his PhD from the Indian Statistical Institute in Kolkata before coming to Courant as a post-doctoral fellow in 1963.

He has spent his entire professional life there, serving two terms as its director (1980-1984 and 1992-94).

http://www.hindustantimes.in/news/5967_195...01600060001.htm

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Link on Vedic Mathematics: http://www.cs.rpi.edu/~moorthy/vm/

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History of Ganit:
http://krishnascience.com/Vaisnava%20Libra...mathematics.htm

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<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><span style='color:red'>India’s Scientific Heritage :
Mechanics and Mechanical Science</span>
By Suresh Soni

In Bhaskaracharya’s book, Siddhant Shiromani (written in 12th century) in Shlokas 53-56, of the mechanics of the Goladhyaya, the water wheel has been described.

In Vaisheshik Darshan by Sage Kanaad, it is mentioned that (work) or action means motion. There are five kinds of motion:

1. Utpekshan (Upward motion)
2. Avkshepan (Downward motion)
3. Aakunchan (Motion due to the release of tensile stress)
4. Prasaran (Shearing motion)
5. Gaman (General motion)

It has also analysed the different motions on the basis of reason:
1. because of propulsion—continuous pressure.
2. because of effort—such as moving of the hands.
3. because of the gravity—just as something falls down.
4. because of fluidity or liquidity—with the impact or influence of minute particles.

In his book, The Physics, Dr. N.G. Dongre compares the velocity mentioned in the vast commentary written in the 1st century in Prashastpad Bhashya to Newton’s Laws of Motion (1675)

Prashastpad writes,
Vego Panchasu Dravyeshu Nimit—
Visheshapekshat Karmano
Jayate Niyatdik Kriya Prabandh Hetuh
Sparshvad
Dravyasanyog Vishesh Virodhi Kvachit
Karan Gun Purv Kramenotpadyate.

“Motion is caused by the five substances or matter and is created by special objects. It gets created and destroyed also by actions done in the regular direction.”

The above mentioned commentary of Prashastpad can be divided into three parts, and then we can find the striking similarity with Newton’s Laws of Motion.

1. Vegah Nimittvisheshat Karmano Jayate
The change of motion is due to impressed force. (Principia)

2. Vegah Nimittapekshat Karmano Jayate Niyatdik Kriya Prabandh Hetuh
The change of motion is proportional to the motive force impressed and is made in the direction of the right line in which the force is impressed. (Principia)

3. Vegah Sanyogvisheshvirodhi
To every action there is always an equal and opposite reaction. (Principia)

Here, the definition of Vaisheshik is given along with Newton’s Law of Motion, that velocity or force is a physical entity created by motion or work.

Elastic Forces
Elasticity is the name given to the property because of which rods, etc. vibrate and emit sound. Vaisheshik Philosophers knew this. It is mentioned in Udayan’s Nyay Karikavli.

Stithisthapaksanskarah Kshitah
Kvachichchturshvapi
Ateendriyosau Vigyeyah Kvachit
Spandepi Karanam.—59

In the other kinds of matter, solid or liquid the invisible force created in the substance is the cause of vibration.

In Bhaskaracharya’s book, Siddhant Shiromani (written in 12th century) in Shlokas 53-56, of the mechanics of the Goladhyaya, the water wheel has been described.

Tamradimayasyamkushrupa-
nalasyambupurnasya.-53
Ek Kudajalantardvitiyamagram
Tvadhomukham Ch Bahih
Yugapanmukt Chet K Nalen
Kundabdahih Patati.-54
Nemyam Baddhva Ghatikashchakram
Jalayantravat Tatha
Dharyam
Nalakprachyutsalilam Patati Yatha Tadghati Madhye.-55
Bhramati Tatastat Satatam Purnghateebhih Samakrishtam
Chakrachyutam Tadudakam Kunde Yati
Pranalikaya.-56

That is, if one takes a copper rod, folds it like an elephant driver’s hook and dips one end in a vessel of water and leaves the other end face downwards outside, then all the water of the vessel will flow out of the tap. Tie the vessels and place them in a circle. Place the two ends of the axis in such a way that the water that falls from the tap, falls into the vessel. This way, the circle will go on continuously and the water that falls from the circle, falls into the reservoir through the drain.

Analysing the book Samarangan Sutradhar, edited by Bhoj in 1150 AD, Rao Saheb K.V. Vajhe’s information about the machine in 1926, conveys the impression of a developed mechanical knowledge. From the point of view of all machines, something has been said about some basic or fundamental things.

Prakritya Parthivam Sthiram Shesheshu
Sahja Gatih
Atah Prayen Sa Janya Kshitavev
Prayatnatah.
—(Samarangan-31 Sutradhar)

The earth in naturally stationary. All machines, with respect to this static earth, are forms of motion produced in matter by artificial means.
(This book is available with Ocean Books(P) Ltd, 4/19, Asaf Ali Road, New Delhi-110 002.)

http://www.organiser.org/dynamic/modules.p...pid=185&page=23
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<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->Gargi College introduces course in Vedic mathematics
Shweta Sharma
http://cities.expressindia.com/fullstory...sid=239988

New Delhi, June 7: Even as Delhi University
is seriously looking at ways to make its mathematics curriculum
interesting, one of the university's colleges seems to have taken a
lead.

Gargi College in South Campus has introduced an add-on course in Vedic
Mathematics for the academic year 2007-08 with a view to make maths fun
for students. The one-year course will incorporate the ancient and
time-tested formula of mathematical knowledge to make the subject
interesting.

The concept of Vedic maths, which is widely being used in classrooms
across the country, offers a general multiplication method that allows
one-line divisions and one-line square roots. This unifying quality,
experts feel, makes mathematics easy and encourages innovation.

By introducing the course, Gargi College will be the first college in DU
to offer the course. The college is aiming at helping students,
especially ones preparing for CAT and banking exams, solve maths
quickly.

"As we come across many students who aspire to crack the CAT and Banking
Sector Entrances, we believe that such a course will help students speed
up their calculations and help them solve equations in a much lesser
time than expected," said Dr Promila Kumar, coordinator for the course.

The simplicity of Vedic Mathematics means that calculations can be
carried out mentally (though the methods can also be written down).
Pupils of the subject can invent their own methods rather than being
limited to the one 'correct' method.

The classes for the course will be held once a week for two hours. While
course will be open to all students who have enrolled themselves in the
college, the admission will be carried out on first-cum-first-serve basis.

"The college is trying to also rope in guest faculty lecturers who are
teachers at good institutions that prepare the students for various
entrance examinations," Dr Kumar said.

Gargi's move highlights a recent trend shaping up in the higher
education sector where universities are laying emphasis on holistic
methods to impart additional education by way of add-on courses in order
to make the curriculum more interactive and innovative.<!--QuoteEnd--><!--QuoteEEnd-->

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Amazing math calculation techniques


sulva-sutras

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Unsung Newtons of India
-Researchers trace calculus roots to wizards of Kerala <!--emo&:beer--><img src='style_emoticons/<#EMO_DIR#>/cheers.gif' border='0' style='vertical-align:middle' alt='cheers.gif' /><!--endemo-->

G.S. MUDUR
The Telegraph

New Delhi, Aug. 13: Isaac Newton may have developed one of the most elegant and useful tools of mathematics using ideas that had originated in Kerala more than 200 years before his time, new research suggests. <!--emo&:cool--><img src='style_emoticons/<#EMO_DIR#>/specool.gif' border='0' style='vertical-align:middle' alt='specool.gif' /><!--endemo-->

Science historians have long attributed the origins of calculus — a bedrock of mathematics, physics and even economics — to Newton and other 17th-century European mathematicians.

But researchers in Britain have gathered evidence that a basic component of calculus, developed by mathematicians in Kerala during the 14th and 15th centuries, was passed on to Jesuit scholars who may have carried it to Europe.

George Gheverghese Joseph at the University of Manchester and Dennis Almeida at the University of Exeter analysed mathematical contributions of Madhava, Nilakantha and other mathematicians who lived in Kerala between 1340 and 1540. They also searched through obscure Jesuit documents scattered in archives in Italy, Portugal, Spain and the Netherlands.

“We have strong circumstantial evidence that mathematics from the Kerala school influenced the development of modern mathematics in Europe centuries later,” Joseph told The Telegraph.

Their research suggests Jesuit scholars had visited Kerala at the time, and one of their tasks was to gain some understanding of Indian mathematics. “There is evidence of motivation and evidence of opportunity. There was also a corridor of communication… we also know that the Jesuit scholars were in touch with leading European mathematicians of their time,” Joseph said.

“The brilliance of Newton’s work at the end of the 17th century stands undiminished, especially when it came to the algorithms of calculus. But Madhava and Nilakantha should stand shoulder to shoulder with him,” Joseph said.

Madhava and Nilakantha developed a basic component of calculus called “infinite series”. The Kerala school also discovered the pi series, and had used it to compute pi up to 17 decimal places. The two UK researchers argue that knowledge carried by the Jesuit scholars and passed on to contemporary mathematicians may have eventually reached Newton.

The great English physicist is himself known to have acknowledged his debt to past thinkers, saying: “If I have seen farther, it is by standing on the shoulders of giants.”

The research, funded by the UK Arts and Humanities Research Council, was part of an effort by Joseph to gather new evidence for the possibility of transmission of knowledge from India to Europe. He was seeking fresh information for incorporation into a yet-to-be-published third edition of his book, The Crest of the Peacock: the Non-European Roots of Mathematics.

While the beginnings of modern mathematics are usually viewed as a European achievement, the discoveries in medieval Kerala between the 14th and 15th centuries have either been ignored or forgotten, Joseph said.

One of the first references to the contribution of the Kerala school was published in a paper in the Journal of the Royal Asiatic Society in 1935. During the 1970s and 1980s, another journal had highlighted medieval Kerala mathematics. <!--emo&:clapping--><img src='style_emoticons/<#EMO_DIR#>/clap.gif' border='0' style='vertical-align:middle' alt='clap.gif' /><!--endemo-->

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Indians predated Newton 'discovery' by 250 years

A little known school of scholars in southwest India discovered one of the founding principles of modern mathematics hundreds of years before Newton according to new research.

Dr George Gheverghese Joseph from The University of Manchester says the 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350.

The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries. <!--emo&:angry:--><img src='style_emoticons/<#EMO_DIR#>/mad.gif' border='0' style='vertical-align:middle' alt='mad.gif' /><!--endemo-->

The team from the Universities of Manchester and Exeter reveal the Kerala School also discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places.

And there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.

That knowledge, they argue, may have eventually been passed on to Newton himself.

Dr Joseph made the revelations while trawling through obscure Indian papers for a yet to be published third edition of his best selling book 'The Crest of the Peacock: the Non-European Roots of Mathematics' by Princeton University Press.

He said: "The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten.

"The brilliance of Newton's work at the end of the seventeenth century stands undiminished - especially when it came to the algorithms of calculus.

"But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.

"There were many reasons why the contribution of the Kerala school has not been acknowledged - a prime reason is neglect of scientific ideas emanating from the Non-European world - a legacy of European colonialism and beyond.

"But there is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written."

He added: "For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.

"Certainly it's hard to imagine that the West would abandon a 500-year-old tradition of importing knowledge and books from India and the Islamic world.

"But we've found evidence which goes far beyond that: for example, there was plenty of opportunity to collect the information as European Jesuits were present in the area at that time.

"They were learned with a strong background in maths and were well versed in the local languages.

"And there was strong motivation: Pope Gregory XIII set up a committee to look into modernising the Julian calendar.

"On the committee was the German Jesuit astronomer/mathematician Clavius who repeatedly requested information on how people constructed calendars in other parts of the world. The Kerala School was undoubtedly a leading light in this area.

"Similarly there was a rising need for better navigational methods including keeping accurate time on voyages of exploration and large prizes were offered to mathematicians who specialised in astronomy.

"Again, there were many such requests for information across the world from leading Jesuit researchers in Europe. Kerala mathematicians were hugely skilled in this area."

[Hauma Hamiddha]

It is interesting that only now they are discussing these matters. Almost a century ago Brijendranath Seal had shown how bhAskara of the yAdava period had developed the concept of the derivative as in differential calculus. bhAskara had used the term tatkAlika for the derivative. He clear distinguished speed that is sthUlagati and the differential of motion or sUkShma-gati that is velocity and supplies a formula which is essentially the derivative of motion at a point (or slope of the tangent of the curve) to calculate velocity. bhAskara himself clarifies in golAdhyAya that his use of the derivative is an improvement over the approximations of brahmagupta before him. The key point to note is that calculus among the Nambuthiris did not evolve in isolation but is a part of the older mathematical tradition of India. Based on the coeval yAdava kings we can place bhAskara' s birth around 1114 CE, well before Leibniz or Newton.

[Shambhu]

Hindu Wisdom

Fantastic site on how Hindu knowledge far far far predated Western knowledge..