Marcus du Sautoy (1965 - ) is a Professor of Mathematics at University of Oxford. Formerly of All Souls College, he is now a fellow of Wadham College. He has been named by The Independent on Sunday as one of the UK 's leading scientists. In 2001 he won the prestigious Berwick Prize of the London Mathematical Society, which is awarded every two years to reward the best mathematical research by a mathematician under forty.

In The Story of Maths, he says Indians made many of these breakthroughs before Newton was born.
The Story of Maths, a four-part series, will be screened on BBC Four in 2008. The first part looks at the development of maths in ancient Greece , ancient Egypt and Babylon ; the second focuses on India, China and Central Asia and the rest look at how maths developed in the West. The India reel focuses on how several Indians developed theories in maths that were later discovered by Westerners who took credit for them.
Aryabhatta (476–550 AD), who calculated pi, and Brahmagupta (598-670 AD) feature in the film, which also showcases a Gwalior temple, which documents the first inscription of 'zero'. "One of the biggest inventions in India was the number zero. Indians used it long before the West did," said Du Sautoy. "When the West had Roman numerals there was no zero and that is why they were so clumsy. On the other hand, Brahmagupta was one of the key mathematicians in the world because he invented the idea of zero."
The documentary also features the history of Kerala-born mathematician Madhava (1350-1425) who created calculus 300 years before Newton and German mathematician Gottfried Leibniz did, said Du Sautoy. "We learn that Newton invented the mathematical theory calculus in the 17^th century but Madhava created it earlier," Du Sautoy said.
(source: Oxford prof documents India's math contribution – By Naomi Canton, Hindustan Times July 5, 2007).

Not Newton, but Madhava!

Subsets of calculus existed in the Ganita-Yukti-Bhasa two centuries before Isaac Newton published his work, according to a recently published translation of the manuscript.

Prof K Ramasubramanian of IIT-Bombay has recently released two-volume translation of the Ganita-Yukti-Bhasa by Jyesthdeva points to the fact that some subsets of calculus existed in Indian manuscripts almost two centuries before Isaac Newton published his work.

And that an Indian mathematician and astronomer Nilakantha Somayaji spoke, in parts, about a planetary model, credited to Tycho Brahe almost a century later.

In the Tantra Sangraha (The Tantra Sangraha is a treatise on astronomy and related mathematics in elegant verse form, in Sanskrit. It consists of 432 verses.) Nilakantha talks about a planetary model where five planets, which can be seen with the naked eye – Mercury, Venus, Mars, Jupiter and Saturn – move around the sun, which in turn moves around the earth.
The fact remains that a century later, Tycho Brahe published the same planetary model and was credited for it, since no one knew of Nilakantha’s work.

(source: Not Newton, but Madhava! - mumbaimmirror.com).
Dr George Gheverghese Joseph from the University of Manchester and author of best-selling book 'The Crest of the Peacock: the Non-European Roots of Mathematics' said the ' Kerala School ' identified the 'infinite series 'one of the basic components of calculus- -way back in AD1350.
"The beginnings of modern maths is usually seen as a European achievement, but the discoveries in medieval India between the 14^th and 16^th centuries have been ignored or forgotten."
"The brilliance of Newton 's work at the end of the 17^th century stands undiminished - especially when it came to 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."
The discovery is now attributed in math books to British scientist Sir Isaac Newton and his German contemporary Gottfried Leibnitz at the end of the 17^th century. There was strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the 15^th century.
That knowledge may have eventually been passed on to Newton himself, he said.
"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 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.
"There were many such requests for information across the world from leading Jesuit researchers in Europe . Kerala mathematicians were hugely skilled in this area." There were many reasons why the contribution of the Kerala School has not been acknowledged till now. A prime reason, was the "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." "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." 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.
(source: When Kerala scholars beat Newton - rediff.com and Indians Predated Newton 'Discovery' By 250 Years, Scholars Say - sciencedaily.com).

Brian Clegg , author of popular science books has written:

"The characters we use for the numbers arrived here from India via the Arabic world. The Brahmi numerals that have been found in caves and on coins around Mumbai from around the first century AD use horizontal lines for 1 to 3. The squiggles used for 4 to 9, however, are clear ancestors of the numbers we use today. These symbols were gradually taken up by Arabs and came to Western attention in the 13^th century thanks to two books, on written by a traveler from Pisa, the other by a philosopher in Baghdad. The earlier book was written by the philosopher al-Khwarizmi in the 9^th century. The Latin translation Algoritmi de numero Indorum (al-Khwarizmi on the numbers of the Hindus).

The translation of De numero Indorum slightly predates the man who is credited with introducing the system to the West. Leonardo of Pisa, or by his nickname Fibonacci. In the comments in his book Liberabaci, written in 1202, he states that he was “introduced to the art of Indian’s nine symbols” and it was this book that really brought the Hindu system to the West.

(source: Infinity: The Quest to Think the Unthinkable - By Brian Clegg p. 54 - 60).

Carl B. Boyer (1906 – 1976) in his "History of Mathematics" pages 227-228”. “...Mohammed ibn-Musa al-Khwarizmi, ..., who died sometime before 850, wrote more than a half dozen astronomical and mathematical works, of which the earliest were probably based on the Sindhind derived from India. Besides ... [he] wrote two books on arithmetic and algebra which played very important roles in the history of mathematics. ... In this work, based presumably on an Arabic translation of Brahmagupta, al-Khwarizmi gave so full an account of the Hindu numerals that he probably is responsible for the widespread but false impression that our system of numeration is Arabic in origin. ...

Edward Sachau, In a translation of Alberuni ‘s “Indica”, a seminal work of this period (c.1030 AD), writes this in his introduction, “Many Arab authors took up the subjects communicated to them by the Hindus and worked them out in original compositions , commentaries and extracts. A favourite subject of theirs was Indian mathematics..." etc.

“ Al-Khwarizmi wrote numerous books that played important roles in arithematic and algebra. In his work, De numero indorum (Concerning the Hindu Art of Reckoning), it was based presumably on an Arabic translation of Brahmagupta where he gave a full account of the Hindu numerals which was the first to expound the system with its digits 0,1,2,3,....,9 and decimal place value which was a fairly recent arrival from India. Because of this book with the Latin translations made a false inquiry that our system of numeration is arabic in origin. The new notation came to be known as that of al-Khwarizmi, or more carelessly, algorismi; ultimately the scheme of numeration making use of the Hindu numerals came to be called simply algorism or algorithm, a word that, originally derived from the name al-Khwarizmi, now means, more generally, any peculiar rule of procedure or operation.

Interestingly, as the article notes, “The Hindu numerals like much new mathematics were not welcomed by all. In 1299 there was a law in the commercial center of Florence forbidding their use; to this day this law is respected when we write the amount on a check in longhand .”

“It is now universally accepted that our decimal numbers derive from forms, which were invented in India and transmitted via Arab culture to Europe, undergoing a number of changes on the way. We also know that several different ways of writing numbers evolved in India before it became possible for existing decimal numerals to be marred with the place-value principle of the Babylonians to give birth to the system which eventually became the one which we use today. Because of lack of authentic records, very little is known of the development of ancient Hindu mathematics. The earliest history is preserved in the 5000-year-old ruins of a city at Mohenjo Daro, located Northeast of present-day Karachi in Pakistan. Evidence of wide streets, brick dwellings an apartment houses with tiled bathrooms, covered city drains, and community swimming pools indicates a civilisation as advanced as that found anywhere else in the ancient Orient.

These early peoples had systems of writing, counting, weighing, and measuring, and they dug canals for irrigation. All this required basic mathematics and engineering. “The special interest of the Indian system is that it is the earliest form of the one, which we use today. Two and three were represented by repetitions of the horizontal stroke for one. There were distinct symbols for four to nine and also for ten and multiples of ten up to ninety, and for hundred and thousand.”

“…Knowledge of the Hindu system spread through the Arab world, reaching the Arabs of the West in Spain before the end of the tenth century. The earliest European manuscript, which came from the Hindu numerals were modified in north-Spain from the year 976.” And finally an important point for those who maintain that the concept of zero was also evident in some other civilisations: “Only the Hindus within the context of Indo-European civilisations have consistently used zero.”

(source: Hindu contribution to Mathematics - By B Shantanu - indiacause.com).
David Mumford, the eminent mathematician writes in his review of the book, Mathematics in India by Kim Plofker:
"Did you know that Vedic priests were using the so-called Pythagorean theorem to construct their fire altars in 800 BCE?; that the differential equation for the sine function, infinite difference form, was described by Indian mathematician-astronomers in the fifth century CE?; and that 'Gregory's' series PI/4 = 1 -1/3+1/3-… was proven using the power series for arctangent and, with ingenious summation methods, used to accurately compute PI in southwest India in the fourteenth century?
(source: Mathematics in India - Reviewed by David Mumford - AMS American Mathematical Society - Volume 57 Number 3).

Gopala and Hemachandra and rhythmic patterns
Donald Knuth (1938 - ) of Stanford University in The Art of Computer Programming also wrote about this:
"Before Fibonacci wrote his work, the sequence Fn had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes. The number of such rhythms having n beats altogether is Fn+1; therefore both Gopala (before 1135) and Hemachandra (c. 1150) mentioned the numbers 1, 2, 3, 5, 8, 13, 21, ... explicitly."
The system that Fibonacci introduced into Europe came from India and used the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 with, most importantly, a symbol for zero 0.

(source: Who was Fibonacci? and Origins of Fibonacci number and Fibonacci numbers or Hemecandra numbers? and Gopala and Hemachandra numbers everywhere - sepiamutiny.com Hemachandra).

Ian G. Pearce ( ? ) has written: “Mathematics has long been considered an invention of European scholars, as a result of which the contributions of non-European countries have been severely neglected in histories of mathematics. Worse still, many key mathematical developments have been wrongly attributed to scholars of European origin. This has led to so-called Eurocentrism. ...The purpose of my project is to highlight the major mathematical contributions of Indian scholars and further to emphasize where neglect has occurred and hence elucidate why the Eurocentric ideal is an injustice and in some cases complete fabrication.”

“It is through the works of Vedic religion that we gain the first literary evidence of Indian culture and hence mathematics. Written in Vedic Sanskrit the Vedic works, Vedas and Vedangas (and later Sulbasutras) are primarily religious in content, but embody a large amount of astronomical knowledge and hence a significant knowledge of mathematics. ... 'The need to determine the correct times for Vedic ceremonies and the accurate construction of altars led to the development of astronomy and geometry.'”

“I feel it important not to be controversial or sweeping, but it is likely European scholars are resistant due to the way in which the inclusion of non-European, including Indian, contributions shakes up views that have been held for hundreds of years, and challenges the very foundations of the Eurocentric ideology. ... It is almost more in the realms of psychology and culture that we argue about the effect the discoveries of non-European science may have had on the 'psyche' of European scholars. ... To summarize, the main reasons for the neglect of Indian mathematics seem to be religious, cultural and psychological”

(source: Indian Mathematics: Redressing the balance' - 'Abstract' - By Ian G. Pearce – '(IGP-IM:RB) 'Mathematics in the service of religion: I. Vedas and Vedangas' and Conclusion.

For more refer to The Infinitesimal Calculus: How and Why it Was Imported into Europe - By C. K. Raju and
Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ - By C. K. Raju

Remarking on this valuable contribution specially the discovery of number from one to nine and zero, which is considered to be the greatest and the most important, next only to the introduction of letters, Prof. Halsted of USA holds that no discovery in Arithmetic has contributed so much in the development of human intelligence and power. The Hindus can claim to be superior to the Greeks for the introduction of this system.
(source: Ancient Indian Culture At A Glance - By Swami Tattwananda Calcutta, Oxford Book Co. 1962 p. 121).
Zero is the embodiment of purna (full), lopa (absence), akasa (universe), bindu (dot), sunya (circle), in Indian literary and cultural traditions. The concept got concretized in the form of a symbol like dot or circle to fill up the empty space created in Indian decimal place-value concept. The scientific advances of the West would have been impossible had scientists continued to depend upon the Roman numerals and been deprived of the simplicity and flexibility of the decimal system and its main glory, the zero.

A 10^th century traveler Masaudi, in his Arabic work Meadows of Gold, records that a Hindu Raja called Pandit who counted nine digits by memory. Abu Zafar Muhammad Al Khwarizm also mentions Hindu mathematicians, as does Al Beruni. In the Journal of the Bengal Asiatic Society (1907 p. 475), Feroz Abadi is quoted to have given the history of ‘Hindsa’ (= 0).

The number ‘10’ is a special contribution of Hindu arithmetic. So the zero was called ‘Hindsa’ in Persian.

(source: Hinduism: Its Contribution to Science and Civilization - By Prabhakar Balvant Machwe p. 10-14).

Muhammad ibn Musa al-Khawarazmi 772-773 A.D. who journeyed east to India to learn the sciences of that time. He introduced Hindu numerals, including the concept of zero, into the Arab world. Abu Abdulla Muhammad Ibrahim-al-Fazari translated Sidhanta from Sanskrit into Arabic, which, according to George Sarton (1884-1956) the great Harvard historian of science, wrote in his monumental Introduction to the History of Science, provided "possibly the vehicle by means of which the Hindu numerals were transmitted from India to Islam".

***
Algebra

Brahmagupta gives the following rules concerning operations carried out on what he calls “fortunes” (dhana), “debts” (rina) and “nothing” (kha).

A debt minus zero is a debt.
A fortune minus zero is a fortune.
Zero (shunya) minus zero is nothing. (kha).
A debt subtracted from zero is a fortune.
So a fortune subtracted from zero is a debt.
The product of zero multiplied by a debt or fortune is zero.
The product of zero multiplied by itself is nothing.
The product or the quotient of two fortunes is one fortune.
The product or the quotient of two debts is one debt.
The product or the quotient of a debt multiplied by a fortune is a debt.
The product or the quotient of a fortune multiplied by a debt is a debt.

Modern algebra was born, and the mathematician had thus formulated the basic rules: by replacing “fortune” and “debt” respectively with “positive number” and “negative number”, we can see that at that time the Indian mathematicians knew the famous “rule of signs” as well as all the fundamental rules of algebra.

(source: The Universal History of Numbers - By Georges Ifrah p 439).

Florian Cajori (1859 - 1930) Swiss-born U.S. educator and mathematician whose works on the history of mathematics says:

"Indians were the “real inventors of Algebra”

(source: Is India Civilized - Essays on Indian Culture - By Sir John Woodroffe Ganesh & Co. Publishers 1922 p. 182).

Friedrich Rosen (1805-1837) edited and translated in 1831, The Algebra of Mohammed ben Musa. This is the oldest Arabic on mathematics and it shows that the Arabs borrowed algebra from India.

(source: German Indologists: Biographies of Scholars in Indian Studies writing in German - By Valentine Stache-Rosen p.24-25).

Algebra went to Western Europe from the Arabs - i.e. (Al-jabr, adjustment) who adopted it from India rather than from Greece. Sir Monier-Williams, T. S. Colebrooke, and Macdonell hold that the Arabs got Algebra from the Hindus. The great Indian leaders in this field, as in astronomy were Aryabhata, Brahmagupta, and Bhaskara. The last appears to have invented the radical sign and many algebraic symbols. These men created the conception of a negative quantity, without which algebra would have been impossible; they found the square root of 2, and solved, in the eighth century A.D., indeterminate equations of the second degree that were unknown to Europe until the days of Euler a thousand years later. They expressed their science in poetic form and gave to mathematical problems a grace characteristic to India's Golden Age.
Henry Thomas Colebrooke (1765-1837) wrote: "They (the Hindus) understood well the arithmetic of surd roots; they were aware of the infinite quotient resulting from the division of finite quantities by cipher; they knew the general resolution of equations of the second degree, and had touched upon those of higher denomination, resolving them in the simplest cases, and in those in which the solution happens to be practicable by the method which serves for quadratics; they had attained a general solution of indeterminate problems of the first degree; they had arrived at a method for deriving a multitude of solutions or answers to problems of the second degree from a single answer found tentatively."
"And this, says Colebrooke in conclusion, was as near an approach to a general solution of such problems as was made until the days of La Grange."
(source: Miscellaneous Essays - By H. T. Colebrooke Volume II p. 416 - 418).
Aryabhata (475 A.D. - 550 A.D.) is the first well known Indian mathematician. Born in Kerala, he completed his studies at the university of Nalanda. In the section Ganita (calculations) of his astronomical treatise Aryabhatiya (499 A.D.) he made the fundamental advance in finding the lengths of chords of circles, by using the half chord rather than the full chord method used by Greeks. He gave the value of pi as 3.1416, claiming, for the first time, that it was an approximation. (He gave it in the form that the approximate circumference of a circle of diameter 20000 is 62832.) He also gave methods for extracting square roots, summing arithmetic series, solving indeterminate equations of the type ax - by = c, and also gave what later came to be known as the table of Sines. He also wrote a text book for astronomical calculations, Aryabhatasiddhanta. Even today, this data is used in preparing Hindu calendars (Panchangs). In recognition to his contributions to astronomy and mathematics, India's first satellite was named Aryabhata.
Soviet historians, K. Antonova, G. Bongard-Levin, and G. Kotovsky, authors of A History of India, Moscow, Volume I and II 1973, have spoken highly of scientists of ancient India and their high originality:
"In the ancient period and in the early Middle Ages lived the outstanding mathematicians Aryabhatta (5-6th centuries), Varahamihira (6th century) and Brahmagupta (late 6th and early 7th centuries), whose discoveries anticipated many scientific achievements of modern times. Aryabhata knew that pi equaled 3.1416. The theorem known to us as Pythagoras' theorem was also known at that time. Aryabhata proposed an original solution in whole numbers to the linear equations with two unknowns that closely resembles modern solutions.
"The ancient Indians evolved a system for calculation using zero, which was later taken over by the Arabs (the so-called Arabic numerals) and alter from them by other peoples. The Aryabhatta school was also familiar with sine and cosine.
"Scholars of the Gupta period were already acquainted with the movement of the heavenly bodies, the reasons for eclipses of the Sun and the Moon. Aryabhatta put forward a brilliant thesis with regard to the Earth's rotation on its axis."
"Aryabhatta's follower, Brahmagupta, put forward solutions for a whole series of equations."
"Indian scholars of this period also scored important successes in the sphere of astronomy. Certain astronomical treatises of this period have been preserved, and these siddhantas bear witness to the high level of astronomical knowledge attained by the ancient Indians."
"Brahmagupta (many centuries before Newton) suggested that objects fall to the ground as a result of terrestrial gravity."
"Interesting material relating to astronomy, geography and mineralogy is found in Varahamihira's work Brihat-samhita...."
(source: A History of India - By K. Antonova, G. Bongard-Levin, and G. Kotovsky Moscow, Volume I and II 1973 p. 169-171).
Aryabhatta was a great astronomer of remarkable originality. He is famous for his suggestions of the diurnal revolution of the earth on its own axis. Another important conclusion was about the apparent motion of the sun and the moon. He observes: "The starry vault is fixed: it is the earth which, moving on its own axis, seems to cause the rising and the setting of the planets and stars."
(source: Main Currents in Indian Culture - By S. Natarajan - The Institute of Indo-Middle East Cultural Studies. 1960. p 62-63).
Yavadvipa, the ancient name for Java, to which Sugriva sent search parties looking for Sita, is a Sanskrit name mentioned in the Ramayana. Aryabhatta wrote that when the sun rose in Sri Lanka, it was midday in Yavakoti (Java) and midnight in the Roman land. In the Surya Siddanata reference is also made to the Nagari Yavakoti with golden walls and gates.
(source: India and World Civilization - By D. P. Singhal Pan Macmillan Limited. 1993. p. 323).

Mnemonic and shorthand code letters were used by the Hindu astronomer Aryabhat, who composed his Aryabhatiya in 499 A.D. He answers the question: “How many times does the Earth rotate in a Mahayuga?” by the sutra – Ngishi Bunlrukshshru. Its letters count up to 15,82,23,75,200.

The second Aryabhatta (II) has also given such cryptic numberal-alphabets:

Kanadhajhajhujhila = 1599993
Mudayasinadha = 58179

(source: Hinduism: Its Contribution to Science and Civilization - By Prabhakar Balvant Machwe p. 10-14).

Comparing the Hindus and the Greeks as regards their knowledge of algebra, Sir Mountstuart Elphinstone says:
"There is no question of the superiority of the Hindus over their rivals in the perfection to which they brought the science. Not only is Aryabhatta superior to Diaphantus (as is shown by his knowledge of the resolution of equations involving several unknown quantities, and in general method of resolving all indeterminate problems of at least the first degree), but he and his successors press hard upon the discoveries of algebraists who lived almost in our own time!"

(source: History of India - By Mountstuart Elphinstone London: John Murray Date of Publication: 1849 p. 131).
The Aryabhatiya was translated into Latin in the 13^th century. Through this translation European mathematicians eventually learned methods for calculating the squares of triangles and the volumes of spheres, as well as square and cube roots. He had conceptualized the ideas about the cause of eclipses and the sun being the source of moonlight a thousand years before the Europeans. A revolutionary thinker in many areas, Aryabhata gave the radius of the planetary orbits in terms of the radius of the earth-sun orbit – that is, their orbits as basically their periods of rotation around the sun. He explained that the glow of the moon and planets was the result of reflected sunlight. And with incredible astuteness, he conceptualized the orbits of the planets as ellipses, a thousand years before Kepler reluctantly (he originally preferred circles) came to the same conclusion. His value for the length of the year at 365 days, six hours, twelve minutes, and thirty seconds, however, is a slightly overestimate; the true value is fewer than 365 days and 6 hours.

"Brahmagupta became the head of the astronomical observatory at Ujjain, the foremost mathematical center of ancient India, where great mathematicians such as Varahamihira had worked and built a strong school of mathematical astronomy. The Brahmasphutasidhanta contains 25 chapters, the first ten of which are arranged by topics such as true longitudes of the planets, lunar eclipses, solar eclipses, rising and settings, the moon’s crescent, the moon’s shadow, conjunctions of the planets with the fixed stars. A large part of the Brahmasphutsidhanta was translated into Arabic in the early 770s and became the basis of various studies by the astronomer Ya’qub ibn Tariq. In 1126 it was translated into Latin. This translation, along with other associated texts translated from Arabic, provided the basis for the Indo-Arabic stage of Western astronomy. The culmination of southern Indian astronomy was the tradition begun by Madhava in Kerala right before 1400. Madhava was renowned for his derivation of the infinite series for pi and the power series for trigonometric functions. His pupil Paramesvara attempted to correct the lunar parameters by conducting a long series of eclipse observations between 1393 and 1432. In these observations he used an astrolabe, an instrument devised to measure the positions of heavenly bodies, to determine the angle of altitude of the eclipsed body and possibly, the time of the phase of the eclipses."

(source: Lost Discoveries: The Ancient Roots of Modern Science - By Dick Teresi p. 133 - 136).

In the Jewish Encyclopedia Vol. XII p 689, it is noted,
"Aryabhatta, the noted Hindu astronomer who lived about 476 A.D. and who is called the Newton of the country, wrote many works on Algebra and Geometry. He first discovered the rotation of the earth round its own axis. As a Jewish writer says the theory that earth is a sphere revolving round its own axis which immortalized Copernicus, was previously known to the Hindus, who were instructed in the truth of it by Aryabhatta."
Jogesh Chandar Roy (1859-1965) Eminent scholar, educationist, writer, linguist, historian. Owing to his talent was conferred many accolades like D.Litt., Acharya, Bidyanidhi, Roy Bahadur etc. He held that the Vedic sages first admitted that the world is round ohterwise the advent of dawn (Usha) in the hymns, before sunrise becomes meaningless."
(source: Ancient Indian Culture At A Glance - By Swami Tattwananda Calcutta, Oxford Book Co. 1962 p. 126).
Arya Bhatta (476 - 550 AD) Father of Astronomy, who in the fifth century AD that is over a millennium and a half ago very accurately calculated many aspects of the spinning earth.
Arya Bhatta"s seminal work Aryabhatiyam was translated in to Arabic in the ninth century and subsequently it journeyed further west. Four hundred years later in the thirteenth century this treatise on astronomy was translated into Latin. The Latin version of Aryabhatiyam provided the foundation for growth of astronomy in Europe . I want my readers to appreciate that the Hindu astronomers of India built the foundation for European astronomy to stand and flourish. Arya Bhatta in a chapter of his treatise entitled Gola, which means circle or sphere, very categorically demonstrates the sphericity of earth, way before any European astronomer even had the vaguest inkling as to the size and shape of our planet. Arya Bhatta"s calculation of the equatorial circumference of earth at 39,968 km is only marginally less (by 62 km) of 40,076 km that we accept today. His calculated duration of one complete rotation of earth round its axis, which in common parlance is stated as 1 day, is absolutely correct at 23 hours 56 minutes and 4.1 seconds. Arya Bhatta also calculated the value of Pi with remarkable accuracy, and laid the foundation of many disciplines of mathematics that included trigonometry and mensuration.
(source: Sea level rise and inundation of coastal India – By Nichiketa Das - indiacause.com)

Brahmagupta (598 A.D. - 665 A.D.) is renowned for introduction of negative numbers and operations on zero into arithmetic. His main work was Brahmasphutasiddhanta, which was a corrected version of old astronomical treatise Brahmasiddhanta. This work was later translated into Arabic as Sind Hind. He formulated the rule of three and proposed rules for the solution of quadratic and simultaneous equations. He was the first mathematician to treat algebra and arithmetic as two different branches of mathematics. He gave the solution of the indeterminate equation Nx²+1 = y². He is also the founder of the branch of higher mathematics known as "Numerical Analysis".
The Hindus were aware of the length of diameter and circumference of the earth. According to Brahmagupta and Bhaskarachary the diameter is 7182 miles, some calculate it to be 7905 miles, modern scientists take it to be 7918 miles. For the sake of astronomical experiments the Hindus introduced Sanka Yantra and Ghati Yantra, the apparatus for measurement.
(source: Ancient Indian Culture At A Glance - By Swami Tattwananda Calcutta, Oxford Book Co. 1962 p. 126).
After Brahmagupta, the mathematician of some consequence was Sridhara, who wrote Patiganita Sara, a book on algebra, in 750 A.D. Even Bhaskara refers to his works. After Sridhara, the most celebrated mathematician was Mahaviracharaya or Mahavira. He wrote Ganita Sara Sangraha in 850 A.D., which is the first text book on arithmetic in present day form. He is the only Indian mathematician who has briefly referred to the ellipse (which he called Ayatvrit). The Greeks, by contrast, had studied conic sections in great detail.
Bhaskara (1114 A.D. - 1185 A.D.) or Bhaskaracharaya is the most well known ancient Indian mathematician. He was born in 1114 A.D. at Bijjada Bida (Bijapur, Karnataka) in the Sahyadari Hills. He was the first to declare that any number divided by zero is infinity and that the sum of any number and infinity is also infinity. He is famous for his book Siddhanta Siromani (1150 A.D.). It is divided into four sections - Leelavati (a book on arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere - celestial globe), and Grahaganita (mathematics of the planets). Leelavati contains many interesting problems and was a very popular text book. Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it "inverse cyclic". Bhaskara can also be called the founder of differential calculus. He gave an example of what is now called "differential coefficient" and the basic idea of what is now called "Rolle's theorem". Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries later, Newton and Leibniz developed this subject. As an astronomer, Bhaskara is renowned for his concept of Tatkalikagati (instantaneous motion).

(source: Ancient Indian Mathematicians and http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bhaskara_II.html).
For more refer to The Infinitesimal Calculus: How and Why it Was Imported into Europe - By C. K. Raju and
Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ - By C. K. Raju

“A Persian translation of the Veeju-Ganitu was made in India,” says Mr. Edward Strachey, “in the year 1634, by Ata Oollah Rusidee.” The same gentlemen says, “Foizee, in 1587, translated the Leelavatee, a work on arithmetic, mensuration,” etc. from which work it appears that “Bhaskara must have written about the end of the 12^th century..”

“We must not,” adds Edward Strachey author of Bija ganita; or, The algebra of the Hindus, “be too fastidious in our belief, because we have not found the works of the teachers of Pythagoras; we have access to the wreck only of their ancient learning; but when such traces of a more perfect state of knowledge; we see that the Hindoo algebra 600 years ago, had, in the most interesting parts, some of the most curious modern European discoveries, and when we see, that it was at that time applied to astronomy, we cannot reasonably doubt the originality and the antiquity of mathematical learning among the Hindoos.”

(source: A View of the History, Literature, and Mythology of the Hindoos - By William Ward (1769-1823) volume II p 329 London 1822).

Sir Mountstuart Elphinstone wrote: "In the Surya Siddhanta is contained a system of trigonometry which not only goes beyond anything known to the Greeks, but involves theorem which were not discovered in Europe till two centuries ago."
(source: Sanskrit Civilization - By G. R. Josyer p. 2).
The discovery of the law of gravitation which immortalized Newton was known in India by Bhaskaracharya long before the birth of Newton. In support of the assumption of this view there is sufficient evidence in a verse in Sidhanta Siromany by its author. Bhaskaracharya holds that when the earth which is endowed with the power of attraction drags with her own power heavy objects on the sky it appears that objects are falling but actually they are not falling, they are only being dragged by the power of attraction of the earth. When everything on the sky drags each other equally where will the earth fall: It is explained that earth, planets, stars, moon, sun etc - each of them is being dragged by the other with its respective power of attraction and as a result of this attraction none of them is removed from its axis.
(source: Ancient Indian Culture At A Glance - By Swami Tattwananda Calcutta, Oxford Book Co. 1962 p. 127).
Sir William Wilson Hunter wrote: "The Hindus attained a very high proficiency in arithmetic and algebra independently of any foreign influence." The romance of the composition of Lilavati - the standard Hindu text book on Arithmetic by Bhaskaracharya - is very interesting and charming. It deals not only with the basic elements of the science of arithmetic but also with questions of interest, of barter, of permutations and combinations, and of mensuration. Bhaskaracharya knew the law of gravitation. The Surya Siddhanta is based on a system of trigonometry. Professor Wallace says: "In fact it is founded on a geometrical theorem, which was not known to the geometricians of Europe before the time of Vieta, about two hundred years ago. And it employs the sine of arcs, a thing unknown to the Greeks." The 47th proposition of Book I of Euclid, which is ascribed to Pythagoras was known long ago to the Hindus and must have been learnt from them by Pythagoras.
(source: Indian Culture and the Modern Age - By Dewan Bahadur K. S. Ramaswami Sastri Annamalai University. 1956 p. 67).
For more refer to chapter on Greater India: Suvarnabhumi and Sacred Angkor

Geometry

Geometry, like Astronomy, owes its origin in India to religion, and Grammar and Philosophy too were similarly inspired by religion.
As George Frederick William Thibaut (1848-1914) author of Mathematics in the making in Ancient India, remarked: "The want of some rule by which to fix the right time for the religious altar gave the first impulse to astronomical observations; urged by this the priest, remained watching night after night the advancement of the moon through the circle of the Nakshatras...The laws of phonetics were investigated....the wrong pronunciation of a single letter of the text; grammar and etymology had the task of securing the right understanding of the holy texts. And Thibaut then lays down the principle, which should never be overlooked by Indian historians, that whatever science "is closely connected with the Ancient Indian religion, must be considered as having sprung up among the Indians themselves, and not borrowed from other nations."
Geometry was developed in India from the rules of the construction of the altars. The Black Yajur Veda (V.4.11) enumerates the different shapes in which altars could be constructed and Baudhayana and Apastamba furnish us with full particulars about the shape of these chitis and the bricks which had to be employed for their construction. The Sulva Sutras date from the eighth century before Christ. The geometrical theorem that the square of the hypotenuse is equal to the squares of the other two sides of a rectangular triangle is ascribed by the Greeks to Pythagoras; but it was known in India at least two centuries before, and Pythagoras undoubtedly learnt this rule from India.
(source: Journal of the Asiatic Society of Bengal, 1875. p. 227 and A History of Civilization in Ancient India Based on Sanscrit Literature - By Romesh Chunder Dutt p. 240-243)
Vedic altars and sacrificial places were constructed according to strict geometrical principles. The Vedic (altar) had to be stacked in a geometrical form with the sides in fixed proportions, and brick altars had to combine fixed dimensions with a fixed number of bricks. Again, the surface areas were so designed that altars could be increased in size without change of shape, which required considerable geometrical ingenuity.

Geometrical rules found in the Sulvasutras, therefore, refers to the construction of squares and rectangles, the relation of the diagonal to the sides, equivalent rectangles and squares, equivalent circles and squares, conversion, of oblongs into squares and vice versa, and the construction of squares equal to the sum or difference of two squares. In such relations a prior knowledge of the Pythagorean theorem, that the square of the hypotenuse of a right-angled triangle is equal to the sum of squares of the other two sides, is disclosed.
In measurement and construction of altars the priests formulated the Pythagorean theorem (by which the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other side) several hundred years before the birth of Christ.
As every schoolchild knows, the most important theorem in geometry is that of Pythagoras. Yet, there is no evidence that either the statement or the proof was known by the man to whom it is credited. The earliest statement can be found in the Sulbasutra of Baudhyana. Baudhayana has preserved its germination in religious rituals. The fact that ancient Indians knew this theorem was recognized quite early by some European scholars. Among the first was G. Thibaut, a historian of science, who left the impression that in geometry the Pythagoreans were the pupils of the Indians. Scholars unhappy with this idea tried to refute it, thought their refutation was, as Abraham Seidenberg, noted, were no more haughty dismissals.

The Formula known today as the Pythagorean Theorem was first postulated by Indian mathematician - Baudhayana in the 6th century C. E. long before Europe's math whizzies. In 497 C.E. Aryabhatta calculated the value of "pi" as 3.1416. Algebra, trigonometry and the concepts of algorithm, square root originated in India. Quadratic equations were propounded by Sridharacharya in the 11th century.

The largest number used by Greeks and Romans were 106, whereas Indians used numbers as big as 10 to the power of 53, as early as 5000 BCE. Even geometry called Rekha Ganita in ancient India, was applied to draft mandalas for architectural purposes and for creating temple motifs.

Professor H. G. Rawlinson writes: " It is more likely that Pythagoras was influenced by India than by Egypt. Almost all the theories, religions, philosophical and mathematical taught by the Pythagoreans, were known in India in the sixth century B.C., and the Pythagoreans, like the Jains and the Buddhists, refrained from the destruction of life and eating meat and regarded certain vegetables such as beans as taboo" "It seems that the so-called Pythagorean theorem of the quadrature of the hypotenuse was already known to the Indians in the older Vedic times, and thus before Pythagoras

(source: Legacy of India 1937, p. 5).

Romesh Chunder Dutt, the famous Indian historian holds that the world is indebted to the Hindus for Geometry and not to the Greeks.

(source: Ancient Indian Culture At A Glance - By Swami Tattwananda Calcutta, Oxford Book Co. 1962 p. 124).

Professor Maurice Winternitz is of the same opinion: "As regards Pythagoras, it seems to me very probable that he became acquainted with Indian doctrines in Persia." (Visvabharati Quarterly Feb. 1937, p. 8).

It is also the view of Sir William Jones (Works, iii. 236), Colebrooke (Miscellaneous Essays, i. 436 ff.). Schroeder (Pythagoras und die Inder), Garbe (Philosophy of Ancient India, pp. 39 ff), Hopkins (Religions of India, p. 559 and 560) and Macdonell (Sanskrit Literature, p. 422).

(source: Eastern Religions & Western Thought - By S. Radhakrishnan ISBN: 0195624564 p. 143).

Ludwig von Schröder German philosopher, author of the book Pythagoras und die Inder (Pythagoras and the Indians), published in 1884, he argued that Pythagoras had been influenced by the Samkhya school of thought, the most prominent branch of the Indic philosophy next to Vedanta.

(source: In Search of The Cradle of Civilization: : New Light on Ancient India - By Georg Feuerstein, Subhash Kak & David Frawley p. 252).

" Nearly all the philosophical and mathematical doctrines attributed to Pythagoras are derived from India."
Sir William Temple, (1628-1699) English statesman and diplomat, in his Essay upon the Ancient and Modern Learning (1690) he wrote:
"From these famous Indians, it seems most probable that Pythagoras learned, and transported into Greece and Italy, the greatest part of his natural and moral philosophy, rather than from the Aegyptians...Nor does it seem unlikely that the Aegyptians themselves might have drawn much of their learning from the Indians..long before..Lycurgus, who likewise traveled to India, brought from thence also the chief principles of his laws."
Temple's ideas remained in isolation in his period until they were revived in the middle of the 18th century when a battle raged between the 'believers' and the 'infidels' on the question of the value of Mosaic interpretation of history.
(source: Much Maligned Monsters: A History of European Reactions to Indian Art - By Partha Mitter p. 191).
Aryabhata, found the area of a triangle, a trapezium and a circle, and calculated the value of "pi" ( the relation of diameter to circumference in a circle) at 3.1416 - a figure not equaled in accuracy until the days of Purbach (1423-61) in Europe. Bhaskara anticipated the differential calculus, Aryabhata drew up a table of sines, and the Surya Siddhanta provided a system of trigonometry more advance than anything known to the Greeks. He had tabulated the sine function (unknown in Greece) for every 3³/₄º of arc from 3³/₄º to 90º. By 670 the system had reached northern Mesopotamia, where the Nestorian bishop Severus Sebokht praised its Hindu inventors as discoverers of things more ingenious than those of the Greeks. Muslims began the acquisition of foreign learning, and, by the time of the Caliph al-Mansur (d. 775), such Indian and Persian astronomical material as the Brahma-sphuta-siddhanta and the Shah's Tables had been translated into Arabic.
A 3,000-year-old ritual was resurrected at Panjal in Kerala in April 1975. A 12-day Agnicayana, or Atiratra, was performed on a bird-shaped altar of a thousand bricks. The altar was a geometricians' delight.

The area of each layer of the altar, for instance, was seven and a half times a square purusa, the size of the sacrificer or the Yajamana. A fifth of the size of the Yajamana, panchami, was the basic unit of the bricks.

The rules for measurement and construction of sacrificial altars are found in the Sulba Sutras, the earliest documents of geometry in India. Sulba means cord. Of the various Sulba Sutras, those of Baudhayana, Apastamba and Katyayana are best known. The mathematical knowledge in the texts comes from the creation of altars or bricks in various shapes-rhombus, isosceles trapezium, square, rectangle, isosceles right-angled triangle or circle. A square-shaped altar sometimes had to become circular without any change in the area or vice-versa. Obviously, the authors of the Sulba texts knew the value of pi, which is the ratio of the circumference to the diameter of a circle.

The theory of right angles is attributed to Greek philosopher Pythagoras (6th century BC). But Baudhayana mentions that the diagonal of a rectangle produces by itself both (the areas) produced separately by its two sides. In simple terms, this means that the square of the diagonal is equal to the sum of the squares of two sides. In the next rule he says that the rectangles for which the theorem is true have the sides as 3 and 4 [32+42=52], 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36. The theorem is given in all the Sulba Sutras.

Eminent mathematician A. K. Bag, he says tackling of mathematical and geometrical problems with rational numbers and irrational numbers [such as square-root of 2] was a unique achievement of early Indians. They even had technical terms such as dvikarani, trikarani and panchakarani (for square-roots of 2, 3 and 5) and so on and gave their values to a high degree of approximation.

The mathematics in Sulba texts also involves a highly sophisticated brick technology. Ten types of bricks were used to build the altar at Panjal.
Sir Monier-Williams says: "To the Hindus is due the invention of algebra and geometry, and their application to astronomy."
(source: Indian Wisdom - By Monier Williams p. 185).
Count Magnus Fredrik Ferdinand Bjornstjerna author of Theogony of the Hindus says: "We find in Ayeen-Akbari, a journal of the Emperor Akbar, that the Hindus of former times assumed the diameter of a circle to be to its periphery as 1,250 to 3,927. The ratio of 1,250 to 3,927 is a very close approximation to the quandrature of a circle, and differs very little form that given by Metius of 113 to 355. In order to obtain the result thus found by the Brahmans, even in the most elementary and simplest way, it is necessary to inscribe in a circle a poligon of 768 sides, an operation, which cannot be performed arithmetically without the knowledge of some peculiar properties of this curved line, and at least an extraction of the square root of the ninth power, each to ten places of decimals. The Greeks and Arabs have not given anything so approximate."
Professor Wallace says: "However ancient a book may be in which a system of trigonometry occurs, we may be assured it was not written in the infancy of the science. Geometry must have been known in India long before the writing of Surya Siddanata." which is supposed by the Europeans to have been written before 2000 B. C. E.
(source: Sanskrit Civilization - By G. R. Josyer p. 2-3).
Influence of Hindu Geometry on Greeks:
In his monumental work, The origin of mathematics, Archive for History of Exact Sciences. vol. 18, 301-342, Abraham Seidenberg remarks: "By examining the evidence in the Shatapatha Brahmana, we now know that Indian geometry predates Greek geometry by centuries. For example, the earth was represented by a circular altar and the heavens were represented by a square altar and the ritual consisted of converting the circle into a square of an identical area. There we see the beginnings of geometry! Two aspects of the 'Pythagoras' theorem are described in the Vedic literature. One aspect is purely algebraic that presents numbers a, b, c for which the sum of the squares of the first two equals the square of the third. The second is the geometric, according to which the sum of the areas of two square areas of different size is equal to another square. The Babylonians knew the algebraic aspect of this theorem as early as 1700 BCE, but they did not seem to know the geometric aspect. The Shatapatha Brahmana, which precedes the age of Pythagoras, knows both aspects. Therefore, the Indians could not have learnt it from the Old-Babylonians or the Greeks, who claim to have rediscovered the result only with Pythagoras. India is thus the cradle of the knowledge of geometry and mathematics."
So, contrary to the European belief that Hindus were influenced by the Greek geometry, the facts prove that it is the other way round. Most of the aspects of planar geometry described by Euclid and other Greek mathematicians were already known to Indians at least 2500 years before the Greeks. In fact, there are proofs which hint towards the fact Greeks were influenced by the ancient Hindu Mathematics and Geometry. Bibhuti Bhushan Datta in his book "Ancient Hindu Geometry" states:

"...One who was well versed in that science was called in ancient India as samkhyajna (the expert of numbers), parimanajna (the expert in measuring), sama-sutra-niranchaka (Uinform-rope-stretcher), Shulba-vid (the expert in Shulba) and Shulba-pariprcchaka (the inquirer into the Shulba). Of these term, viz, 'sama-sutra-niranchaka' perhaps deserves more particular notice. For we find an almost identical term, 'harpedonaptae' (rope-stretcher) appearing in the writings of the Greek Democritos (c. 440 BC). It seems to be an instance of Hindu influence on Greek geometry. For the idea in that Greek term is neither of the Greeks nor of their acknowledged teachers in the science of geometry, the Egyptians, but it is characteristically of Hindu origin." The English word 'Geometry' has a Greek root which itself is derived from the Sanskrit word 'Jyamiti'. In Sanskrit 'Jya' means an arc or curve and 'Miti' means correct perception or measurement.
The Sulba Sutras, however, date from about the eighth century B.C. E. and Dr. Thibault has shown that the geometrical theorem of the 47th proposition, Book I, which tradition ascribes to Pythagoras, was solved by the Hindus at least two centuries earlier, thus confirming the conclusion of Von Schroeder that the Greek philosopher owed his inspiration to India.
(source: History of Hindu Chemistry, Volume I p. XXIV ).

A. L. Basham, foremost authority on ancient India, writes in The Wonder That Was India:

"Medieval Indian mathematicians, such as Brahmagupta (seventh century), Mahavira (ninth century), and Bhaskara (twelfth century), made several discoveries which in Europe were not known until the Renaissance or later. They understood the import of positive and negative quantities, evolved sound systems of extracting square and cube roots, and could solve quadratic and certain types of indeterminate equations." Mahavira's most noteworthy contribution is his treatment of fractions for the first time and his rule for dividing one fraction by another, which did not appear in Europe until the 16th century.

B. B. Dutta writes: "The use of symbols-letters of the alphabet to denote unknowns, and equations are the foundations of the science of algebra. The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra."

The great Indian mathematician Bhaskaracharya (1150 C.E.) produced extensive treatises on both plane and spherical trigonometry and algebra, and his works contain remarkable solutions of problems which were not discovered in Europe until the seventeenth and eighteenth centuries. He preceded Newton by over 500 years in the discovery of the principles of differential calculus.

A. L. Basham writes further, "The mathematical implications of zero (sunya) and infinity, never more than vaguely realized by classical authorities, were fully understood in medieval India. Earlier mathematicians had taught that X/0 = X, but Bhaskara proved the contrary. He also established mathematically what had been recognized in Indian theology at least a millennium earlier: that infinity, however divided, remains infinite, represented by the equation /X = ."

In the 14th century, Madhava, isolated in South India, developed a power series for the arc tangent function, apparently without the use of calculus, allowing the calculation of to any number of decimal places (since arc tan 1 = /4). Whether he accomplished this by inventing a system as good as calculus or without the aid of calculus; either way it is astonishing. Stanley Wolpert says: " An untutored Kerala mathematician named Madhava developed his own system of calculus, based on his knowledge of trigonometry around A.D. 1500, more than a century before either Newton or Liebnitz.

(source: An Introduction to India - By Stanley Wolpert p. 195).

By the fifteenth century C. E. use of the new mathematical concepts from India had spread all over Europe to Britain, France, Germany, and Italy, among others. A. L. Basham states also that

"The debt of the Western world to India in this respect [the field of mathematics] cannot be overestimated. Most of the great discoveries and inventions of which Europe is so proud would have been impossible without a developed system of mathematics, and this in turn would have been impossible if Europe had been shackled by the unwieldy system of Roman numerals. The unknown man who devised the new system was, from the world's point of view, after the Buddha, the most important son of India. His achievement, though easily taken for granted, was the work of an analytical mind of the first order, and he deserves much more honor than he has so far received."

Carl Friedrich Gauss ( 1777-1855), German scientist and mathematician, was considered as the "prince of mathematics. He is frequently called the founder of modern mathematics, who also studied Sanskrit.

Gauss "was said to have lamented that Archimedes in the third century B.C. E. had failed to foresee the Indian system of numeration; how much more advanced science would have been."

Unfortunately, Eurocentrism has effectively concealed from the common man the fact that we owe much in the way of mathematics to ancient India.

In ancient India, mathematics served as a bridge between understanding material reality and the spiritual conception. Vedic mathematics differs profoundly from Greek mathematics in that knowledge for its own sake (for its aesthetic satisfaction) did not appeal to the Indian mind. The mathematics of the Vedas lacks the cold, clear, geometric precision of the West; rather, it is cloaked in the poetic language which so distinguishes the East. Vedic mathematicians strongly felt that every discipline must have a purpose, and believed that the ultimate goal of life was to achieve self-realization and love of God and thereby be released from the cycle of birth and death.

After this period, India was repeatedly raided by muslims and other rulers and there was a lull in scientific research. Industrial revolution and Renaissance passed India by. Before Ramanujan, the only noteworthy mathematician was Sawai Jai Singh II, who founded the present city of Jaipur in 1727 A.D. This Hindu king was a great patron of mathematicians and astronomers. He is known for building observatories (Jantar Mantar) at Delhi, Jaipur, Ujjain, Varanasi and Mathura. Among the instruments he designed himself are Samrat Yantra, Ram Yantra and Jai Parkash.

More recently, intuitive Indian mathematical genius Srinivas Ramanujan (1887-1920), a friend to all numbers, was invited to Cambridge by Prof. G. H. Hardy, who recognized his brilliance at the sight of his first equation solution. Julian Huxley called Ramanujan "the greatest mathematician of the century." At the age of thirty he developed a formula for partitioning any natural number, which led to the solving of the Waring problem, expressing an integer as the sum of squares, cubes, or higher powers of a few integers. One day Hardy complained about the cab number that brought him to visit Ramanujan, "1729" as a dull number. Ramanujan responded instantly, " No Hardy, 1729 is a wonderful number! That is the only number which is the sum of two different sets of cubes, 1 and 12, and 9 and 10."

(source: An Introduction to India - By Stanley Wolpert p. 195).

Mountstuart Elphinstone wrote: "Their geometrical skill is shown among other forms by their demonstrations of various properties of triangles, especially one which expresses the area in the terms of the three sides, and was unknown in Europe till published by Clavius, and by their knowledge of the proportions of the radius to the circumference of a circle, which they express in a mode peculiar to themselves, by applying one measure and one unit to the radius and circumference. This proportion, which is confirmed by the most approved labors of Europeans, was not known out of India until modern times!"

(source: History of India - By Mountstuart Elphinstone London: John Murray Date of Publication: 1849 p. 130).

Srinivas Ramanujan: A Life of the Genius

Ramanujan is one of India´s great intellectual heroes, a mathematical genius who attributed his brilliance to a personal relationship with a Hindu Goddess - Namagiri. His work has been used to help unravel knots as varied as polymer chemistry and cancer, yet how he arrived at this theorems is still unknown. By age twelve he had mastered trigonometry so completely that he was inventing sophisticated theorems that astonished teachers. Mathematicians have mined his theorems ever since. They've figured out how to prove them. They've put them to use. Only recently, a lost bundle of his notebooks turned up in a Cambridge library. That set mathematics off on a whole new voyage of discovery. And where did all this unproven truth come from? Ramanujan was quick to tell us. He simply prayed to Sarasvathi, the Goddess of Learning, and she informed him.

His twenty-one major mathematical papers are still being plumbed for their secrets, and many of his ideas are used today in cosmology and computer science. The unsettling thing is, none of us can find any better way to explain the magnitude of his eerie brilliance.

(source: http://www.uh.edu/engines/epi495.htm ) John H. Lienhard (source: The Man Who Knew Infinity: A Life of the Genius Ramanujan - by Robert Kanigel)..(source: Ramanujan and Computing the Mathematical face of God). For more on Ramanuja, refer to chapter on Quotes321_340).

Vedic Mathematics

"Vedic Mathematics" is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles, with which any mathematical problem — be it arithmetic, algebra, geometry or trigonometry — can be solved. The system is based on 16 Vedic sutras or aphorisms, which are actually word-formulae describing natural ways of solving a whole range of mathematical problems. Some examples of sutras are "By one more than the one before", "All from 9 & the last from 10", and "Vertically & Crosswise". These 16 one-line formulae originally written in Sanskrit, which can be easily memorized, enables one to solve long mathematical problems quickly.

Born in the Vedic Age, but buried under centuries of debris, this remarkable system of calculation was deciphered towards the beginning of the 20th century, when there was a great interest in ancient Sanskrit texts, especially in Europe. However, certain texts called Ganita Sutras, which contained mathematical deductions, were ignored, because no one could find any mathematics in them. These texts, it's believed, bore the germs of what we now know as Vedic Mathematics.

Vedic math was rediscovered from the ancient Indian scriptures between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960), a scholar of Sanskrit, Mathematics, History and Philosophy. He studied these ancient texts for years, and after careful investigation was able to reconstruct a series of mathematical formulae called sutras.
Bharati Krishna Tirthaji, who was also the former Shankaracharya of Puri, India, delved into the ancient Vedic texts and established the techniques of this system in his pioneering work — Vedic Mathematics (1965), which is considered the starting point for all work on Vedic math. It is said that after Bharati Krishna's original 16 volumes of work expounding the Vedic system were lost, in his final years he wrote this single volume, which was published five years after his death.

(source: Vedic Mathematics - about.com). For more refer to chapter on Glimpses VIII and Vedic Math websites).

The Indic Mathematical tradition

Jean-Étienne Montucla (1725-1799) French author of Histoire des mathematiques (1798):

“The ingenious number-system, which serves as the basis for modern arithmetic, was used by the Arabs long before it reached Europe . It would be a mistake, however, to believe that this invention is Arabic. There is a great deal of evidence, much of it provided by the Arabs themselves that this arithmetic originated in India .” [Montucla, I, p. 375J.

John Walls (1616-1703) referred to the nine numerals as Indian figures [Wallis (1695), p. 10]

Cataneo (1546) le noue figure de gli Indi, “the nine figures from India ”. [Smith and Karpinski (1911), p.3

Willichius (1540) talks of Zyphrae! Nice, “Indian figures”. [Smith and Karpinski (1911) p. 3]

The Crafte of Nombrynge (c. 1350), the oldest known English arithmetical tract: II fforthermore ye most vndirstonde that in this craft ben vsed teen figurys, as here bene writen for esampul 098 ^ 654321... in the quych we vse teen figwys of Inde. Questio II why Zen figurys of Inde? Soiucio. For as I have sayd afore thei werefondefrrst in Inde. [D. E. Smith (1909).

Petrus of Dada (1291) wrote a commentary on a work entitled Algorismus by Sacrobosco (John of Halifax, c. 1240), in which he says the following (which contains a mathematical error): Non enim omnis numerus per quascumquefiguras Indorum repraesentatur “Not every number can be represented in Indian figures”. [Curtze (1.897), p. 25.

Around the year 1252, Byzantine monk Maximus Planudes (1260—1310) composed a work entitled Logistike Indike (“Indian Arithmetic”) in Greek, or even Psephophoria kata Indos (“The Indian way of counting”), where he explains the following: “There are only nine figures.

These are: 123456789 - [figures given in their Eastern Arabic form]

A sign known as tziphra can be added to these, which, according to the Indians, means ‘nothing’. The nine figures themselves are Indian, and tziphra is written thus: 0”. [B. N., Pans. Ancien Fonds grec, Ms 2428, f” 186 r”]

Around 1240, Alexandre de Ville-Dieu composed a manual in verse on written calculation (algorism). Its title was Carmen de Algorismo, and it began with the following two lines: Haec algorismus ars praesens dicitur, in qua Talibus Indorumfruimur bis quinquefiguris.

“Algorism is the art by which at present we use those Indian figures, which number two times five”. [Smith and Karpinski (1911), p. 11]

In 1202, Leonard of Pisa (known as Fibonacci), after voyages that took him to the Near East and Northern Africa, and in particular to Bejaia (now in Algeria), wrote a tract on arithmetic entitled Liber Abaci (“a tract about the abacus”), in which he explains the following:

“Cum genitor meus a patria publicus scriba in duana bugee pro pisanis mercatoribus ad earn confluentibus preesset, me in pueritia mea ad se uenire faciens, inspecta utilitate el cornmoditate fiutura, ibi me studio abaci per aliquot dies stare uoluit et doceri. Vbi a mirabii magisterio in arte per nouem figuras Indorum introductus. . . Novem figurae Indorum hae sun!: cum his itaque novemfiguris. et turn hoc signo o. Quod arabice zephirum appellatur, scribitur qui libel numerus: “My father was a public scribe of Bejaia, where he worked for his country in Customs, defending the interests of Pisan merchants who made their fortune there. He made me learn how to use the abacus when I was still a child because he saw how I would benefit from this in later life. In this way I learned the art of counting using the nine Indian figures... The nine Indian figures are as follows:

987654321 - [figures given in contemporary European cursive form].

“That is why, with these nine numerals, and with this sign 0, called zephirum in Arab, one writes all the numbers one wishes.”[Boncompagni (1857), vol.1]

Rabbi Abraham Ben MeIr Ben Ezra (1092—1167), after a long voyage to the East and a period spent in Italy , wrote a work in Hebrew entitled: Sefer ha mispar (“Number Book”), where he explains the basic rules of written calculation. He uses the first nine letters of the Hebrew alphabet to represent the nine units. He represents zero by a little circle and gives it the Hebrew name of galgal (“wheel”), or, more frequently, sfra (“void”) from the corresponding Arabic word. However, all he did was adapt the Indian system to the first nine Hebrew letters (which he naturally had used since his childhood).

In the introduction, he provides some graphic variations of the figures, making it clear that they are of Indian origin, after having explained the place-value system: “That is how the learned men of India were able to represent any number using nine shapes which they fashioned themselves specifically to symbolize the nine units.” (Silberberg (1895), p.2: Smith and Ginsburg (1918): Steinschneider (1893).

Around the same time, John of Seville began his Liberalgoarismi de practica arismetrice (“Book of Algoarismi on practical arithmetic”) with the following:

“Numerus est unitatum cot/echo, quae qua in infinitum progredilur (multitudo enim crescit in infinitum), ideo a peritissimis Indis sub quibusdam regulis et certis lirnitibus infinita numerositas coarcatur, Ut de infinitis dfinita disciplina traderetur etfuga subtilium rerum sub alicuius artis certissima Jege ten eretur:

“A number is a collection of units, and because the collection is infinite (for multiplication can continue indefinitely), the Indians ingeniously enclosed this infinite multiplicity within certain rules and limits so that infinity could be scientifically defined: these strict rules enabled them to pin down this subtle concept.
[B. N., Paris, Ms. lat. 16 202, p 51: Boncompagni (1857), vol. I, p. 261

C. 1143, Robert of Chester wrote a work entitled: Algoritmi de numero Indorum (“Algoritmi: Indian figures”), which is simply a translation of an Arabic work about Indian arithmetic. [Karpinski (1915); Wallis (1685). p. 121

C. 1140, Bishop Raymond of Toledo gave his patronage to a work written by the converted Jew Juan de Luna and archdeacon Domingo Gondisalvo: the Liber Algorismi de numero Indorum (“Book of Algorismi of Indian figures) which is simply a translation into a Spanish and Latin version of an Arabic tract on Indian arithmetic. [Boncompagni (1857), vol. 11

C. 1130, Adelard of Bath wrote a work entitled: Algoritmi de numero Indorum (“Algoritmi: of Indian figures”), which is simply a translation of an Arabic tract about Indian calculation. [Boncompagni (1857), vol. Ii

C. 1125, The Benedictine chronicler William of Malmesbury wrote De gestis regum Anglorum, in which he related that the Arabs adopted the Indian figures and transported them to the countries they conquered, particularly Spain. He goes on to explain that the monk Gerbert of Aurillac, who was to become Pope Sylvester II (who died in 1003) and who was immortalized for restoring sciences in Europe, studied in either Seville or Cordoba , where he learned about Indian figures and their uses and later contributed to their circulation in the Christian countries of the West.

L Malmesbury (1596), f” 36 r’; Woepcke (1857), p. 35J

Written in 976 in the convent of Albelda (near the town of Logroño , in the north of Spain ) by a monk named Vigila, the Coda Vigilanus contains the nine numerals in question, but not zero. The scribe clearly indicates in the text that the figures are of Indian origin:

“Item de figuels aritmetice. Scire debemus Indos subtilissimum ingenium habere et ceteras gentes eis in arithmetica et geometrica et ceteris liberalibu.c disciplinis concedere. Et hoc manifèstum at in novem figuris, quibus quibus designant unum quenque gradum cuiu.slibetgradus. Quatrum hec sunt forma:

9 8 7 6 5 4 3 2 1.

“The same applies to arithmetical figures. It should be noted that the Indians have an extremely subtle intelligence, and when it comes to arithmetic, geometry and other such advanced disciplines, other ideas must make way for theirs. The best proof of this is the nine figures with which they represent each number no matter how high. This is how the figures look:

9 8 7 6 5 4 3 2 1

(source: The Indic Mathematical tradition - By Kosla Vepa).

Grammar
"Probably in no other single sphere have Western scholars been so indebted to traditional India as in that of grammar.
According to Sir Monier-Williams (Eng. Sanskrit scholar 1819-1899):
"The Panini grammar reflects the wondrous capacity of the human brain, which till today no other country has been able to produce except India."
(source: Hindu Superiority - By Har Bilas Sarda p. 229).
Sir William Wilson Hunter has observed:
"The grammar of Panini stands supreme among the grammars of the world, alike for its precision of statement, and for its thorough analysis of the roots of the language and of the formative principles of words. By employing an algebraic terminology it attains a sharp succinctness unrivalled in brevity, but at times enigmatical. It arranges, in logical harmony, the whole phenomena which the Sanskrit language presents, and stands forth as one of the most splendid achievements of human invention and industry. So elaborate is the structure, that doubts have arisen whether its complex rules of formation and phonetic change, its polysyllabic derivatives, its ten conjugations with their multiform aorists and long array of tenses, could ever have been the spoken language of a people."
(source: The Indian Empire - By Sir William Wilson Hunter p. 142). For more refer to chapter on Greater India: Suvarnabhumi and Sacred Angkor

Panini, the legendary Sanskrit grammarian of 5th century BC, is the world's first computational grammarian! Panini's work, Ashtadhyayi (the Eight-Chaptered book), is considered to be the most comprehensive scientific grammar ever written for any language.

"The Panini grammar reflects the wondrous capacity of the human brain, which till today no other country has been able to produce except India."

The science of linguistics owes much to the brilliant ancient Sanskrit grammarian Panini, whose 4th century B.C. Ashtadhyayi ("Eight Chapters") was the first scientific analysis of any alphabet.

Leonard Bloomfield (1887-1949) American linguist and author of Language, published in 1933) characterization of Panini's Astadhyayi ("The Eight Books")
"as one of the greatest monuments of human intelligence is by no means an exaggeration; no one who has had even a small acquaintance with that most remarkable book could fail to agree. In some four thousand sutras or aphorisms - some of them no more than a single syllable in length - Panini sums up the grammar not only of his own spoken language, but of that of the Vedic period as well. The work is the more remarkable when we consider that the author did not write it down but rather worked it all out of his head, as it were. Panini's disciples committed the work to memory and in turn passed it on in the same manner to their disciples; and though the Astadhayayi has long since been committed to writing, rote memorization of the work, with several of the more important commentaries, is still the approved method of studying grammar in India today, as indeed is true of most learning of the traditional culture."
While in the classical world scholars were dealing with language in a somewhat metaphysical way, the Indians were telling us what their language actually was, how it worked, and how it was put together. The methods and techniques for describing the structure of Sanskrit which we find in Panini have not been substantially bettered to this day in modern linguistic theory and practice. We today employ many devices in describing languages that were already known to Panini's first two commentators. The concept of "zero" which in mathematics is attributed to India, finds its place also in linguistics.
"It was in India, however, that there rose a body of knowledge which was destined to revolutionize European ideas about language. The Hindu grammar taught Europeans to analyze speech forms; when one compared the constituent parts, the resemblances, which hitherto had been vaguely recognized, could be set forth with certainty and precision."

(source: Traditional India - edited by O. L. Chavarria-Aguilar refer to chapter on Grammar - By Leonard Bloomfield Hall - Place of Publication: Englewood Cliffs, NJ Date of Publication: 1964 p. 109-113).
Ancient Indian work on grammar was not only objective, systematic, and brilliant than that done in Greece or Rome but is illustrative of their scientific methods of analysis. Although the date of Panini's grammar, the Ashtadhyayi, ("Eight Chapters"), which comprises about four thousand sutras or aphorisitic rules, is uncertain, it is the earliest extant scientific grammar in the world, having written no later than the fourth century B.C. But prior grammatical analysis is clearly evidenced by the fact that Panini himself mentions over sixty predecessors in the field. For example, the sounds represented by the letters of the alphabet had been properly arranged, vowels and diphthongs separated from mutes, semivowels, and sibilants, and the sounds had been grouped into guttturals, palatals, cerebrals, dentals, and labials.
Panini and other grammarians, especially Katyayana and Patanjali, carried the work much further, and by the middle of the second century B.C. Sanskrit had attained a stereotyped form which remained unaltered for centuries. Whilst Greek grammar tended to be logical, philosophical and syntactical, Indian grammar was the result of an empirical investigation of language done with the objectivity of an anatomist dissecting a body.

At a very early date India began to trace the roots, history, relations and combinations of words. By the fourth century B.C. she had created for herself the science of grammar, and produced probably the greatest of all known grammarians, Panini. The studies of Panini, Patanjali and Bhartrihari laid the foundations of philology; and that fascinating science of verbal genetics owed almost its life in modern times to the rediscovery of Sanskrit.
It is the discovery of Sanskrit by the West and the study of Indian methods of analysis that revolutionized Western studies of language and laid the foundation of comparative philology. Panini's Sanskrit grammar, produced in about 300 B.C. E. is the shortest and the fullest grammar in the world. Until the mid 19th century, in fact, Panini's great grammar remained the best standard guide to the study of Sanskrit, an inspiration to students of language everywhere. Even Otto Bohtlingk and Rudolf Roth, whose monumental Sanskrit-German Dictionary, called the "St Petersburg Lexicon" because it was published by the Russian Imperial Academy of Sciences from 1852 to 1875, owed a great debt to Panini's remarkable "Eight Chapters."
(source: An Introduction to India - By Stanley Wolpert p. 196).
Linguistics
'Sanskrt' is not a language but a linguistic process.
A L Basham says that the very science of phonetics arose in Europe only after the discovery' of Sanskrt and its grammar by the West. (Paanini, the seminal thinker, constructed the Ashtaadhyaayee - "the Eight Matters to be Studied" in the 5th cent. BC). His 'structures' constitute a scientific presentation of grammar, phonetics, etymology, linguistics, etc. all rolled into one, not excluding the implied "sociology" of listening to, collecting and statistically evaluating forms of usage in the then spoken language. But, except for scholars like Naom Chomsky, no one working in linguistics overtly acknowledges this debt and Paanini has yet to be admitted to the pantheon of science of which Archimedes, Euclid, Socrates, Plato, Newton, Einstein, the Quantum Mechanicists, etc. are the present members. Paanini's work is of immense importance to modern research in the forms of human speech and, possibly, in the mapping of the spread of families of languages (not just of the Indo-European). Such mapping is being currently carried out in the Americas, very likely without the help of Paanini's ideas, in tracing the waves of migration of people that were to become "Red Indians" towards the end of the last Ice Age, from Northeastern Asia, across the Bering Strait, spreading southwards and across the land as far as Tierra del Fuego (the "Land of Fire"; "tierra" = dharaa, by the way) at the southern tip of South America.
One among the major contributions of the Indian Ancients is the arrangement of letters in the scripts (aksharamalas) of major Indian languages (Urdu excepted). That and the mode of having one unique symbol per syllable (and the mode of formation of compound consonants) whereby, with every letter having a fixed and invariable pronunciation, the script "is adapted to the expression of every gradation of sound" (source: Practical Grammar of the Sanskrit Language - By Sir Monier-Williams 1857).
(source: Whence and Whither of Indian Science - Can we integrate with our past and carry on from there? – Contributed by S. N. Balasubrahmanyam - (Retd) Professor of Organic Chemistry at the Indian Institute of Science, Bangalore).

Panini to the rescue

Research team turns to the "world's first computational grammarian!".

Panini, the legendary Sanskrit grammarian of 5th century BC, is the world's first computational grammarian! Panini's work, Ashtadhyayi (the Eight-Chaptered book), is considered to be the most comprehensive scientific grammar ever written for any language.

According to Prof Rajeev Sangal, Director of IIIT (Hyderabad) and an expert on language computation, Panini's epic treatise on grammar came to the rescue of language experts in making English unambiguous. English is more difficult (as far as machine translations are concerned) with a high degree of ambiguity. Some words have different meanings, making the analysis (to facilitate translations) a difficult process. Making it disambiguous is quite a task, where Panini's principles might be of use.

Ashtadhyayi, the earlier work on descriptive linguistics, consists of 3,959 sutras (or principles). These highly systemised and technical principles, some say, marked the rise of classical Sanskrit.

Sampark, the multi-institute effort launched to produce a translation engine, enabling users to translate tests from English to various languages, will use some of the technical aspects enunciated by Panini. "We looked at alternatives before choosing Panini," Prof Sangal says. Incidentally, Prof Sangal co-authored a book, Natural Language Processing - A Panini Perspective, a few years ago.

Besides the technical side, Panini would be of great help to researchers on the translation engine on the language side too. A good number of words in almost all the Indian languages originate from Sanskrit. "That is great because Indian languages are related to each other," Prof Sangal points out.

(source: Panini to the rescue - thehindu.com). Refer to chapter on Sanskrit.
Science
The revolutionary contents of the Vedas
For a quick glimpse at what unsung surprises may lie in the Vedas, let us consider these renditions from the Yajur-veda and Atharva-veda, for instance.

" O disciple, a student in the science of government, sail in oceans in steamers, fly in the air in airplanes, know God the creator through the Vedas, control thy breath through yoga, through astronomy know the functions of day and night, know all the Vedas, Rig, Yajur, Sama and Atharva, by means of their constituent parts."

" Through astronomy, geography, and geology, go thou to all the different countries of the world under the sun. Mayest thou attain through good preaching to statesmanship and artisanship, through medical science obtain knowledge of all medicinal plants, through hydrostatics learn the different uses of water, through electricity understand the working of ever lustrous lightening. Carry out my instructions willingly." (Yajur-veda 6.21)

" O royal skilled engineer, construct sea-boats, propelled on water by our experts, and airplanes, moving and flying upward, after the clouds that reside in the mid-region, that fly as the boats move on the sea, that fly high over and below the watery clouds. Be thou, thereby, prosperous in this world created by the Omnipresent God, and flier in both air and lightning." (Yajur-veda 10.19).

" The atomic energy fissions the ninety-nine elements, covering its path by the bombardments of neutrons without let or hindrance. Desirous of stalking the head, ie. The chief part of the swift power, hidden in the mass of molecular adjustments of the elements, this atomic energy approaches it in the very act of fissioning it by the above-noted bombardment. Herein, verily the scientists know the similar hidden striking force of the rays of the sun working in the orbit of the moon." (Atharva-veda 20.41.1-3).

(source: Searching for Vedic India - By Devamitra Swami p. 155 - 157). For more refer to chapter on Vimanas and Advanced Concepts).

Medieval Arab scholar Sa'id ibn Ahmad al-Andalusi (1029-1070) wrote in his Tabaqat al-'umam, one of the earliest books on history of sciences:

"The first nation to have cultivated science is India. ... 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 kings of China have stated that the kings of the world are five in number and all the people of the world are their subjects. They mentioned the king of China, the king of India, the king of the Turks, the king of the Persians, and the king of the Romans.

"... They referred to the king of India as the "king of wisdom" because of the Indians' careful treatment of 'ulum [sciences] and all the branches of knowledge.

"The Indians, known to all nations for many centuries, are the metal [essence] of wisdom, the source of fairness and objectivity. They are people 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] ... After all that they have surpassed all other peoples in their knowledge of medical sciences ..."

In his book al-Andalusi goes on to give details of several Indian texts on astronomy and tells us that the Arab scholars used them in preparing their own almanacs.
" Ancient Indian theories lacked an empirical base, but they were brilliant imaginative explanations of the physical structure of the world, and in a large measure, agreed with the discoveries of modern physics."
(source: 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”).

- A. L. Basham, Australian Indologist
Two system of Indian thought propound physical theories suggestively similar to those of Greece. Kanada, founder of the Vaishehika philosophy, held that the world was composed of atoms as many in kind as the various elements. The Jains approximated to Democritus by teaching that all atoms were of the same kind, producing different effects by diverse modes of combination. Kanada believed light and heat to be varieties of the same substance; Udayana taught that all heat comes from the sun; and Vachaspati, like Newton, interpreted light as composed of minute particles emitted by substances and striking the eye. Musical notes and intervals were analyzed and mathematically calculated in the Indian treatises on music. and the Pyrthogorean Law was formulated by which the number of vibrations, and therefore the pitch of the note, varies inversely as the length of the string between the point of attachment and the point of touch.
***

The calculation of eclipses was given by Indian astronomers, refer to verses from Varahamihira's texts, which give the true reasons for eclipses as the earth's and moon's shadows (no rAhu kEtu here).
For more refer to History of Indian Science & Technology
Education
The world's first university was established at Takshashila (northwest region of India) in approximately 700 B.C. The Universities in ancient India were entirely residential. It was considered that a University should contain at least 21 Professors well versed in Philosophy, Theology and Law; pupils were given free tuition, free boarding, and students who went to an educational institution - be the king or a peasant - lived and boarded together. Ashramas, Viharas and Parishads were great centers of culture and attracted large numbers.
When Alexander reached Punjab in 327 BC, Takshashila, the world's oldest university was already established as a place of learning. John Keay in his book India: a History" writes:
"Students went there to learn the purest Sanskrit. Kautilya, whose Arthashashtra is the classic Indian treatise on statecraft, is said to have been born there in the third century BC. It was also in Taxila that, in the previous century, Panini compiled a grammar more comprehensive and scientific than any dreamed of by Greek grammarians. The glory for the western world is the library of Alexandria, which was sanctioned by Ptolemy I Soter, the successor of Alexander of Macedonia in around 300 BC. While the Maurya empire was in power in India..."
Dr. Ernest Binfield Havell (1861-1934) principal to the Madras College of Art in the 1890s and left as principal of the Calcutta College of Art some 20 years later. He wrote several books, including his book, Indian Architecture - Its Psychology, Structure and History from the First Mohammedan Invasion to the Present Day has remarked:
"From the Guru the student would pass, about the age of sixteen, to one of the great universities that were the glory of ancient and medieval India. Benares, Taxila, Vidarbha, Ajanta, Ujjain or Nalanda. Benares was the stronghold of learning in Buddha's days. Taxila was known at the time of Alexander's invasion, was known to all of Asia as the leading seat of Hindu scholarship, renowned above all for its medical school; Ujjain was held in high repute for astronomy, Ajanta for the teaching of art. The facade of one of the ruined buildings at Ajanta suggests the magnificence of these old universities."

(source: Story of Civilization: Our Oriental Heritage - By Will Durant MJF Books.1935 p. 556-557).
When Cyrus the Great (558-530 B.C.), came to the throne, the city of Takshasila, was already a center of learning and trade. Young men from Magadha were sent there to finish their education. The Jataka tales show that young men from all over the civilized part of India sought education in this city, as well as from Persia and Mesopotamia.
The campus accommodated 10,500 students and offered over sixty different courses in various fields, such as science, mathematics, medicine, politics, warfare, astrology, astronomy, music, religion, and philosophy. The minimum age for admission was 16 years and students from as far as Babylonia, Greece, Syria, Arabia, and China came to study at the university. Taxila, stood on the banks of the river Vitasa in the northwest of the Indian subcontinent.
Panini, the great Sanskrit grammarian, Charaka, the author of famous treatise on medicine, and Chanakya, writer of Artha Shastra -- these august names are associated with Taxila. Promising minds from far flung regions converged there to study the Vedas and all branches of secular knowledge. Takshasila or Taxila, as the Greeks called it over 2,000 years ago, was at one of the entrances to the splendor that was India. Its antiquity is rooted both in epic texts like the Ramayana, Mahabharata and the other Puranas. The Jakatas are full of references to Taxila - over 100 in fact. We gleam a good many details about it from them. Mention is made of world-renowned professors who taught the Vedas, the Kalas, Shilpa, Archery and so on. King Kosala and Jivaka, the famous physician were students of the University, the latter learning medicine under Rishi Atreya. Great stress was laid on the study of Sanskrit and Pali literature.
The University of Vikramasila accommodated 8,000 people. It was situated on a hill in Magadha on the banks of the Ganga and flourished for four centuries. It was destroyed along with Nalanda by the Mohammedan invasion. They speak of Kulapatis in those times; the technical meaning of the word is 'one who feeds' and teaches 10,000 students'. Kanva was one such Kulapati. Kalidasa speaks of the various kinds of knowledge taught and learnt under the guidance of Kanva.
The University of Nalanda built in the 4th century BCE was one of the greatest achievements of ancient India in the field of education. Buddha visited Nalanda several times during his lifetime. The Chinese scholar and traveler Hiuen Tsang stayed here in the 7th century, and has left an elaborate description of the excellence, and purity of monastic life practiced here. About 2,000 teachers and 10,000 students from all over the Buddhist world, lived and studied in this international university. In this first residential international university of the world, 2,000 teachers and 10,000 students from all over the Buddhist world lived and studied here.
It had ten thousand students, one hundred lecture-rroms, great libraries, and six immense blocks of dormitories four stories high; its observatories, said Yuan Chwang, "were lost in the vapors of the morning, and the upper rooms towered above the clouds." The old Chinese pilgrim loved the learned monks and shady groves of Nalanda so well he stayed there for five years.

(source: Story of Civilization: Our Oriental Heritage - By Will Durant MJF Books.1935 p. 556-557 and Facets of Indian Culture - By R. Srinivasan Publisher: Bhartiya Vidya Bhavan p. 237-239).
The Gupta kings patronized these monasteries, built in old Kushan architectural style, in a row of cells around a courtyard. Ashoka and Harshavardhana were some of its most celebrated patrons who built temples and monasteries here. Recent excavations have unearthed elaborate structures here. Hiuen Tsang had left ecstatic accounts of both the ambiance and architecture of this unique university of ancient times. The Nalanda university counted on its staff such great thinkers as Nagarjuna, Aryadeva, Vasubhandu, Asanga, Sthiramati, Dharmapala, Silaphadra, Santideva and Padmasambhava. The ancient universities were the sanctuaries of the inner life of the nation. Another large university was established at Nalanda around 500 B.C. Approximately one mile long and half-mile wide, this campus housed a large library, called Dharam gunj (Treasure of Knowledge), that spread over three buildings, known as Ratna Sagar, Ratnadevi, and Ratnayanjak. Among other facilities, the university included 300 lecture halls, several laboratories, and an astronomical research observatory called Ambudharavlehi. The university used handwritten manuscripts for teaching and attracted students and staff from many countries, including China, Korea and Japan. According to the Chinese traveler Hieun Tsang, the campus housed 10,000 students, 2,000 professors, and a large administrative staff.
(source: The Hindu Mind - Fundamentals of Hindu Religion and Philosophy for All Ages - By Bansi Pandit B & V Enterprises, Inc ISBN: 0963479849 p. 302).

These universities were sacked, plundered, looted by the Islamic onslaught.

According to historian Will Durant:
"The Mohemmedans destroyed nearly all the monasteries, Buddhist or Hindu, in northern India. Nalanda was burned to the ground in 1197 and all its monks were slaughtered; we can never estimate the abundant life of ancient India from what these fanatics spared."
(source: Story of Civilization: Our Oriental Heritage - By Will Durant MJF Books.1935 p. 558).
The Moghuls neglected practical and secular learning, especially the sciences. Throughout their long rule, no institutions was established comparable to modern university, although early India had world-famous centers of learning such as Taxila, Nalanda and Kanchi. Neither the nobles nor the mullas were stirred into learning...
For more on education, refer to chapter on Education in Ancient India).
Chemistry and metallurgy
Sir Mountstuart Elphinstone has written: "Their (Indians) chemical skill is a fact more striking and more unexpected." "They knew how to prepare sulphuric acid, nitric acid and muratic acid; the oxide of copper, iron, lead (of which they had both the red oxide and litharge), tin and zinc: the suphuret of iron, copper, mercury, and antimony, and arsenic; the sulphate of copper, zinc and iron; and carbonates of lead and iron. Their modes of preparing these substances were sometimes peculiar."
(source: History of Hindu Chemistry - By Mountstuart Elphinstone Volume I, Introduction, p. xii and 54).
Chemistry developed from two source - medicine and industry. Something has been said about the chemical excellence of cast iron in ancient India, and about the high industrial development of Gupta Period, when India was looked to, even by Imperial Rome, as the most skilled of the nations in such chemical industries as dyeing, tanning, soap-making, glass and cement. As early as the second century B.C. Nagarjuna devoted an entire volume to mercury. By the sixth century Indians were far ahead of Europe in industrial chemistry; they were masters of calcination, distillation, sublimation, steaming, fixation, the production of light without heat, the mixing of anesthetic and soporific powders, and the preparation of metallic salts, compounds and alloy.
Abundant evidence available suggests that the ancient Indians were highly skilled in manufacturing and working with iron and in making and tempering steel. The analysis of zinc alloys like brass, from archaeological excavations, testify that the zinc distillation process was known in India as early as 150 B.C. Indian steel, famous worldwide, is mentioned in history books which tell us that when Alexander invaded India, Porus, otherwise known as Purushottam, presented him with thirty pounds of steel, thus indicating its high value.
South India was a region that was renowned for metallurgy and metalwork in the old days. In Karnataka, fine steel wires were being produced for use as strings in musical instruments, at a time when the western world was using animal gut for the same purpose. Kerala, besides its large iron smelting furnaces, boasted of special processes such as the metal mirror of Aranmula. High quality steel from Tamil Nadu was exported all over the world since Roman times. The Konasamudram region in Andhra Pradesh was famous for producing the world renowned Wootz steel - the raw material for King Saladin's fabled Damascus Sword. The tempering of steel was brought in ancient India to a perfection unknown in Europe till our own times. King Porus is said to have selected, as special valuable gift for Alexander, not gold or silver, but thirty pounds of steel. The Muslims took much of this Indian chemical science and industry to the Near East and Europe; the secret of manufacturing "Damascus" blades, for example, was taken by Arabs from the Persians, and by the Persians from India.

Persians considered Indian swords to be the best, and the phrase, " Jawabi hind, literally meaning " Indian answer," meant "a cut with the sword made of Indian steel." That the art of metarllurgy was highly developed in ancient India is further reaffirmed by the fact that the Gypsies, who originated in India, are highly skilled craftsmen, and it has been suggested that the art of the forge may have been transmitted to Europe through Gypsies. Steel was manufactured in ancient India, and it was being exported to China at least by the fifth century A.D. That the Arabs also imported steel from India is testified to by Al Kindi, who wrote in the ninth century.

Coinage dating from the 8th Century B.C. to the17th Century A.D. Numismatic evidence of the advances made by Smelting technology in ancient India. The image of Nataraja the God of Dance is made of five metals (Pancha-Dhatu). This technology of mixing two or more metals and deriving superior alloys has been observed and noted by the Greek Historian Philostratus. The Makara (Spire) over Hindu temples were always adorned with brass or gold toppings (Kamandals). The earliest reference to the advances made in Smelting technology in India are by Greek historians viz, Philostratus and Ktesias in the 4th century B.C.

Great progress was made in India in mineralogy and metallurgy. The mining and extensive use of gold, silver, and copper was undertaken in the Indus Valley in the third century B.C. In the vedic period extensive use was made of copper, bronze, and brass for household utensils, weapons, and images for worship. Patanjali, writing in the second century B.C. in his Lohasastra, gives elaborate directions for many metallurgic and chemical processes, especially the preparation of metallic salts, alloys, and amalgams, and the extraction, purification, and assaying of metals. The discovery of aqua regia ( a mixture of nitric and hydrochloric acid to dissolve gold and platinum) is ascribed to him. Numerous specimens of weapons made of iron have been excavated, probably belonging to the fourth century B.C. Iron clamps and the iron stag found at the Bodhgaya temple point to the knowledge of the process of manufacturing iron as early as the third century B.C.
Horace Hyman Wilson (1786-1860) says: "The Hindus have the art of smelting iron, of welding it, and of making steel, and have had these arts from times immemorial."
(source: History of British India - By James Mill volume II p. 47).
The finest Damascus steel was made by a process known only to Indians. The original Damascus steel-the world's first high-carbon steel-was a product of India known as wootz. Wootz is the English for ukku in Kannada and Telugu, meaning steel. Indian steel was used for making swords and armour in Persia and Arabia in ancient times. Ktesias at the court of Persia (5th c BC) mentions two swords made of Indian steel which the Persian king presented him. The pre-Islamic Arab word for sword is 'muhannad' meaning from Hind.

Wootz was produced by carburising chips of wrought iron in a closed crucible process. "Wrought iron, wood and carbonaceous matter was placed in a crucible and heated in a current of hot air till the iron became red hot and plastic. It was then allowed to cool very slowly (about 24 hours) until it absorbed a fixed amount of carbon, generally 1.2 to 1.8 per cent," said eminent metallurgist Prof. T.R. Anantharaman, who taught at Banares Hindu University, Varanasi. "When forged into a blade, the carbides in the steel formed a visible pattern on the surface." To the sixth century Arab poet Aus b. Hajr the pattern appeared described 'as if it were the trail of small black ants that had trekked over the steel while it was still soft'.

The carbon-bearing material packed in the crucible was a clever way to lower the melting-point of iron (1535 degrees centigrade). The lower the melting-point the more carbon got absorbed and high-carbon steel was formed. In the early 1800s, Europeans tried their hand at reproducing wootz on an industrial scale. Michael Faraday, the great experimenter and son of a blacksmith, tried to duplicate the steel by alloying iron with a variety of metals but failed. Some scientists were successful in forging wootz but they still were not able to reproduce its characteristics, like the watery mark. "Scientists believe that some other micro-addition went into it," said Anantharaman. "That is why the separation of carbide takes place so beautifully and geometrically."

(source: Lost knowledge - The Week June 2001).

Hindus made the best swords in the ancient world, they discovered the process of making Ukku steel, called Damascus steel by the rest of the world (Damas meaning water to the Arabs, because of the watery designs on the blade). These were the best swords in the ancient world, the strongest and the sharpest, sharper even than Japanese katanas. Romans, Greeks, Arabs, Persians, Turks, and Chinese imported it. The original Damascus steel-the world's first high-carbon steel-was a product of India known as wootz. Wootz is the English for ukku in Kannada and Telugu, meaning steel. Indian steel was used for making swords and armor in Persia and Arabia in ancient times. Ktesias at the court of Persia (5th c BC) mentions two swords made of Indian steel which the Persian king presented him. The pre-Islamic Arab word for sword is 'muhannad' meaning from Hind. So famous were they that the Arabic word for sword was Hindvi - from Hind.

The crucible process could have originated in south India and the finest steel was from the land of Cheras, said K. Rajan, associate professor of archaeology at Tamil University, Thanjavur, who explored a 1st century AD trade centre at Kodumanal near Coimbatore. Rajan's excavations revealed an industrial economy at Kodumanal. Pillar of strength The rustless wonder called the Iron Pillar near the Qutb Minar at Mehrauli in Delhi did not attract the attention of scientists till the second quarter of the 19th century. The inscription refers to a ruler named Chandra, who had conquered the Vangas and Vahlikas, and the breeze of whose valour still perfumed the southern ocean. "The king who answers the description is none but Samudragupta, the real founder of the Gupta empire," said Prof. T.R. Anantharaman, who has authored The Rustless Wonder. Zinc metallurgy travelled from India to China and from there to Europe. As late as 1735, professional chemists in Europe believed that zinc could not be reduced to metal except in the presence of copper. The alchemical texts of the mediaeval period show that the tradition was live in India. In 1738, William Champion established the Bristol process to produce metallic zinc in commercial quantities and got a patent for it. Interestingly, the mediaeval alchemical text Rasaratnasamucchaya describes the same process, down to adding 1.5 per cent common salt to the ore.

(source: Saladin's sword - The Week - June 24, 2001 - http://netinfo.hypermart.net/telingsteel.htm).

Nanotechnology might be of raging interest to scientists world-over now. But Indians had used nano materials in the 16th century "unwittingly" and enabled Arab blacksmiths in making "Damascus steel sword" which was stronger and sharper.

Delivering a talk on 'The contributions of elemental carbon to the development of nano science and technology' at the Indian Institute of Chemical Technology (IICT) Nobel laureate Robert F. Curl said that carbon nanotechnology was much older than carbon nano science. For the Damascus sword, Indians produced the raw material -- mined iron ore and exported it. He said that up to the middle of 18th century, the steel swords depended on this particular material and when the mines in India stopped, "they lost the technology." The Damascus sword when subjected to scrutiny by an electron microscope in 2006 had shown to contain large amounts of nanotubes.

(source: Nanotechnology not new to India , says Nobel laureate - the hindu.com).

Iron Pillar - The Rustless Wonder and a Unique Scientific Phenomenon from Ancient India. A product of great metallurgical ingenuity
Traditional Indian iron and steel are known to have some very special properties such as resistance to corrosion. This is substantiated by the 1600-year-old, twenty-five feet high iron pillar next to the Qutub Minar in New Delhi, believed to have been installed during Chandragupta Maurya's reign. The famous iron pillar in Delhi belonging to the fourth-fifth century A.D. is a metallurgical wonder. This huge wrought iron pillar, 24 feet in height 16.4 inches in diameter at the bottom, and 6 1/2 tons in weight has stood exposed to tropical sun and rain for fifteen hundred years, but does not show the least sign of rusting or corrosion. Evidence shows that the pillar was once a Garuda Stambha from a Vishnu temple. This pillar was plundered by Islamic hoards from a temple dedicated to Vishnu and added as a trophy in the Quwwat al-Islam mosque in Delhi. Made of pure iron, which even today can be produced only in small quantities by electrolysis. Such a pillar would be most difficult to make even today. Thus, the pillar defies explanation.

The pillar is believed to have been made by forging together a series of disc-shaped iron blooms. Apart from the dimensions another remarkable aspect of the iron pillar is the absence of corrosion which has been linked to the composition, the high purity of the wrought iron and the phosphorus content and the distribution of slag.
Even with today's advances, only four foundries in the world could make this piece and none are able to keep it rust free. The earliest known metal expert (2,200 years ago ) was Rishi Patanjali.
The pillar is a solid shaft of iron sixteen inches in diameter and 23 feet high. What is most astounding about it is that it has never rusted even though it has been exposed to wind and rain for centuries! The pillar defies explanation, not only for not having rusted, but because it is apparently made of pure iron, which can only be produced today in tiny quantities by electrolysis! The technique used to cast such a gigantic, solid pillar is also a mystery, as it would be difficult to construct another of this size even today. The pillar stands as mute testimony to the highly advanced scientific knowledge that was known in antiquity, and not duplicated until recent times. Yet still, there is no satisfactory explanation as to why the pillar has never rusted!

(source: Technology of the Gods: The Incredible Sciences of the Ancients - By David Hatcher Childress p. 80).
The Delhi Iron Pillar is a testimony to the high level of skill achieved by the ancient Indian ironsmiths in the extraction and processing of iron.
Refer to Delhi Iron Pillar - By Prof. R. Balasubramaniam - Professor Department of Materials and Metallurgical Engg Indian Institute of Technology, Kanpur 208016.
Contributed to this site by Prof. R. Balasubramaniam. URL: http://home.iitk.ac.in/~bala
The pillar is a classical example of massive production of high class iron and is the biggest hand-forged block of iron from antiquity. It is a demonstration of the high degree of accomplishment in the art of iron making by ancient Indian iron and steel makers. It has been said that the Indians were the only non-European people who manufactured heavy forged pieces of iron and the pieces were of the size that the European smiths did not learn to make more than one thousand years later.
The iron pillar near New Delhi is an outstanding example of Gupta craftmanship. Its total height inclusive of the capital is 23 feet 8 inches. Its entire weight is 6 tons. The pillar consists of a square abacus, the melon shaped member and a capital. According to Percy Brown, this pillar is a remarkable tribute to the genius and manipulative dexterity of the Indian worker. Dr. Vincent Smith says: "It is not many years since the production of such a pillar would have been an impossibility in the largest foundries of the world and even now there are comparatively few where a similar mass of metal could be turned out."
(source: Ancient India - By V. D. Mahajan p. 543).
The iron pillar has an inscription in Samskritam written in Brahmi script. It is a Vishnu Dhvaja on a hill called Vishnupaada. Installed by King Chandra.

"He, on whose arm fame was inscribed by the sword, when, in battle in the Vanga countries, he kneaded (and turned) back with (his) breast the enemies who, uniting together, came against (him);-he, by whom, having crossed in warfare the seven mouths of the (river) Sindhu, the Vâhlikas were conquered;-he, by the breezes of whose prowess the southern ocean is even still perfumed;-
(Line 3.)-He, the remnant of the great zeal of whose energy, which utterly destroyed (his) enemies, like (the remnant of the great
glowing heat) of a burned-out fire in a great forest, even now leaves not the earth; though he, the king, as if wearied, has quitted this earth, and has gone to the other world, moving in (bodily) form to the land (of paradise) won by (the merit of has) actions, (but) remaining on (this) earth by (the memory of his) fame;-

(L. 5.)-By him, the king,-who attained sole supreme sovereignty in the world, acquired by his own arm and (enjoyed) for a
very long time; (and) who, having the name of Chandra, carried a beauty of countenance like (the beauty of) the full-moon,-having in faith fixed his mind upon (the god) Vishnu, this lofty standard of the divine Vishnu was set up on the hill (called) Vishnupada."

(source: yahoogroups - Indian Civilization).
The excellent state of preservation of the Iron Pillar, near the Qutb Minar at Mehrauli in Delhi, despite exposure for 15 centuries to the elements has amazed corrosion technologists
In 1961, the pillar (23 feet and 8 inches, and 6 tonnes) was dug out for chemical treatment and preservation and reinstalled by embedding the underground part in a masonry pedestal. Chemical analyses have indicated that the pillar was astonishingly pure or low in carbon compared with modern commercial iron.
Traditional Indian iron and steel are known to have some very special properties such as resistance to corrosion. This is substantiated by the 1600-year-old, twenty-five feet high iron pillar next to the Qutub Minar in New Delhi, believed to have been installed during Chandragupta Maurya's reign. Reports of an international seminar conducted by the National Metallurgical Laboratory at Jamshedupur in 1963 on the Delhi Iron Pillar, showed that the pillar's corrosion resistance was not merely the result of some fortuitous circumstances or Delhi's low humidity, but the product of great metallurgical ingenuity. In fact, rust-proof iron has been found in very humid areas as well. A temple, dedicated to the Goddess Mookambika, is located in Kolur in Kodachadri Hills in Karnataka - a region which receives a heavy annual monsoon. A slender iron pillar near the Mookambika temple stands unrusted despite the severe climatic conditions that it is subjected to.

(source: Center for Indian Knowledge Systems - http://www.ciks.org/methist.html)
The iron pillar near Qutub Minar at New Delhi is in the news, thanks to the research by Prof. R. Balasubramaniam of IIT, Kanpur and his team of metallurgists. The pillar is said to be 1,600 years old. A protective layer of `misawite' — a compound made up of iron, oxygen and hydrogen on the steel pillar, which is said to contain phosphorus - is claimed as the reason for the non-corrosive existence.

(source: Iron pillar and nano powder - http://www.hinduonnet.com/thehindu/seta/stories/2002082900020200.htm

All this historical evidence points to the fact that there existed a body of knowledge in the fields of metallurgy and metalworking which, if rediscovered and re-implemented, could revolutionize the country's iron and steel industry.
The Periplus mentions that in the first century A.D. Indian iron and steel were being exported to Africa and Ethiopia. Indian metallurgists were well known for their ability to extract metal from ore and their cast products were highly valued by the Romans, Egyptians, and Arabs.
Even in technology Indian contribution to world civilization were significant. The spinning wheel is an Indian invention, and apart from its economic significance in reducing the cost of textiles, is one of the first examples of the belt-transmission of power. The stirrup, certainly the big-toe stirrup, is of second century B.C. Indian origin. The ancient blow-gun (nalika), which shot small arrows or iron pellets, may well have been a forerunner of the air-gun which is supposed to have been invented by the Europeans in the sixteenth century.
More important is the fact that India supplied the concept of perpetual motion to European thinking about mechanical power. The origin of this concept has been traced to Bhaskara, and it was taken to Europe by the Arabs where it not only helped European engineers to generalize their concept of mechanical power, but also provoked a process of thinking by analogy that profoundly influenced Western scientific views. The Indian idea of perpetual motion is in accordance with the Hindu belief in the cyclical and self-renewing nature of all things.
In fact, rust-proof iron has been found in very humid areas as well. A temple, dedicated to the Goddess Mookambika, is located in Kolur in Kodachadri Hills in Karnataka - a region which receives a heavy annual monsoon. A slender iron pillar near the Mookambika temple stands unrusted despite the severe climatic conditions that it is subjected to.
Galvanising feat

The oldest among the triad of metallurgical marvels of ancient India is the extraction of zinc. Zinc is better known as a constituent of brass than a metal in its own right. Brass with 10 per cent zinc glitters like gold.

The earliest brass objects in India have been unearthed from Taxila (circa 44 BC). They had more than 35 per cent zinc. "This high content of zinc could be put in only by direct fusion of metallic zinc and copper," said Prof. T.R. Anantharaman. The other process, which is no more in use, is by heating zinc ore and copper metal at high temperatures, but the zinc content in brass then cannot be more than 28 per cent.

Zinc smelting is very complicated as it is a very volatile material. Under normal pressure it boils at 913 degrees centigrade. To extract zinc from its oxide, the oxide must be heated to about 1200 degrees in clay retorts. In an ordinary furnace the zinc gets vapourised, so there has to be a reducing atmosphere. By an ingenious method of reverse distillation ancient metallurgists saw to it that there was enough carbon to reduce the heat.

Proof of the process came from excavations at Zawar in Rajasthan. The Zawar process consisted of heating zinc in an atmosphere of carbon monoxide in clay retorts arranged upside down, and collecting zinc vapour in a cooler chamber placed vertically beneath the retort.

Zinc metallurgy traveled from India to China and from there to Europe. As late as 1735, professional chemists in Europe believed that zinc could not be reduced to metal except in the presence of copper. The alchemical texts of the mediaeval period show that the tradition was live in India.

(source: Lost knowledge - The Week June 2001).

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(Continued...)

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