The Indic Mathematical Tradition 6000 BCE To ?

[Husky]

http://www.ivarta.com/columns/OL_051210.htm
<!--QuoteBegin-->QUOTE<!--QuoteEBegin--><b>Does no one remember the Hindu contribution to Mathematics?</b>

Whenever I read about the great “Arabic” contribution to Mathematics and Science (often in an apologetic tone of “how could these great people come to such a pass?”) the thing that really upsets me is the complete omission of any reference to the Hindu contribution to mathematics and numbers.

Slightly more than a year ago (Aug ’04), in an article in the Sunday Times www.michaelportillo.co.uk/articles/...press/islam.htm, Michael Portillo, eminent Conservative party leader in the UK and a one-time aspirant to the leadership of the Tory Party, wrote that, “Islam brought back to the West knowledge of architecture, mathematics and astronomy that had been lost during the Dark Ages.”

In response, I wrote, 

“…The phrase “brought back” is at best, condescending and at worse, historically inaccurate.

For this knowledge, which Arab traders brought to Europe (typified in the Arabic numeral system - itself a misnomer, since the Arabs did not invent it but merely acted as the purveyors of this knowledge) was not Islamic or Arabic. In fact much of this knowledge was originally derived from ancient Vedic literature from India and passed through Arab traders and conquests to Middle East and eventually reaching Europe.

To quote from Carl B. Boyer in his "History of Mathematics", “...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. ... [pages 227-228]...”.

In a translation of Alberuni ‘s “Indica”, a seminal work of this period (c.1030 AD), Edward Sachau, 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.  

Needless to say, the letter never got published.

Then, more recently, while reading the “The World is Flat”, by Thomas L. Friedman www.thomaslfriedman.com/worldisflat.htm, I came across this text in Chapter 11, "The Unflat World" (Pg 405), "As Nayan Chanda, the editor of YaleGlobal Online pointed out to me, it was the Arab-Muslim world that gave birth to algebra and algorithms, terms both derived form Arabic words. In other words, noted Chanda, "The entire modern information revolution, which is built to a large degree on algorithms, can trace its roots all the way back to Arab-Muslim civilization and the great learning centres of Baghdad and Alexandria," which first introduced these concepts, then transferred them to Europe through Muslim Spain.

Dismayed, I wrote the following email to Nayan:

“May I respectfully point out that is not historically accurate and continuing research is providing evidence that the roots of the so-called Arab contribution to Mathematics and Science were further east in the lands of India and in the works of Indian mathematicians and scholars from several centuries ago.”

“I hope that you will re-consider your views in the light of these excerpts and a significant body of research that is now publicly available on this subject. I would be more than happy to provide more details if you wish.”

No acknowledgement was expected and none was received. I wanted to copy Thomas Friedman on it but could not find his contact details on his website – the only email address was that of his literary agent and PR agency.

This apparently widespread misunderstanding and ignorance - about the Hindu contribution to the number system and sciences - prompted me to dig deeper. Here is what I found:

From an online research piece on Al-Khwarizmi and his work (by Shawn Overbay, Jimmy Schorer, and Heather Conger) http://www.ms.uky.edu/~carl/ma330/projec...hwa21.html 

“ 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 (ernie.bgsu.edu).”

From a very well-researched online article, “Numbers: Their History and Meaning” http://home.c2i.net/greaker/comenius/9899/...rals/india.html

“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.

And later in the article, “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.”



and further “…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.”

Fortunately, online encyclopaedias came across as less biased and more open in acknowledging the true source of the “Arabic” number system. For example, from MSN Encarta http://encarta.msn.com/encyclopedia_761578...athematics.html 

“The system of numbers that we use today, with each number having an absolute value and a place value (units, tens, hundreds, and so forth) originated in India. Mathematicians in India also were the first to recognize zero as both an integer and a placeholder. When the Indian numeration system was developed is not known, but digits similar to the Arabic numerals used today have been found in a Hindu temple built about 250 bc. 

In the 5th century Hindu mathematician and astronomer Aryabhata studied many of the same problems as Diophantus but went beyond the Greek mathematician in his use of fractions as opposed to whole numbers to solve indeterminate equations (equations that have no unique solutions). Aryabhata also figured the value of “P” (pi)  accurately to eight places, thus coming closer to its value than any other mathematician of ancient times. In astronomy, he proposed that Earth orbited the sun and correctly explained eclipses of the Sun and Moon. 

The earliest known use of negative numbers in mathematics was by Hindu mathematician Brahmagupta about ad 630. He presented rules for them in terms of fortunes (positive numbers) and debts (negative numbers).



…The best-known Indian mathematician of the early period was Bhaskara, who lived in the 12th century. Bhaskara supplied the correct answer for division by zero as well as rules for operating with irrational numbers. Bhaskara wrote six books on mathematics, including Lilavati (The Beautiful), which summarized mathematical knowledge in India up to his time, and Karanakutuhala, translated as “Calculation of Astronomical Wonders.”

The reality is that the so-called “Arab” contribution to mathematics was substantially built on prior knowledge of the Hindus and the Greeks and while the Greek influence and origins are frequently acknowledged, the Hindu contribution is very rarely mentioned.

We need to spread awareness about this and try and establish the facts whenever an opportunity arises – unless we do that, this “history” will be lost and become so little-known and distant as to become a myth.

Talking of forgotten Indian contribution to sciences and arts, here is another example of a glaring error in a recent news story in <b>“TIME” Magazine</b> and an email I sent in response www.time.com/time/europe/magazine/a...1129488,00.html

“May I point out two inaccuracies in your recent news story on an exhibition on Arab Science in Paris titled, “Ahead of Their Time” (Time Magazine, Nov 21, ’05; Pp48-49) by Ann Morrison?

In a paragraph about the Arab’s interest in astronomy, Ann writes, “…Though the Arabs built many observatories during the Golden Age, not many survived. But viewers can see current images of two of these amazing outdoor structures in the Indian cities of Delhi and Jaipur…”

The observatories that Ann refers to in this paragraph were not built by Arabs but by the Hindu ruler Sawai Raja Jai Singh between 1724-1730 and were amongst the five that he built in Northern India (the other three were at Varanasi, Ujjain and Mathura) and are called Jantar Mantar (actually “Yantra Mantra”, yantra for instrument and mantra for formula).

The observatory in Delhi has also been depicted in a postage stamp and was the logo of the 1982 Asian Games, held in New Delhi, India.

To call them examples of Arab interest in the sciences is inaccurate and misleading.

In a later paragraph which details the interest of Arab scholars in astrology, Ann writes, “…Another manuscript illustration from 17th century India, Astrologers working on a Nativity”, shows a procession of music makers and gift bearers wending their way through palace walls toward a newborn who would grow up to be the 14th century warrior Tamerlane...”

Again, this is an example of Indian art (and Indian interest in astrology) rather than having anything to do with Arabs or Arab art. Tamerlane himself was not an Arab king but from Central Asia (as were the Mughals).

As usual, I received neither an acknowledgement nor a response. 

For those of you who would like to read more:

Here’s Alberuni on Pre-Islamic India's Science, Math, and Architecture http://www.infinityfoundation.com/mandala/...umar-v_math.htm

And an interesting article on the origin of the decimal system
answering-islam.org.uk/Science/math.html

B Shantanu<!--QuoteEnd--><!--QuoteEEnd-->(That last link, answering-islam, is a christo site.)

"This apparently widespread misunderstanding and ignorance about the Hindu contribution..." is the conclusion Shantanu draws from the eternally repeating pattern of them not taking his verifiable facts and printing retractions or at least addendums.

But he and others ought to know the real reasons TIME (famous for marking Kashmir as specifically independent from India on their map of the country) and the motivated lying by other christowestern publishers and 'researchers'/'scholars'. The idea is to negate Hindu civilisation. Why do Hindus think any real researcher or journalist or writer would purposefully avoid sharing a discovery that may negate some previous misconceptions they had and therefore not publish what they have now learnt to be the facts? Hindus need to think about why anyone would not publish truths once they learnt about it.

To assume it was all 'some sort of benign mistake' is just people's own delusion. The sooner we wake up to this, the sooner we will take our matters into our own hands and stop letting the liars lie with impunity, stop letting them try to prevent our learning/teaching our Samskritam, stop letting them try to elect/crown people in our country, stop letting them lie and lecture us about "religious freedom" and "racism" ( <!--emo&:blink:--><img src='style_emoticons/<#EMO_DIR#>/blink.gif' border='0' style='vertical-align:middle' alt='blink.gif' /><!--endemo--> what the? - don't ask. Only possessing the oxymoron known as 'christologic' will allow one to understand <i>that</i> - and does one really want to be possessed by christologic?)