Not Aztec. It was the Mayans from same part of the world

But already in the early 19th century, when it was discovered that the concept of the zero had originated in India,

Methematics,astronomy, medicine and linguistics have many roots. India is just one of them.

In this context, is it true that native South Americans too have the concept of zero? Aztecs, perhaps. May be someone can shed some light on that.

Hear hear!

And thanks for the interesting links and additional information, Prof. Rajeev .

1. Calculate series expansions of sin / cos and inverse tan.
2. From these they got equivalents of gregories series for pi.
3. I think there were also continued fraction expansions and these are probably the algorithms used to compute stuff

On the application, it is the same as it had been all over the ancient world: astronomy. Incidentally, even the napier log tables were actually tables of -log ( sin (x) ) and – log (cos (x) ) for the same reson.

http://www.pas.rochester.edu/~rajeev/canisiustalks.pdf

Beyond shallow issues of national pride, it is useful to know how important mathematical ideas were discovered; because it can help us to cope with today’s problems. Isn’t that the point of studying any kind of history? Discoveries are not made in a straightforward, deductive way. We work in a fog of ignorance with occasional flashes of insight, and many steps backwards. `Reverse-engineering’ (not actual copying) of competitor’s ideas always plays a bigger part in research than people acknowledge. It would not be shocking if the flourishing of European mathematics (just about the time that missionaries arrived in Kerala) was helped by such a process.I would need hard evidence to be convinced that the missionaries actually transmitted whole mathematical works to Europe. More likely that the European mathematicians heard of some of the results and fragments of theory and were stimulated to think in certain directions as a result.

Methematics,astronomy, medicine and linguistics have many roots. India is just one of them. Many modern branches of science, like physics, grew out of these original fields.

It was not the proverbial `white man’ who brought the work of Madhava and his school to light. Credit goes to K. V. Sharma (and his collagues like K. S. Shukla). Also to George Geverghese Joseph for publicizing the history. But Western scholars are indeed the ones that unearthed many other aspects of India’s forgotten intellectual history.

http://www.siddha.com.my/ubb/Forum3/HTML/000053-8.html

On recognizing the past: the Kerala School

Ethnocentrism has been a characteristic of most great civilizations. The Greeks, the Chinese, the Hindus, the Arabs, all imagined themselves in their respective glory days to be unique in some ways, perhaps superior to others.

So during the first few centuries of modern science many European thinkers imagined that they were the first to discover the scientific mode, and that others had done little, if any, in the field of scientific research.

At the same time, starting with the European Enlightenment in the 18th century, scholars began to probe into humanity’s cultural legacies. From the untiring quest of such scholars much of ancient history, from Greek and Egyptian to Chinese, Hindu, and Arab science came to be uncovered from their long-forgotten relics. This was and is a slow process. But already in the early 19th century, when it was discovered that the concept of the zero had originated in India, Laplace, one of te greatest mathematicians of the age, wrote: “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.”

The quest for the forgotten past has continued, not only through archeology which unearths and reconstructs lost civilizations but also by deciphering ancient scripts and translating fading manuscripts in leaves, parchments, and such. One of the results from such efforts was reported by the British scholar Charles Whish in 1835 in the Transactions of the Royal Asiatic Society of Great Britain and Ireland. Whish wrote about mathematicians in Kerala whose significant works had been all but forgotten. He also asserted that some of their ideas were essentially the fluxions of Newton: the derivatives that form the core of differential calculus which is at the core of practically all modern higher mathematics. He went on to unravel in the ancient manuscripts the equivalent of what we now call infinite series, particularly of some trigonometric functions and of pi. Whish’s discoveries were so revolutionary in their interpretation and so demanding in their claims that they was set aside and ignored.

More than a century later, some Indian historians of mathematics referred back to this paper and pursued the matter to greater depths. More importantly, they have brought all of this to the attention of the larger international establishment.

Unfortunately, in the meanwhile, historical scholarship had morphed into quarrels over priorities: Indian scholars, in their understandable anger at Western marginalizing of their culture and heritage, accused the European mindset as ethnocentric in interpretations of history; European scholars, in their difficult-to-erase conviction that their own civilization was the one that had developed the results of modern science and mathematics, accused others of excessive claims, fueled by chauvinism rather than facts.

Leaving aside these controversies which are certain to be resolved in due course, it seems to be now established that the contributions between the 13th and the 16th centuries of what is called the Kerala school of mathematics were path-breaking. To that school belonged such creative mathematicians as Madhva of Sangamagramma who formulated the notion of limit to infinity (a key concept in calculus), Nilakantha who derived an infinite series for pi/4 (the so-called Gregory series), the astronomer Paramesvara who wrote extensively on planetary motions, Jyesthadeva’s 16th century text Yuktibhasa in Malayalam, rich in astronomy and mathematics. One Hindu historian has suggested that their results were transmitted to European thinkers via Portuguese missionary-scholars, and inspired the Scientific Revolution.

It is fashionable these days to pay frequent and explicit homage to the Islamic world as the root of modern science. Beyond its factual basis, many political forces are at play in drumming up this view. The facts of history may be blown up or belittled, depending on who writes the history, and for what purpose. In this context, the time has come to publicize to the world more vociferously that some of the seeds for those roots were sown in India.

The eloquent, persuasive and scholarly publications of some Indian historians of science have been gradually accomplishing this in recent years.

What matters ultimately – or should matter, as I see it – is not national boost or cultural pride but setting the record straight. After all, great thinkers, be they scientists or mathematicians, poets or philosophers, have sprung over the ages from every culture and creed, and they all deserve to be acknowledged in just and fair ways for their contributions, since they all deserve humanity’s collective respect and homage.

This news has been around for a while. But unfortunately the world takes notice only when it is announced and endorse by z white westerners.

I don’t think the news is specifically about Kerala. IT just happens the jesuits happened to be there in large numbers during those times and they obtained it from there. Panchanga is common all over India.

For those who wish to explore further here are some links:

The Infitisimal Calculus: How and Why It was Imported Into Europe http://www.indianscience.org/essays/31-%20E–Infinitesimal%20Calculus.PDF

More info http://indiancalculus.info/

http://indiancalculus.info/book_details.htm#Part%20II