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== Background ==

== Background ==

For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century.chester and Exeter says it knows where the true credit lies — and it's with someone else completely. The "Kerala school," a little-known group of scholars and mathematicians in fourteenth century India, identified the "infinite series" — one of the basic components of calculus — around 1350.

For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century. The true credit lies with the ancient Indian Mathematics systems. '''The "Kerala school,'''" a little-known group of scholars and mathematicians '''in fourteenth century India, i'''dentified the "infinite series" — one of the basic components of calculus— around 1350.  

The beginnings of modern maths is usually seen as a European achievement buried under the brilliant strategy that Ward Churchill says of <nowiki>''but the knowledge systems of India have been ignored or forgotten," he said. "The brilliance of Newton'</nowiki>s work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.

The beginnings of modern maths and of all other knowledge systems has been seen as a European achievement. This has been made possible through the brilliant strategy of the East India Company traders who under the guise of 'stydying the ' that Ward Churchill says of <nowiki>''but the knowledge systems of India have been ignored or forgotten," he said. "The brilliance of Newton'</nowiki>s work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.

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

"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."

== Summary ==

== Summary ==

As we have mentioned earlier, the essence of Calculus is the use of limits. We end this brief article with the following quotes, the first by Charles Seife in “Zero:The Biographyof a Dangerous Idea” (Viking, 2000; Rupa & Co. 2008):

As we have mentioned earlier, the essence of Calculus is the use of limits. We end this brief article with the following quotes, the first by Charles Seife in “Zero:The Biographyof a Dangerous Idea” (Viking, 2000; Rupa & Co. 2008):

 “The Greeks could not do this neat little mathematical trick. They didn’t have the concept of a limit because they didn’t believe in zero. The terms in the infinite series didn’t have a limit or a destination; they seemed to get smaller and smaller without any particular end in sight. As a result the Greeks couldn’t handle the infinite. They  pondered the concept of void but rejected zero as a number, and they toyed with the concept of infinite but refused to allow infinity – numbers that are infinitely small and infinitely large – anywhere near the realm of numbers. This is the biggest failure in the Greek Mathematics, and it is the only thing that kept them from discovering Calculus.

 <blockquote>“The Greeks could not do this neat little mathematical trick. They didn’t have the concept of a limit because they didn’t believe in zero. The terms in the infinite series didn’t have a limit or a destination; they seemed to get smaller and smaller without any particular end in sight. As a result the Greeks couldn’t handle the infinite. They  pondered the concept of void but rejected zero as a number, and they toyed with the concept of infinite but refused to allow infinity – numbers that are infinitely small and infinitely large – anywhere near the realm of numbers. This is the biggest failure in the Greek Mathematics, and it is the only thing that kept them from discovering Calculus.

Unlike Greece, India never had the fear of the infinite or of the void. Indeed, it embraced them. Indian mathematicians did more than simply accept zero. They transformed it changing its role from mere placeholder to number. The reincarnation was what gave zero its power. The roots of Indian mathematics are hidden by time. Our numbers (the current system) evolved from the symbols that the Indians used; by rights they should be called Indian numerals rather than Arabic ones. Unlike the Greeks the Indians did not see the squares in the square numbers or the areas of rectangles when they multiplied two different values. Instead, they saw the interplay of numerals—numbers stripped of their geometric significance. This was the birth of what we now know of as algebra.”

</blockquote>Unlike Greece, India never had the fear of the infinite or of the void. Indeed, it embraced them. Indian mathematicians did more than simply accept zero. They transformed it changing its role from mere placeholder to number. The reincarnation was what gave zero its power. The roots of Indian mathematics are hidden by time. Our numbers (the current system) evolved from the symbols that the Indians used; by rights they should be called Indian numerals rather than Arabic ones. Unlike the Greeks the Indians did not see the squares in the square numbers or the areas of rectangles when they multiplied two different values. Instead, they saw the interplay of numerals—numbers stripped of their geometric significance. This was the birth of what we now know of as algebra.”

 

And finally, a quote by the famous mathematician John von Neumann:

And finally, a quote by the famous mathematician John von Neumann:

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

<blockquote>''“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”''</blockquote>

== Further reading ==

== Further reading ==

Interested readers can find mathematical and historical  details in the following articles (and references therein):

Interested readers can find mathematical and historical  details in the following articles (and references therein):

1) K. V. Sarma, K. Ramasubramanian, M. D. Srinivas and M. S. Sriram, “Ganita-Yukti-Bhasha (Rationales in MathematicalAstronomy) of Jyeshthadeva”, Springer (2008).

1) K. V. Sarma, K. Ramasubramanian, M. D. Srinivas and M. S. Sriram, “Ganita-Yukti-Bhasha (Rationales in MathematicalAstronomy) of Jyeshthadeva”, Springer (2008).

2) K. Ramasubramanian and M. D. Srinivas, “Studies in the History of Indian Mathematics”  Ed. by C. S. Seshadri, Hindustan Book Agency, New Delhi, pgs. 201 – 286 (2010).

2) K. Ramasubramanian and M. D. Srinivas, “Studies in the History of Indian Mathematics”  Ed. by C. S. Seshadri, Hindustan Book Agency, New Delhi, pgs. 201 – 286 (2010).

 3)T. Padmanabhan, “Dawn of Science : Calculus is  developed in Kerala”, Resonance pgs. 106 -115 (Feb 2012).  

3)T. Padmanabhan, “Dawn of Science : Calculus is  developed in Kerala”, Resonance pgs. 106 -115 (Feb 2012).  

 

4) “Science and Technology in Ancient India”, Ed. Editorial Board, Vijnan Bharati, Mumbai (2006).

4) “Science and Technology in Ancient India”, Ed. Editorial Board, Vijnan Bharati, Mumbai (2006).

# https://bharathgyanblog.wordpress.com/2013/09/21/calculus-was-discovered-in-india/

# https://bharathgyanblog.wordpress.com/2013/09/21/calculus-was-discovered-in-india/

# Joseph, G.G., (2000).''The Crest of the Peacock: Non-European Roots of Mathematics. New Jersey:P''rinceton University Press

# Joseph, G.G., (2000).''The Crest of the Peacock: Non-European Roots of Mathematics. New Jersey:P''rinceton University Press

# ''For America to Live, Europe Must Die"'' Speech by Russell Means http://www.informationclearinghouse.info/article19048.htm

# ''For America to Live, Europe Must Die"'' Speech by Russell Means http://www.informationclearinghouse.info/article19048.htm