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== The discovery of the Kerala School of Mathematics ==

== The discovery of the Kerala School of Mathematics ==

A relatively recently discovered field is what goes by the name of the “Kerala School of Mathematics” which flourished in a tiny corner of present-'''day Kerala during ~ 1300-1600 CE'''.  Many details about the work of this school and the story of the mathematicians who contributed to it are only now being researched. '''This despite the fact that this work was brought to the attention of western scientists almost 200 years ago'''.  In 1834,  an Englishman named Charles  M. Whish  published an article  entitled <blockquote>"

A relatively recently discovered field is what goes by the name of the “Kerala School of Mathematics” which flourished in a tiny corner of present-'''day Kerala during ~ 1300-1600 CE'''.  Many details about the work of this school and the story of the mathematicians who contributed to it are only now being researched. '''This despite the fact that this work was brought to the attention of western scientists almost 200 years ago'''.  In 1834,  an Englishman named Charles  M. Whish  published an article  entitled <blockquote>"“On the Hindu quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four sastras, the Tantrasangraham, Yukti-Bhasha, Caruna-Padhati and Sadratnamala” in a journal called the ‘Transactions of the Royal Asiatic Society’ of Great Britain and Ireland. '''But the article was long ignored'''.

“On the Hindu quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four sastras, the Tantrasangraham, Yukti-Bhasha, Caruna-Padhati and Sadratnamala” in a journal called the ‘Transactions of the Royal Asiatic Society’ of Great Britain and Ireland. '''But the article was long ignored'''.

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  "</blockquote>

== 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):

 <blockquote>"

 <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.

“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>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:

<blockquote>"

<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>

''“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 ==