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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 'studying pagan cultures & civilising the savages', digested and assimilated as their own, the native knowledge systems.

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 'studying pagan cultures & civilising the savages', digested and assimilated as their own, the native knowledge systems.

Of course the self-styled Western scholars and their Indian recruits like Joseph (2000) claim that indian systems have been ignored or overlooked & see it as a simple outcome of Christian colonialism and not as a well-organised strategy to not only control global resources but also the knowledge systems.  He attributes other factors like "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," exposes the perfidy of the Christians who used local Sanskrit scholars to translate our texts to steal our knowledge and 'digest' it to claim as their own.   

Of course the self-styled Western scholars and their Indian recruits like Joseph (2000) claim that indian systems have been ignored or overlooked & see it as a simple outcome of Christian colonialism and not as a well-organised strategy to not only control global resources but also the knowledge systems.  He attributes other factors like "There is also little knowledge of the ancient  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," exposes the perfidy of the Christians who used local Sanskrit scholars to translate our texts to steal our knowledge and 'digest' it to claim as their own.   

== Knowledge and Indian civilization ==

== Knowledge and Indian civilization ==

Most of the amazing science and technology knowledge systems of the modern world are credited to have started around the time of the Renaissance movement in Europe in ~ the 15th century. These knowledge systems are generally traced back to roots in the civilization of Ancient Greece, and occasionally, that of Ancient Egypt. Notably both these civilisations were destroyed, their indigenous population decimated or converted to Christianity or Islam by the invaders and their knowledge digested and presented as ancient knowledge. Hence, most of the heroes we are taught about in school and college are European or Greek.

Most of the amazing science and technology knowledge systems of the modern world are credited to have started around the time of the in Europe in ~ the 15th century. These knowledge systems are generally traced back to roots in the civilization of Ancient Greece, and occasionally, that of Ancient Egypt. Notably both these civilisations were destroyed, their indigenous population decimated or converted to Christianity or Islam by the invaders and their knowledge digested and presented as ancient knowledge. Hence, most of the heroes we are taught about in school and college are European or Greek.

 As for India, or even China, it would appear that they have played a minimal role in this magical story. Most Western accounts of the “Ascent of Man” do not devote even a single line to India’s contributions and the world is kept largely ignorant of India's great contribution to  the world in every aspect of knowledge. This is due to the creation of Indology, a system totally unique to colonial India, started by the East India Company to not only digest, but regurgitated as western marvels of science and technology. Post independence, this evil startegy was continued through a dedicated and well-paid bad of brown sepoys wh delineralely neglected any scholarly studies on our history and heritage and specialised in higlihting the <nowiki>''</nowiki>.  Incidentally, this is in contrast to the attitude in almost any other country – people elsewhere have a keen interest and fierce pride and celebrate their own contributions to world knowledge and heritage. Several countries also make a living out of their past through tourism!

 As for India, or even China, it would appear that they have played a minimal role in this magical story. Most Western accounts of the “Ascent of Man” do not devote even a single line to India’s contributions and the world is kept largely ignorant of India's great contribution to  the world in every aspect of knowledge. This is due to the creation of Indology, a system totally unique to colonial India, started by the East India Company to not only digest, but regurgitated as western marvels of science and technology. Post independence, this evil startegy was continued through a dedicated and well-paid bad of brown sepoys wh delineralely neglected any scholarly studies on our history and heritage and specialised in higlihting the <nowiki>''</nowiki>.  Incidentally, this is in contrast to the attitude in almost any other country – people elsewhere have a keen interest and fierce pride and celebrate their own contributions to world knowledge and heritage. Several countries also make a living out of their past through tourism!

 However, there does exist, thanks in part to valiant individual efforts, some kind of a background awareness that the Indian civilization is in fact one of the most ancient and glorious, and that India has contributed enormously, perhaps even predominantly, to the growth of world civilization and knowledge in practically every field, ranging from the mundane and practical to the unworldly and spiritual.

 However, there does exist, thanks in part to valiant individual efforts, some kind of a background awareness that the Indian civilization is in fact one of the most ancient and glorious, and that India has contributed enormously, perhaps even predominantly, to the growth of world civilization and knowledge in practically every field, ranging from the mundane and practical to the unworldly and spiritual.

== The Lineage ==

== The Lineage ==

Mādhava (c.1340–1420) of Sangamagrāma

Mādhava (c.1340–1420) of Sangamagrāma, Pioneer of the Kerala School, discovered many of the basic ideas of Calculus. The only works of his which seem to be extant are Venvāroha and Sphutacandrāpati.

 Pioneer of the Kerala School, discovered many of the basic ideas of Calculus.

 

 

Nīlakantha Somayājī (c. 1444–1550) of Kundāgrama monumental works are Tantrasangraha and Āryabhatiya-bhāsya.

Jyesthadeva (c. 1530)

Jyesthadeva (c. 1530)

Author of the celebrated Ganita Yuktibhāsā (in Malayalam prose).

Author of the celebrated Ganita Yuktibhāsā (in Malayalam prose).

== 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>“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.

</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.”