Changes

== 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. The true credit lies with the ancient Indian Mathematics systems. '''The "Kerala school,'''" a little-known group of scholars and mathematicians (notably Madhava & Nilakantha) '''in fourteenth century India, i'''dentified 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 Bharat's Mathematics systems. '''The "Kerala school,'''" a little-known group of scholars and mathematicians (notably Madhava & Nilakantha) '''in fourteenth century India, i'''dentified the "infinite series" — one of the basic components of calculus— around 1350.  

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 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.   

Of course the self-styled Western scholars and their Bharat's 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 Bharat's civilization ==

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.

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 Bharat's 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.

== Some well-known early Indic contributions to Mathematics ==

== Some well-known early Indic contributions to Mathematics ==

In the sciences, seminal contributions have in fact been made by Ancient India to mathematics, astronomy, chemistry, metallurgy, the list is long.

In the sciences, seminal contributions have in fact been made by Ancient India to mathematics, astronomy, chemistry, metallurgy, the list is long.

 Some Indian contributions to mathematics are well known (at least in India) : the zero, the decimal place value system and the commonly used numerals, the so-called Indo-Arabic numerals (called Arabic numerals in the West) were discovered in Ancient India. In fact, the importance of these is such that without these, mathematics (and science, commerce, etc.) as we know it would not have even existed!

 Some Bharat's contributions to mathematics are well known (at least in India) : the zero, the decimal place value system and the commonly used numerals, the so-called Indo-Arabic numerals (called Arabic numerals in the West) were discovered in Ancient India. In fact, the importance of these is such that without these, mathematics (and science, commerce, etc.) as we know it would not have even existed!

 Further, few are aware that there has been a continuous unbroken tradition of mathematics in India from at least a thousand BCE (and perhaps even several thousand BCE) to ~ 200 years ago, and then again in the modern era.  

 Further, few are aware that there has been a continuous unbroken tradition of mathematics in India from at least a thousand BCE (and perhaps even several thousand BCE) to ~ 200 years ago, and then again in the modern era.  

Summation of series (Sankalita in Sanskrit) (i.e., Integration ).

Summation of series (Sankalita in Sanskrit) (i.e., Integration ).

Instantaneous velocity (of planets) and derivatives.

Instantaneous velocity (of planets) and derivatives.

Besides arriving at the infinite series, that several forms of rapidly convergent series could be obtained is remarkable. Further, many equations that we use in Calculus which are attributed to western mathematicians were clearly known to the Indian mathematicians. They laid the foundations of Calculus, which is recognized as one of the foundations of modern science, and which has applications in many fields including engineering and economics.

Besides arriving at the infinite series, that several forms of rapidly convergent series could be obtained is remarkable. Further, many equations that we use in Calculus which are attributed to western mathematicians were clearly known to the Bharat's mathematicians. They laid the foundations of Calculus, which is recognized as one of the foundations of modern science, and which has applications in many fields including engineering and economics.

These mathematicians also made important contributions to astronomy, but those will be the subject of a separate article. In fact,  much of this work seems to have arisen from an interest in predicting planetary positions, sunrise, sunset etc. to a very high accuracy for the  conduct of worldly affairs. 

These mathematicians also made important contributions to astronomy, but those will be the subject of a separate article. In fact,  much of this work seems to have arisen from an interest in predicting planetary positions, sunrise, sunset etc. to a very high accuracy for the  conduct of worldly affairs. 

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. Bharat's 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 Bharat's mathematics are hidden by time. Our numbers (the current system) evolved from the symbols that the Bharat'ss used; by rights they should be called Bharat's numerals rather than Arabic ones. Unlike the Greeks the Bharat'ss 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:

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 Bharat's 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).