The Indian Legacy in Calculus – Fundamentals of Mathematics

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As most of us already know, mathematics plays a crucial part in our school, college and university curriculum. However it is sad to note that most parts of India hardly know anything about our own country’s inherent legacy in fundamental mathematics. One of the most useful and elegant areas of mathematics is calculus. Without calculus much of basic sciences, engineering and medicine would break down. Calculus plays a pivotal role in explaining anything from dynamics of galaxies to motion of electrons. It is in this context we need to remember and celebrate the true Indian legacy in this fundamental branch of mathematics.

Growing up as a kid in a small village in Palakkad district of Kerala and doing my school and university education in various parts of South India, people like me were never ever aware of the historical Indian contribution to calculus. Ironically, in later years when I became a professional astrophysicist, it was from western scientists I came to know that my adjacent district in Kerala i.e. Thrissur had actually produced one of the earliest works which can be linked to present day calculus and trigonometric series.

Modern day historians and professional mathematicians have unravelled that the ancient scholar Madhavacharya has done some outstanding work in the theory of differentials, integrals and infinite series which form a major part of calculus. The ancient texts show that the concept of Taylor’s theorem and Maclaurin’s series (which were found much later in the western world) were used by Madhavacharya during his time. The concept of differentials, integrals, factorials and infinite trigonometric series in mathematics being developed and used by Madhavacharya in such ancient times is an excellent example of the long term vision and insight of our ancestors.

An Artist’s Impression of Madhava of Sangamagrama (Image Credits: Famous-Mathematicians.com)

The present day historians find that Sangamagrama Madhavan, a 15th century Indian mathematician-astronomer, led the foundation and establishment of the Kerala School of Mathematics which flourished between 1300 A.D. and 1700 A.D. This clearly shows that the key principles of modern day calculus which were researched in India at the time pre-dates Isaac Newton and Gottfried Leibniz (who are considered as modern day founders of calculus) by about two centuries. This mathematical legacy is something to be recognised and celebrated by our country’s professional academicians and intellectuals.

The Iringatappally Mana, which is believed to have been the birthplace of Sangamagrama Madhavan (Image Credits: The New Indian Express)

On the contrary, even if you are a science stream school student plus a mathematics student at bachelor’s and master’s level in India, there is hardly anything in our conventional syllabus or textbooks highlighting or recognising the mathematical works of ancient Indian scholars like Madhavacharya and many others. For many decades, textbooks used in Indian school and college education highlighted works only emanating from the west and nothing from the east at all. The initial history based research crediting Madhava and his school of mathematics for their fundamental contributions were accepted in England & Ireland but not in India, ironically. The western scientists and journals were kinder and more receptive to accept the contributions from ancient India compared to India-based journals and editors who tend to cast aspersions on any medieval contributions from our homeland.

It is unfortunate to see the pure apathy of many Indian academics when it comes to accepting home-grown legitimate contributions in basic sciences and medicine. It is true that there are some people who make totally frivolous and exaggerated claims pertaining to Indian legacy in science and engineering. Those have to be dealt with caution and discarded depending on a case-to-case basis.

However it is also important not to have a blind prejudice and generalised stigma against the legitimate and authentic work done by ancient scholars and intellectuals in India. After all, it should be a matter of pride of every Indian when the future generation of Indian students learn and take inspiration from superb brains like the Madhavacharya of Sangamagrama and later raw talents like Srinivasa Ramanujan. Let us hope one day such legends get their due credit and recognition in Indian school and university textbooks! It would be a befitting tribute to the sharp intellect of our wise gurus who toiled centuries ago.

Aswin Sekhar @aswinsek 

Author: Dr Aswin Sekhar, is an Indian scientist based at University of Oslo, Norway

Views presented here are of the Author.

 

Featured Image: Indian postage stamp in honour of the mathematical prodigy Srinivasa Ramanujan (Image Credits: India Post)

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