Thread by @Bharathgyan

Calculus originated from Indian

This study of Calculus, while it has had its roots in the age old Indian philosophies, blossomed & took on a finite form between 1300s CE & 1600s CE, with a line of stalwart mathematicians such as Madhava, Nilakantha, Acyuta Pisarati and so on.

They worked on & leveraged the platform established by Pingala, Aryabhata, Brahmagupta, Bhaskara I & II and so on during earlier centuries.

It culminated in a number of works coming out of the Kerala School of Mathematics and Astronomy, 500 years and more before Arabia and Europe started using such techniques.
India called its works on Calculus by names such as
Yuktibhasa & Kuttakadhyaya

Yukti with similar root as Yoga, Yug means to connect, unite, join. Yukti as a term for Calculus was chosen since Calculus as we have seen, is a technique of uniting, summing, integrating many little parts to yield the whole.
Bhasa means rationale, proof, explanation.

Yuktibhasa is a work that contains proofs & explanation for integrating to arrive at solutions.
Yukti also denotes trick. Yuktibhasa is that work which contains explanations on tricks to arrive at solutions for difficult problems in mathematics.
Truly a case of tricking infinity.

One of the chapters in Brahmasphuta Siddhanta of Brahmagupta from 680 CE is called Kuttakadhyaya as it deals with summations and integrations of the parts. Kuttaka means to split, to break into many parts.

While many modern educated minds still grapple with Integral Calculus, all this was written over 1400 years ago by the presently imagined to be illiterate Indian ancestors.

Some Indian Terminologies used in Calculus

Instantaneous velocity, a frequently measured parameter using Calculus, has a specific terminology in Indian text. It was referred to as Tatkalika Gati. Gati means speed. Kala means time. Tat Kalika means at that instant.

Summation was denoted by the word Sankalita.
Sankhya means numbers, count. Sankalan means to aggregate, collate.

Newton is credited with first having used such techniques of Calculus to calculate the instantaneous velocities of planets, which are
constantly moving with time. But these techniques as we have seen were already being put to use more than 800 – 900 years before Newton’s times.

Not only that, by Newton’s times, they had made their way to Europe having been translated from the Arabic version as well as directly translated from the Samskrt originals by the Jesuits who came to Kerala.

In hindsight, Newton’s discovery is perhaps the first modern application of the infinitely profound, ancient Indian expression of knowledge.

Experts find strong reason to believe that India’s Calculus could have been the key principle behind the Principia Mathematica itself. The difference being that, the Indian approach stemmed from a seamless transition between Spirituality, Philosophy and Sciences.

While the world is now slowly beginning to acknowledge that Indian Calculus has provided the basis for modern mathematics, it is the texts
on Calculus from India which have provided the strongest evidence to trace back the travel of Mathematics from India to the West.

While Calculus has integrated the West with the East, the differential in philosophy though, is yet to be bridged. It only seems to be getting more limiting, approaching infinitesimally small levels of tolerance, instead of infinite love and peace.

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