## The Origins of Calculus

Calculus is a branch of mathematics that explores variables and how they change by looking at them in infinitely small pieces called infinitesimals. Calculus, as it is practiced today, was invented in the 17th century by British scientist Isaac Newton and German scientist Gottfried Leibnitz. They independently developed the principles of calculus in the traditions of geometry and symbolic mathematics.

While these two discoveries are most important to calculus as it is practiced today, they were not isolated incidents. At least two others are known: Archimedes (287 to 212 B.C.) in Ancient Greece and Bhāskara II (A.D. 1114 to 1185) in medieval India developed calculus ideas long before the 17th century. Tragically, the revolutionary nature of these discoveries either wasn’t recognized or was so buried in other new and difficult-to-understand ideas that they were nearly forgotten until modern times.

Sir Isaac Newton

Sir Isaac Newton was a mathematician and scientist, and he was the first person credited with developing calculus. It is an incremental development, as many other mathematicians had part of the idea. Newton’s teacher, Isaac Barrow, said “the fundamental theorem of calculus” was present in his writings, but somehow he didn’t realize the significance of it nor highlight it. As Newton’s teacher, his pupil presumably learned things from him. Fermat invented some of the early concepts associated with calculus: finding derivatives and finding the maxima and minima of equations. Many other mathematicians contributed to both the development of the derivative and the development of the integral.

Gottfried Wilhelm Leibniz

But Gottfried Wilhelm Leibniz independently invented calculus. He invented calculus somewhere in the middle of the 1670s. He said he conceived of the ideas in about 1674 and then published the views in 1684, 10 years later. His paper on calculus was called “A New Method for Maxima and Minima, as Well Tangents, Which is not Obstructed by Fractional or Irrational Quantities.” It was six pages, exceedingly obscure, and was very difficult to understand.

#### The Indian Mathematicians

A team from the Universities of Manchester and Exeter states that the real credit for the first studies in calculus lies with the “Kerala School,” a little-known group of scholars and mathematicians in fourteenth-century India, who identified the “infinite series” – one of the essential components of calculus – around 1350.

Dr. George Joseph, a member of the research team, stated that the findings should not diminish Newton or Leibniz but rather exalt the non-European thinkers whose contributions are often ignored. According to him, the beginnings of modern math is usually seen as a European achievement. Still, the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten. The brilliance of the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with Newton and Leibniz as they discovered the other significant component of calculus, the infinite series. Little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, in which much of the documentation of this remarkable mathematics is written, is also responsible for the suppressed acclaim these mathematicians and scholars receive.

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