Calculus Was Developed in Medieval India

Two British researchers challenged the conventional history of mathematics in June when they reported having evidence that the infinite series, one of the core concepts of calculus, was first developed by Indian mathematicians in the 14th century. They also believe they can show how the advancement may have been passed along to Isaac Newton and Gottfried Wilhelm Leibniz, who are credited with independently developing the concept some 250 years later.

“The notation is quite different, but it’s very easy to recognize the series as we understand it today,” says historian of mathematics George Gheverghese Joseph of the University of Manchester, who conducted the research with Dennis Almeida of the University of Exeter. “It was expressed verbally in the form of instructions for how to construct a mathematical equation.”

Historians have long known about the work of the Keralese mathematician Madhava and his followers, but Joseph says that no one has yet firmly established how the work of Indian scholars concerning the infinite series might have directly influenced mathematicians like Newton and Leibniz.

Joseph and Almeida, who spent three years digging through ancient Indian texts and Vatican archives, believe Jesuit priests brought scientific knowledge from southern India to Western Europe. The priests were missionaries in India in the mid-16th century. They learned local languages and scientific practices and sent meticulous reports back to Europe.