Published By: Sayan Paul

The Forgotten Genius Behind Calculus - Who Was Madhava of Sangamagrama?

Centuries before Newton and Leibniz, a Kerala mathematician laid the groundwork for modern mathematics. 

When we say ancient India was way ahead of the West in science and philosophy, we don't say it just for the sake of it. We truly were. Time and again, Indian minds discovered ideas and concepts that the West would stumble upon much later. The only problem was that we never told our stories loud enough. History, as we know it, has mostly been written from a Western lens, and in that version, many of our brilliant minds were left out. Madhava of Sangamagrama was one of them. He lived sometime between 1340 and 1425 in a small town in Kerala, and laid the early groundwork for calculus, centuries before Newton and Leibniz. He also made major contributions to astronomy and trigonometry, yet today, most people, even in India, have never heard of him.

So, in this story, let's look back at the life and legacy of Madhava, the forgotten genius whose work deserves to be celebrated and taught to every generation.

Who Was Madhava? 

Madhava was likely born around 1340 in Sangamagrama, a small settlement now identified with the town of Irinjalakuda, Kerala. As with many pre-modern figures, details of his life are very sparse. We have no portraits, no personal letters, and not even his own direct writings. What survives are the quotations, citations, and mathematical series that later scholars attributed to him.

He probably belonged to a scholarly Brahmin community that had long engaged with astronomy. Fourteenth-century Kerala, thanks to its thriving spice trade, was a place of porous borders, as Arabian merchants, Chinese sailors, and Sanskrit scholars all intersected here. It’s in this intellectually fertile environment that Madhava began asking the kinds of questions that make history bend a little.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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The Mathematics of Endless Slicing

To appreciate Madhava's contributions, imagine trying to measure a circle with no ruler, or calculating the trajectory of a star without ever seeing a telescope. What Madhava pioneered, through sheer intellect and painstaking calculation, were the early techniques of what we now recognize as infinite series, the foundational building blocks of calculus.

He derived methods to compute trigonometric functions (like sine and cosine) by expressing them as infinite sums. These are the very series that would later reappear in European mathematics, attributed to Newton and Leibniz. His sine series, for instance, involves successively subtracting and adding fractions of increasing complexity, a kind of numerical zigzag that converges, miraculously, to the truth.

(Credit: MathType) 

Most strikingly, Madhava developed a series for π, which we now refer to as the Madhava-Leibniz series:

\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots

Star Charts and Lunar Timetables

But Madhava’s vision wasn’t confined to the page. Rather, it extended to the heavens. He was, after all, both a mathematician and an astronomer. 

Madhava’s treatise Veṇvāroha (meaning “Bamboo Climbing”) offered astronomers a method to calculate the Moon’s position every 40 minutes, a remarkably fine-grained interval for the era. He also compiled precise trigonometric tables, critical for tracking planetary motion, and essential for navigation in a maritime region like Kerala.

(Credit: Cliff Pickover) 

His approach combined mathematical ingenuity with observational discipline. And while telescopes wouldn’t appear for another few centuries, Madhava and his successors were already refining models that challenged, and in some cases anticipated, the heliocentric worldview.

Three Centuries Ahead of Europe 

There is something uncanny about reading Madhava’s work today, because the equations feel familiar. In fact, much of what Newton developed in the 17th century bears a striking resemblance to what Madhava laid down in the 14th century.

This has led to a long-simmering historical question: Could there have been a transfer of knowledge between India and Europe? Jesuit missionaries who arrived in Kerala in the 16th century were known to engage with local scholars. Some believe they may have carried Indian mathematical texts back to Europe. But the evidence is, at best, circumstantial. What we can say with confidence is that Madhava was solving problems that Europe had not yet even formulated.

(Credit: Exploratorium) 

G.G. Joseph, a modern historian of mathematics, described his work as the “crest-jewel” of Indian mathematics, and it’s hard to disagree. As he wrote in 'A Passage to Infinity', “Madhava’s math was a crest-jewel, shining bright in Kerala while Europe was still finding its way.”

The Silence That Followed

If Madhava’s work was so significant, why did it vanish from the global stage? Part of the answer lies in the materials. Palm leaf manuscripts, while ingenious in their own way, were never meant to last centuries. Many of his original writings were likely destroyed by rain or simple decay. What survives comes to us secondhand, through scholars like Jyesthadeva, whose 16th-century Yukti-Bhāṣā preserved much of Madhava’s mathematics.

But you see, preservation is not the same as dissemination. Written in regional languages like Malayalam and Sanskrit, these texts were largely invisible to a Western scientific world enthralled by its own Enlightenment. When a British civil servant named Charles Whish discovered references to Madhava's work in the early 19th century, his claims were dismissed as either mistaken or exaggerated. After all, the story of science had already been cast, and there was little appetite for rewriting the credits.

Even in India, he remains a largely obscure figure. His legacy, like so many others, was buried under colonial epistemologies that mistook absence from Western records as absence from history itself.

Still, Ideas Have a Way of Surviving

Madhava’s intellectual descendants, the Kerala school of astronomy and mathematics, carried his work forward for nearly two centuries. Figures like Nilakantha Somayaji expanded on his astronomy; Jyesthadeva translated his mathematics into accessible prose. And in recent decades, scholars like C.T. Rajagopal and G.G. Joseph have begun recovering Madhava’s place in the story of global science. Books like 'The Crest of the Peacock' have helped shift the narrative, acknowledging the polyphonic, multi-origin roots of modern mathematics.

(Credit: Cliff Pickover) 

Today, there is talk of establishing a research center in Irinjalakuda to honor Madhava. Perhaps it’s a small step toward restoring his name to the historical record, but also a gesture toward a more honest map of human knowledge.