Introduction

Isaac Newton is often regarded as the inventor of calculus, alongside his contemporary, Gottfried Wilhelm Leibniz. However, the prevalent narrative overlooks the significant contributions of Indian mathematicians, particularly those from the Malabar region, to the development of calculus. This article invites you to explore the rich tapestry of calculus's origins, highlighting both Newton's pivotal role and the groundbreaking work of Indian mathematicians, including Aryabhatta.

Isaac Newton's Contributions to Calculus

1. Fundamental Theorem of Calculus
Isaac Newton formulated the relationship between differentiation and integration, demonstrating that these two operations are inverses of each other. This insight laid the foundation for the development of modern calculus. Newton's approach to calculus involved the concept of rates of change, which he used to determine the slope of a curve at a given point. This work later evolved into what we now understand as the derivative.

2. Integration
Newton developed methods for finding areas under curves and solving problems related to accumulation, which are now considered as integral calculus. These techniques were crucial in solving complex mathematical problems and paved the way for the development of advanced calculus.

3. Infinite Series
Another area in which Newton made significant contributions was the use of infinite series to represent functions. His work on Taylor series and power series was pioneering in the field of calculus. These series expansions have become fundamental in various branches of mathematics and physics.

The Controversy of Calculus Invention

The development of calculus involved a prolonged and contentious debate between Newton and Leibniz, as well as their respective followers. While Newton's work on calculus was primarily focused on the unification of differentiation and integration, Leibniz developed a more formal notation and approach to calculus. This controversy, known as the 'Calculus Controversy', led to significant developments in the field and has had lasting impacts on the way we understand and teach calculus today.

Indian Contributions to Calculus

While much of the Western world credits Newton with inventing calculus, there is evidence to suggest that significant developments in calculus originated in ancient India. The School of Astronomy and Mathematics in Malabar, India, was established even before the birth of Christ and was known for its advanced mathematical techniques and astronomical observations.

1. Aryabhatta (2700 BC - 265 BC)
Aryabhatta, born in what is now modern-day Kerala, was one of the earliest members of this school. He made several groundbreaking contributions to mathematics, including the calculation of pi to a remarkable degree of accuracy (3.1416) and the determination of the solar year as 365.358 days. Aryabhatta also propounded a heliocentric model of the universe, which was a notion that had to wait for nearly 4 millennia before being revisited by Copernicus. He was also a pioneer in plane and spherical trigonometry and algebra, concepts that were virtually unknown in Europe during the Dark Ages.

Conclusion

The narrative surrounding the origins of calculus is complex and often oversimplified. While Isaac Newton's contributions were pivotal, the work of Indian mathematicians, especially those from the School of Astronomy and Mathematics in Malabar, should be recognized for their pioneering role in the development of calculus. The integration of these histories not only sheds light on the global origins of mathematics but also underscores the interconnectedness of human knowledge across cultures and epochs.