While Calculus itself sounds less pleasant to me than gauging my eyes out with a fork, the story of its founders and subsequent controversies prove to be an intriguing mystery that is still not 100% solved to this day.

Although the two individuals frequently quarreled over who was the true discoverer of calculus, the math community as a whole can agree that both Isaac Newton and Gottfried Leibniz left a profound impact on this area of mathematics. While their contributions were developed independently, with each mathematician approaching the subject from a varying viewpoint, Newton’s and Leibniz’s ideas provided a strong foundation for future calculus enthusiasts to come.

Isaac Newton, an English physicist and mathematician, began his work on the subject around 1666, however he published relatively none of his work until the time between 1693-1704. His intentions upon beginning this endeavor were to utilize math as a means of better explaining physics, in the sense that he wished to take a more dynamic approach to graphs and numbers than previous math of the time. Newton started out his work by attempting to find the slope of a tangent line to the curve at any point. This led him to discovering differentiation and later its inverse, integration, which resulted in his publishing of the First Fundamental Theorem of Calculus. Today’s experts argue that Newton’s notation was a lot less clear and consistent than Leibniz’s, however his notation for a time derivative is still used today (places a dot over the dependent variable during differentiation).

Leibniz, a German mathematician, published his calculus works in 1684, and approached the subject in a more analytical and less graphical manner than Newton. He was more outspoken regarding his advancements in the subject from an earlier point, and highly valued using logical notation, some of which is still used today. Currently, Leibniz Notation is utilized in calculus, where dx and dy, represent infinitely small increments of x and y respectively. In addition, Leibniz was the first mathematician to begin incorporating the “ʃ” symbol into calculus.

The public may not ever know who the real first inventor of calculus was, but each of these experts were truly innovators in the field.