The history of Calculus is very fascinating. Throughout three eras of time Calculus was developed and added onto. However, before any of that occurred it was founded, independently, by Isaac Newton and Gottfried Wilhelm Leibniz. It was originally called infinitesimal calculus.

Ancient Period

The ancient period introduced some of the ideas that later became integral calculus. In the photo to the left Archimedes used the “method of exhaustion” in order to calculate the area under the parabola.

Medieval Period

Hasan Ibn al-Haythem also known as Alhazen created the sum of fourth powers which is essentially integration of this function. In the 14th century some Indian mathematicians created a less difficult which resulted in differentiation of trigonometric functions.


In Europe, Bonaventura Cavalieri laid the foundation down by signing a treatise. As this occurred more calculus rules were created.


Gottfried Wilhelm Leibniz, the picture on the left, was the first to clearly state the rules of Calculus. Isaac Newton, the picture on the right, developed the use of calculus in his laws of motion and gravitation.


“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

-John Von Neumann

The development of calculus has brought us to one of the most informative type of mathematics. Without calculus we would not be able to compute or solve different types of problem regarding a phone call. We also wouldn’t be able to have cell phones or television.


Math in general means everything to me. Learning about the history of calculus, and about how all the rules were created Is fascinating. It makes me think about how people were able to come together and decide how integration and derivatives should be. Throughout the eras of time more and more people were able to build off what others have accomplished. To me it’s exciting to see what people now can produce after everything they have learned from calculus.