Often, the creation of modern calculus has been attributed to Sir Isaac Newton and Gottfried Willhelm von Leibniz. However, seemingly unknown or even intentionally ignored, by most Europeans, developments in calculus were being formulated on a different part of the globe. India and the Middle East were all portions of the world working on the creation of calculus at the same time as or before, Sir Isaac Newton and Gottfried Willhelm von Leibniz had tried to continue the ever expanding evolution of mathematics with the focal point of calculus. Calculus can be used daily, from using calculus to figure out marginal revenue, to finding the maximum area to a yard.
The history of calculus is typically perceived as a timeline, one that is divided into three periods. The three periods in the historical timeline of calculus include: Anticipation, Development, and Rigorization. The Anticipation portion of the timeline falls first in the sequence of events in the timeline. In the Anticipation portion time period, techniques used by mathematicians involved the use of infinite processes to find areas under curves or to maximize certain quantities. The Development time period includes both Newton and Leibniz’s foundations used to form the mold for calculus, while bringing these techniques together concerning the derivative and integral. Unfortunately, the techniques used were at points, nonsensical. Finally, in the Rigorization timeline of calculus history, mathematicians were challenged for some time to justify and calculate the ideas that were brought together under the Development time period. The Rigorization time period gave solidarity to the foundation of calculus. This is a period where most modern mathematicians had to figure out equations and theories left behind by previous generations, in order to prove their worth in the field of calculus. Some mathematicians are trying to figure out the Riemann Hypothesis, an equation left behind by Bernhard Riemann, it is yet to be solved. Although these time periods, are mostly used in application to the European history of calculus, the ideas hold true to the history of calculus in non-western parts of the world.
Recently, a team of researchers from the universities of Manchester and Exeter, led by Dr. George Gheverghese Joseph have informed the public with the true origins of calculus. The research team made an announcement placing credit of the formation of calculus to the Kerala School. The Kerala School, an almost unheard of collection of scholars and mathematicians in fourteenth century India had identified a crucial part of calculus known as: The Infinite Series. The infinite series is a basic building block to the foundation of calculus and perhaps one of the most influential identifications made in calculus. The Kerala School had identified the infinite series around 1350, over 200 years before calculus was starting to take root in Europe. This of course, should not disparage any work belonging to European scholars; only bring praise to the often forgotten or overlooked scholars in places other than Europe. The scholars at the Kerala School made the first step towards calculus by identifying the infinite series, which basically describes a line that is ever expanding and constantly growing while never meeting each other. Many modern mathematicians spend their time doing just this, discovering the history of math and trying to solve equations previously left behind much like Dr. George Gheverghese Joseph did by unearthing information of the Kerala School.
Another pioneer in the field of calculus was Al-Karaji. Al-Karaji was an Islamic man from the Middle East, who is credited as introducing the theory of algebraic calculus first. He integrated the powers of integers and integer roots in relation to unknown quantities. Proof of his work can be seen in a book written in 1000 A.D.
During these periods of discovery, Europe was the power house of the world. This being said, credit may have not been appropriately given when it was due. Hopefully, with credit of the birth of calculus being attributed to places other than Europe, the realization that calculus has been around much longer than the 17th century with be bestowed on everyone’s minds. Calculus will always be in the front lines however, bringing clarity to some of life’s toughest equations, or trying to figure out the volume of a box.
- Tomforde, M. (n.d.). The History of Calculus. The History of Calculus. Retrieved April 9, 2014, from http://www.uiowa.edu/~c22m025c/history.ht
- News, C. (2007, August 14). Calculus created in India 250 years before Newton: study – Technology & Science – CBC News. CBCnews. Retrieved April 12, 2014, from http://www.cbc.ca/news/technology/calculus-created-in-india-250-years-before-newton-study-1.632433
- History of Calculus. (n.d.). History of Calculus. Retrieved April 11, 2014, from http://www.mscs.dal.ca/~kgardner/History
- Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji. (n.d.). Al-Karaji biography. Retrieved April 12, 2014, from http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Karaji.html
