Even in math, things aren’t always black and white

For many people, studying history can be tedious. For many more, math is worse. That being said, I’d like to discuss both. The following is a study of the history of calculus.

Calculus may conjure up nightmarish memories and may even thrust one into an episode of PTSD. But while the subject itself may not have a broad appeal, the story surrounding its creation and battle for ownership is a fascinating tale involving a titan of intellectual history, Sir Isaac Newton, and his lesser-known but still influential counterpart, Gottfied Leibniz.

Sir Isaac Newton was born on Dec. 25, 1642 in the county of Lincolnshire in England. He never married, dedicating his life to scientific discovery beginning with his years at Trinity College Cambridge. His accomplishments place him at the forefront of scientific achievement. Though known to most of us for his theories on gravitation, his 1687 work Mathematical Principles of Natural Philosophy also outlines his findings on the nature of motion. His work led to advanced in optics, he built the first reflective telescope, and he observed that a prism decomposes white light into the colors of the visible spectrum. In addition to many other scientific contributions, he also claimed to have developed calculus, the mathematical study of change.

The German-born Leibniz (July 1, 1646) also carved out a successful scientific career, in addition to his work in philology and political philosophy. He tweaked the binary number system, which is integral to computers, and invented the Leibniz wheel, which was used to develop the arithmometer, the first mass-produced mechanical calculator. Like Newton, he never married and also claimed to develop calculus.

The debate begins around 1666 when Newton began using differentials, a term used to describe infinitesimal changes in variables, in his work, but did not publish any of these notations until 1693. Evidence suggests exists in Leibniz’s notebooks that he began using differential notations in 1675 and published them in his memoir in 1684.

The two mathematicians corresponded for many years before the dispute flared up. In 1704, a review of Newton’s work on quadrature called into question the attribution of calculus’ development. The review stated that Newton had borrowed ideas from Liebniz. Questions of the origins of the techniques began to emerge, leading Newton’s allies to publish Comercium Epistolicum in 1712. No defense was published to support Leibniz.

Due to the extensive nature of survived Newtonian writings, it has been established that Newton first arrived at the calculations sometime around 1666. At the time, Leibniz was not even engaged in mathematical work. According to Sastry, the debate began to shift to whether or not Leibniz had plagiarized Newton’s work, with national pride (the English vs. the Germans) fanning the flames. It is suspected that Leibniz may have had access to Newton’s work somewhere around 1675. This would suggest that he had the opportunity to copy the work; however, analysis of his notebooks from that time shows that he arrived at the techniques from a different approach as Newton. This being a time before the internet and widespread circulation, both men could have come to the same discovery independently.

Given this information, it is now the common belief among scholars that both men should be credited with the development of calculus. After all the dispute and hard feelings, both men were right. Disputes don’t always have right and wrong answers. They aren’t always black and white.

Now if only politicians and married couples would realize the same thing.


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