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Newton v. Leibniz - The Calculus Controversy

In Latin, the word ‘calculus’ means ‘pebble,’ meaning that small stones were used to calculate things. Calculus is essentially the study of change, and the pebbles represent small, gradual changes that can produce impressive results. The origin of calculus is not the work of a single man, not even the work of the two men pictured above - but like most major discoveries, a gradual build of overlapping discoveries, something very similar to calculus itself. The question over the creation of the branch of mathematics has become one of the fiercest rivalries in modern history - that between Isaac Newton and Gottfried Leibniz.

In 1666 (and perhaps earlier), when Newton was 23 - he had begun work on what he called “the method of fluxions and fluents,” effectively what we know as calculus. Newton’s discovery of calculus was mainly a result of practical use - he needed a method to solve problems in physics and geometry, and calculus was what resulted. On the other hand, Leibniz had become fascinated by the tangent line problem and began to study calculus around 1675. 

The ideas of the two men were similar, although it is unlikely that either of them knew the specifics of the other’s work. The two men spoke in letters often, and discussed mathematics - and although the Royal Society found Leibniz effectively guilty of plagiarism later, this was not likely the case. Both men came to similar discoveries in different ways - Leibniz came to integration first, while Newton began his work with derivatives. 

Although Newton discovered the principles of calculus first - he did not publish them until many years after Leibniz did. Leibniz published his first paper employing calculus in 1684, but Newton did not publish his fluxion notation form of calculus until 1693, and a complete version was not available until 1704! Nonetheless, Newton still came to the discovery first - and although both men are officially credited, Newton is the one that most people remember. 

However, Newton doesn’t deserve all the credit here. The famous dy/dx notation that calculus students have come to love and hate was developed by Leibniz. Although Newton may have come to the discovery first, Leibniz attacked the problems with far better notation - and we have naturally adopted it. Instead of Leibniz’s dx/dt (shown below) notation for derivatives, Newton preferred ‘dot’ notation: 

However, this dot notation can become confusing, especially when used for higher order derivatives, so it has been generally dismissed - except for hardcore Newton fanatics who insist on using his notation. Newton did not even have a standard notation for integration, but frequently switched; but Leibniz used the recognizable integration symbol: 

This has developed into a fantastic controversy over the years - and has become as much of a moral question as it is scientific. Many Leibniz advocates belief that Newton doesn’t deserve full credit because he didn’t publish his findings first - while many others believe that Newton came to the discovery first, so the credit is his. Personally, I have to place myself on the side of Newton - although Leibniz’s notation is wonderful, Newton discovered the principles first. 

Which side are you on?  

(via proofmathisbeautiful)

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