#### Math Review of Leibniz, Newton, and the Development of Calculus

http://schooltutoring.com/help/wp-content/themes/osmosis/images/empty/thumbnail.jpg 150 150 Deborah Deborah http://0.gravatar.com/avatar/63fb4ad5c163b8f83de2f54371b9e040?s=96&d=mm&r=g### Overview

One of the biggest controversies in science in the early 18^{th} century was around the development of a new mathematical tool called calculus. In Europe, the mathematician, philosopher, and scientist Gottfried Leibniz held the attention of the scientific community. The most famous scientist of the day, Sir Isaac Newton, was the champion of Great Britain. According to scientific history, both invented calculus by working independently on different aspects.

### Background

Many mathematical and geometric ideas were already known before calculus was formulated. Archimedes and other Greek geometers, mathematicians in China and India, and thinkers in the Middle East used methods of calculating area and volume, work with infinite series, and other formulas. However, they did not put all those parts together into a system of thought.

### Leibniz

Gottfried Leibniz (1646 -1716) was a German mathematician, philosopher, and scientist who may or may not have been a nobleman. He developed a modern calculating machine, and was an advisor to many political figures in Germany, France, and Austria. One of his many innovations was a version of calculus. He published a paper using the new methods in 1684.

### Newton

Sir Isaac Newton (1642 – 1727) was one of the most famous scientists and mathematicians of his day. He was President of the Royal Society in Great Britain from 1703 to 1727. Newton’s Three Laws are the basic of classical mechanics and physics, especially gravitation. He developed a mathematical “method of fluxions” which was his form of calculus. He described the geometric background in the Principia Mathematica in 1687, in 1693, and in 1704.

### Controversy

In 1711, some of Newton’s partisans in the Royal Society accused Leibniz of plagiarizing Newton’s system. The controversy escalated between the European scientists and the British scientists, fueled by Newton’s supporters in the Royal Society and the political climate of the time. It wasn’t until the 1800’s that British mathematicians began using the notation that Leibniz developed for calculus concepts such as ∫ for integral, and dx and dy for infinitesimal parts of x and y. Historians of science generally regard both Leibniz and Newton as the inventors of calculus, coming at its mathematical concepts from different directions.

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