Mathematics of infinity: Calculus and infinity - Essay Example

Though, it was not until 1967 when Newton first published his ideas. However, far across in France, Gottfried Leibniz started working on his own fundamental ideas and reaching certain breakthroughs in 1675, which he consequently published in 1684 (Tent, 2011). At, the time, scientific communication was still fuzzy, insufficient, and uncoordinated; therefore, this meant that Leibniz and Newton continued with their work independently without reciprocal input or knowledge. This in the end resulted in disputes about their discoveries which have raged on to-date.

Leibniz fundamental ideas and discoveries of calculus emerged from three key interests that he pursued at the time, including, philosophy in which his main aim was on defining a symbolic language which would enable all the processes of argument and reasoning to be written in formulas and symbols that obeyed certain rules. This, therefore, explains why he focused more on developing useful theoretical methods and notations rather than on getting results (Brown, 2012). Leibniz notational language is what is today used in calculus, instead of Newton’s. . On the other hand, Newton, who because of the plague in England could publish his works and was forced to publish almost a decade after Leibniz, was concerned more problems of planetary and gravitational motion.

His approach to calculus, therefore, attempted to comprehend force and motion in terms of infinitesimal change based on time. Newton focused more on and mastered the concepts of quadrature and tangent-definite integration (Gaukroger, 2008). He did not used derivatives, rather, he used fluxions of variables that are denoted by x. similarly, he did not used ant-derivatives; rather he referred to what is known as fluents. In essence, his whole fundamental idea was based on the consideration of lines and planes as generated by points in motion, and bodies as constituted by planes in motion; all these he referred to as fluents.

Fluxions is the term he used to refer to the velocity of fluents (Guicciardini, 2003). Oversimplified analysis of the approach by Newton and that by Leibniz by certain scholar argue that Leibniz approach invented integral calculus while Isaac Newton is credited with the invention of differential calculus (Gaukroger, 2008). However, as has been noted, these are oversimplified analysis, both developed both differentiation and integration versions of calculus (Goldenbaum & Jesseph, 2008). Berkeley’s criticism of the foundations of the calculus as developed by Newton and Leibniz Lord Bishop Berkeley, an 18th Century philosopher, was bothered with the concept of infinitesimals as developed by Newton and Leibniz (D.

Jesseph, 1993); he, therefore, made serious criticisms of calculus that, at one time, he referred to infinitesimals as the glimmers of defunct quantities.