It is interesting to note that the ongoing controversy concerning the so-called conflict between Wilhelm Gottfried Leibniz and Isaac Newton is one that does not bare much merit. Whether one came up with the concepts of calculus are insignificant since the outcome was that future generations benefited. However, the logic of their clash does bear merit.
In proposing that he was the first inventor, Leibniz states that "it is most useful that the true origins of memorable inventions be known, especially of those that were conceive not by accident but by an effort of meditation. The use of this is not merely that history may give everyone his due and others be spurred by the expectation of similar praise, but also that the art of discovery may be promoted and its method become known through brilliant examples.”
Newton on the other had would not allow himself to be usurped by stating that “second inventors have no right. Whether Mr Leibniz found the Method by himself or not is not the Question… We take the proper question to be,… who was the first inventor of the method." In addition, he continued on by stating that "to take away the Right of the first inventor, and divide it between him and that other, would be an Act of Injustice."
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
On January 4, 1643, Isaac New...
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...tics is a sufficient condition for its antecedent. Furthermore, both forms of mathematics do have a non-symmetrical relationship. Simply put, a concept derived from abstract mathematical methods can bear this same concept to a practical application; the reverse may or may not be possible. The reason being is that in abstraction, there is unlimited possibility and some methods have no particular end.
Works Cited
Bardi, Jason Socrates. The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. New York: Thunder's Mouth Press, 2006.
Leibniz, Gottfried Wilhelm., and J. M. Child. The Early Mathematical Manuscripts of Leibniz. Mineola, NY: Dover Publ., 2005.
Newton, Isaac. The Correspondence of Isaac Newton. Vol. 7, 1718-1727. Edited by A. Rupert Hall and Laura Tilling. Cambridge: Cambridge University Press for the Royal Society, 1977.
Abstract—The transition to calculus was a remarkable period in the history of mathematics and witnessed great advancements in this field. The great minds of the 17th through the 19 Centuries worked rigorously on the theory and the application of calculus. One theory started another one, and details needed justifications. In turn, this started a new mathematical era developing the incredible field of calculus on the hands of the most intelligent people of ancient times. In this paper, we focus on an amazing mathematician who excelled in pure mathematics despite his physical inability of total blindness. This mathematician is Leonard Euler.
Look, B. (2007, December 22). Gottfried Wilhelm Leibniz. Stanford University. Retrieved May 2, 2014, from http://plato.stanford.edu/entries/leibniz/
ABSTRACT: It is well known that a central issue in the famous debate between Gottfried Wilhelm Leibniz and Samuel Clarke is the nature of space. They disagreed on the ontological status of space rather than on its geometrical or physical structure. Closely related is the disagreement on the existence of vacuums in nature: while Leibniz denies it, Clarke asserts it. In this paper, I shall focus on Leibniz's position in this debate. In part one, I shall reconstruct the theory of physical space which Leibniz presents in his letters to Clarke. This theory differs from Leibniz's ultimate metaphysics of space, but it is particularly interesting for systematic reasons, and it also gave rise to a lively discussion in modern philosophy of science. In part two, I shall examine whether the existence of vacuums is ruled out by that theory of space, as Leibniz seems to imply in one of his letters. I shall confirm the result of E. J. Khamara ("Leibniz's Theory of Space: A Reconstruction," Philosophical Quarterly 43 [1993]: 472-88) that Leibniz's theory of space rules out the existence of a certain kind of vacuum, namely extramundane vacuums, although it does not rule out vacuums within the world.
John Cottingham, ed. The Cambridge Companion to Descartes. Cambridge, New York: Cambridge University Press, 1992.
mathematical formula can prove”. Leibniz ignored the problems and flaws in society that were so clearly in front of him because his logic rendered them impossible. This is where the conflict first began to arise between Leibniz and Voltaire. Voltai...
Ball, Rouse. “Sir Isaac Newton.” A Short Account of the History of Mathematics. 4th ed. Print.
The Enlightenment characterizes a philosophical movement of the 18th century that emphasized the use of reason to analyze and scrutinize all previously accepted traditions and doctrines. Through this application of scientific method to all aspects of life, the role of science gradually replaced the role of religion. Sir Isaac Newton, quite possibly one of the most intelligent men to exist, played a key role in the development of the enlightenment. He supplied the foundations on which all sciences since him have been built. Without science and reason the enlightenment would have been unthinkable. In fact, historians quote the publishment of Newton's masterpiece Principia in 1687 as the most logical and fitting catalyst to the enlightenment. The scientific advances made by Sir Isaac Newton contributed immensely to the movement of the enlightenment; however, his primary purposes for discovery were not for scientific advancement rather all for the glorification of God, thus Newton's incredible religiousness will be seen in this paper.
Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy. N.p.. Web. 24 Mar 2014. .
This paper presents a development of mathematical analysis, illustrating the contribution of Euler to the development of calculus in the specific examples. Mathematical analysis is a combination of divisions of mathematics that includes differentiation, integration, limits, infinite series and analytic function. First ideas of the concepts of mathematical analysis were established by the ancient Greek mathematicians. All the divisions of calculus, including analysis, had a similar idea: division on the infinitely small elements but the nature of analysis was unfamiliar to the authors of an idea. They developed the principle of infinity and established a method to calculate the area and volume of some plane figures and solids.
Calculus is defined as, "The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus." (Oxford Dictionary). Contrary to any other type of math, calculus allowed Newton and other scientists to process the different motions and dynamic changes in world, such as the orbit of planets in space. Newton first became interested in the subject of mathematics while he was an undergraduate at Cambridge University. Although he did not focus on any of his math classes during his time as an undergraduate because it focused on Greek mathematics, he instead learned
Sir Isaac Newton Jan 4 1643 - March 31 1727 On Christmas day by the georgian calender in the manor house of Woolsthorpe, England, Issaac Newton was born prematurely. His father had died 3 months before. Newton had a difficult childhood. His mother, Hannah Ayscough Newton remarried when he was just three, and he was sent to live with his grandparents. After his stepfather’s death, the second father who died, when Isaac was 11, Newtons mother brought him back home to Woolsthorpe in Lincolnshire where he was educated at Kings School, Grantham. Newton came from a family of farmers and he was expected to continue the farming tradition , well that’s what his mother thought anyway, until an uncle recognized how smart he was. Newton's mother removed him from grammar school in Grantham where he had shown little promise in academics. Newtons report cards describe him as 'idle' and 'inattentive'. So his uncle decided that he should be prepared for the university, and he entered his uncle's old College, Trinity College, Cambridge, in June 1661. Newton had to earn his keep waiting on wealthy students because he was poor. Newton's aim at Cambridge was a law degree. At Cambridge, Isaac Barrow who held the Lucasian chair of Mathematics took Isaac under his wing and encouraged him. Newton got his undergraduate degree without accomplishing much and would have gone on to get his masters but the Great Plague broke out in London and the students were sent home. This was a truely productive time for Newton.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
Foster, Niki. "Who is Gottfried Leibniz." Brief and Straightforward Guide (2011): n. pag. Web. 14 Apr 2011. .