Editing History of calculus (section)

===Legacy===
The rise of calculus stands out as a unique moment in mathematics. Calculus is the mathematics of motion and change, and as such, its invention required the creation of a new mathematical system. Importantly, Newton and Leibniz did not create the same calculus and they did not conceive of modern calculus. While they were both involved in the process of creating a mathematical system to deal with variable quantities their elementary base was different. For Newton, change was a variable quantity over time and for Leibniz it was the difference ranging over a sequence of infinitely close values. Notably, the descriptive terms each system created to describe change was different. 

Historically, there was much debate over whether it was Newton or Leibniz who first "invented" calculus. This argument, the [[Leibniz and Newton calculus controversy]], involving Leibniz, who was German, and the Englishman Newton, led to a rift in the European mathematical community lasting over a century. Leibniz was the first to publish his investigations; however, it is well established that Newton had started his work several years prior to Leibniz and had already developed a theory of [[tangent]]s by the time Leibniz became interested in the question.
It is not known how much this may have influenced Leibniz. The initial accusations were made by students and supporters of the two great scientists at the turn of the century, but after 1711 both of them became personally involved, accusing each other of [[plagiarism]].

The priority dispute had an effect of separating English-speaking mathematicians from those in continental Europe for many years. Only in the 1820s, due to the efforts of the [[Analytical Society]], did [[Leibnizian analytical calculus]] become accepted in England. Today, both Newton and Leibniz are given credit for independently developing the basics of calculus. It is Leibniz, however, who is credited with giving the new discipline the name it is known by today: "calculus". Newton's name for it was "the science of [[fluent (mathematics)|fluent]]s and [[Method of Fluxions|fluxion]]s".

While neither of the two offered convincing logical foundations for their calculus according to mathematician [[Carl Benjamin Boyer|Carl B. Boyer]], Newton came the closest, with his best attempt coming in ''Principia'', where he described his idea of "prime and ultimate ratios" and came extraordinarily close to the [[Limit (mathematics)|limit]], and his ratio of velocities corresponded to a single [[real number]], which would not be fully defined until the late nineteenth century.<ref name=":0">{{Cite journal |last=Boyer |first=Carl B. |date=1970 |title=The History of the Calculus |url=https://www.jstor.org/stable/3027118 |journal=The Two-Year College Mathematics Journal |volume=1 |issue=1 |pages=60–86 |doi=10.2307/3027118 |jstor=3027118 |issn=0049-4925}}</ref> On the other hand, the calculus of Leibniz was from a "logical point of view, distinctly inferior to that of Newton, for it never transcended the view of <math>\frac{dy}{dx}</math> as a quotient of infinitely small changes or differences in ''y'' and ''x''."<ref name=":0" /> However, heuristically, it was a success, despite being a "failure" from a logical point of view.<ref name=":0" />

[[File:Maria Gaetana Agnesi.jpg|thumb|upright=.7|[[Maria Gaetana Agnesi]]]]
The work of both Newton and Leibniz is reflected in the notation used today. Newton introduced the notation <math>\dot{f}</math> for the [[derivative (mathematics)|derivative]] of a function ''f''.<ref>The use of prime to denote the [[derivative]], <math> f'\left(x\right),</math> is due to Lagrange.</ref> Leibniz introduced the symbol <math>\int</math> for the [[integral]] and wrote the [[derivative]] of a function ''y'' of the variable ''x'' as <math>\frac{dy}{dx}</math>, both of which are still in use.

Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on both infinitesimal and [[integral calculus]] was written in 1748 by [[Maria Gaetana Agnesi]].<ref>{{cite book |title=A Biography of Maria Gaetana Agnesi, an Eighteenth-century Woman Mathematician |edition=illustrated |first1=Antonella |last1=Cupillari |publisher=Edwin Mellen Press |year=2007 |isbn=978-0-7734-5226-8 |page=iii |title-link=A Biography of Maria Gaetana Agnesi|contributor-last=Allaire|contributor-first=Patricia R.|contribution=Foreword}}</ref><ref>{{cite web| url=http://www.agnesscott.edu/lriddle/women/agnesi.htm| title=Maria Gaetana Agnesi| first=Elif| last=Unlu|date=April 1995| publisher =[[Agnes Scott College]]}}</ref>