History of Calculus History Research Paper Research

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HISTORY OF CALCULUS
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Introduction
The underlying grand rational of perception and development appears to be swept away by an overemphasis on form and formulas in one of most controversial subdiscipline of mathematicians: calculus. For millennia, calculus has been evolving not only, as is usually simply assumed, as a strict subdiscipline of mathematicians of linear progression but, more importantly, as a philosophical standpoint developed not so much in isolation but in eager, if not, heated, engagement with similar and different standpoints. The history of calculus should, instead, be placed in a wider philosophical and cultural context in order to understand why calculus was – and will be – critical to understanding man's place in universe. Indeed, one most significant reason why calculus was – and still is – developed, i.e. understanding geometrical figures and planetary motion, appears to be clouded by arguments over “infinitesimal” differences only to submerge what calculus originated initially. The understanding of calculus – and, for that matter, history of calculus – should, accordingly, be understood less as a mere list of milestones and major achievements and discoveries of leading mathematicians and more as a more progressive method to understand links connecting calculus and different aspects of culture. 1 The history of calculus is, for current purposes, discussed by highlighting major achievements leading mathematicians – and, for that matter, a string of iconic scientists of different backgrounds – much to provide a roster of milestones and more to understand, hopefully, underlying rationales and, critically, worldviews informing such
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1 Katz, Victor, “Using the History of Calculus to Teach Calculus,” Science & Education 2
(1993): 243–249, accessed November 4, 2020, doi: https://doi.org/10.1007/BF00490066.
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incremental/evolutionary and, sometimes disruptive/revolutionary, achievements. This short essay aims, accordingly, to shed a critical light on a history of calculus in order to understand where calculus is placed in history as a subdiscipline of mathematics and, more importantly, as an expression of worldviews, often colloidal, put into symbolic representations.
The Evolution of Calculus
Often, Newton and Leibniz are credited for “inventing” calculus. 2 This is, predominantly, attributed to a controversy of who actually organized what was once scattered concepts of and applications in geometry, physics and astronomy (and, centuries later, computing), into an organized and more formalized “science” of established rules. 3 In reality, however, calculus, as in all science proper, is a an evolution of long history of mathematical developments only culminating in what has been, perhaps still popularized as Newton vs. Leibniz Controversy. 4, 5 The achievements of Archimedes, despite not a first, are a good staring point to place calculus in a modern context. If anything, Archimedes was able to develop what is now now as method of exhaustion. 6 This method amounts to, simply speaking, to areas of geometrical figures, par...