How Did Isaac Newton Contribute To The Evolution Of Calculus

Abstract—During a one hundred year period, seven great mathematicians made contributions to our mathematical knowledge and notation that enabled the emergence of calculus. All were men of either the Catholic or opposing Protestant faith. Religious politics served as both an impetus and a hindrance to the men’s mathematical advances. The men were Francois Viéte, Simon Stevin, John Napier, Adriaan van Roomen, Galileo Galilei, René Descartes, and Pierre de Fermat.

Index Terms—analytical geometry, decimal notation, differential calculus, logarithms, number theory

I. INTRODUCTION

During the Renaissance Period, prior to Isaac Newton’s discovery of calculus, mathematicians from across Europe began laying the foundation for modern mathematics and

He developed a system of converting fractions to decimal notation, yet without a decimal point [1]. This decimal representation would make “mathematics a serviceable tool” [1]. In keeping with making mathematics serviceable, he advocated “application of the decimal system to all weights and measures and to coinage” [5]. Like other mathematicians of the Renaissance, he challenged Aristotle’s beliefs and predictions. Before Newton and Galileo, he proved that heavier objects do not fall faster than lighter objects as Aristotle predicted [5].

IV. JOHN NAPIER (1550-1617)

John Napier, born in Marchison Castle, Edinburg, Scotland, worked to make calculation simpler, especially for astronomers, by inventing the logarithm [10]. During his time, religious tension between Protestants, of which Napier was one, and Catholics brought peril and bloodshed in the politics of Spain, England, Scotland, and France. Napier invented war machines and wrote in defense of Protestant theology. He considered his personal interest in the development of mathematics secondary to his greatest work on Christian Apologetics, Plaine Discovery of the Whole Revelations of Saint John [13].

In 1594, Napier’s initial logarithms were in effect base 1/e [1]. Working with Brigg, a professor at Oxford, Napier developed logs

2 Pierre de Fermat [11]

Pierre de Fermat, see fig. 2, a Catholic Frenchman, mathematician, and contemporary of Descartes, liked to pose difficult problems. His last theorem, where x, y, z, and n are positive integers has no solution if n is greater than 2, was finally proven by Andrew Wile in 1995 [1].

Number theory fascinated him [11]. Other mathematicians did not share in his interest in number theory. Descartes thought he was an amateur and disagreed with him on the principles of refraction of life, rectification of algebraic curves, and methods for investigating tangents to curves [2]. Apparently, the only other mathematician that he could influence and enjoy an amicable relationship with was Bernard Frenicle de Bessy. Through their correspondence, Fermat began to develop number theory.

Because of his work with tangents to curves and their minimum and maximum points, mathematicians consider him to be the inventor of the differential calculus [2].

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