Abstract—The following is a study of two men who invented calculus, a concept which applies to numerous aspects of modern society. Mathematicians Isaac Newton and Gottfried Wilhelm von Leibniz are credited for the invention of calculus, but it is unsure who should take credit for its invention. Nonetheless, calculus would eventually expand numerous fields in mathematics and science. We will discuss mathematical concepts that Newton and Leibniz studied which relate to the calculus we know today and continue to expand.

Index Terms—Isaac Newton, Leibniz, infinitesimals, color spectrum, fundamental theorem.

I. INTRODUCTION

In the middle of the seventeenth century, mathematics was growing rapidly and numerous mathematics helped to build foundations
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ISAAC NEWTON

A. Background

Isaac Newton was born in the small town of Woolsthorpe, England in 1643. His father died three months before he was born and his mother sent him to live with his grandmother soon after his birth. When Newton was a teenager, he was returned to his mother and was bitter towards her for leaving him when he was a child. This experience caused Newton to develop psychotic tendencies and also led to him becoming a hypochondriac.

Newton attended secondary school at Grantham where he became fascinated with pharmaceutical remedies. He was said to be an inattentive student and learned most of what he knew by self-learning. Newton attended college at Cambridge and was a lower class student who had a job on campus in which he served the more privileged students as their servant. Newton graduated from Cambridge and soon started a professorship at the young age of twenty-six when he had already started making contributions to mathematics.

B. Beginning Contributions to Mathematics

“Isaac Newton laid the foundation for differential and integral calculus” [1]. Much of his work in calculus was science related, specifically in his theory of gravitation and motion. Newton, see Fig. 1, began his first experiments in 1664, when he studied optics and the light
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What he showed was that a prism separates white light into its component colors, associated Newton’s failure to publish his works in an untimely manner was due to the fact that he was “quite sensitive to any form of criticism and more so to any predations of his character” [1]. The competition with Leibniz, as discussed earlier, was rewarding to all of society in the fact that it forced Newton to publish his finding in order to claim that he possibly invented calculus before