November 18, 2024

Vincent Hoang

12th Grade

Fountain Valley High School 

Introduction

Young Isaac Newton, sitting just outside Trinity College in Cambridge, England, was struck by an apple that had fallen from the tree. From that point, Newton had a revelation, a genius discovery: Calculus. Calculus was created by Sir Isaac Newton as a method of explaining the universe, a means of comprehending the mechanical clock that is our world. He was a brilliant mind widely recognized as the “father of calculus”; known for his observations of the world and his contributions to mathematics and physics. 

To Infinity and Beyond

During Newton’s time, physics and mathematics were dominated by algebra and geometry which were only able to understand static shapes and numbers but weren’t able to handle changes much like the real world. Newton understood that to accurately portray the world in numbers, a new volume of mathematics was required. Calculus is the study of an object's rate of change over time and was revolutionary in describing physics. The common language bridging the gap between chemistry, physics, biology, engineering, and communications allows us to accomplish things like city construction, transportation, etc. Calculus can be found anywhere, which is what makes Newton’s contributions so impactful. Every aspect of our lives will involve calculus. His achievements can be found in his first development of infinitesimal calculus and the concept of infinity. 

Newton was troubled by the infinite saying, “For since we are finite it would be absurd for us to determine anything concerning the infinite; for this would be to attempt to limit it and grasp it.” He believed that infinity was impossible to understand as we are not infinite. As author James Gleick expresses in his book Isaac Newton, Newton worked to make sense of the incomprehensible and reasonably had trouble. He created the term “indivisibles”, values so small that they are near zero. By summing these indefinitely small quantities, Newton was able to find the precise changes in the motion of an object through a process we now call integral calculus. 

Laws of Motion

With the framework of calculus set, Newton came up with the fundamental Laws of Motion. These laws make up the foundations of modern engineering and science. These laws include:

• Inertia: An object at rest stays at rest, and an object in motion stays in motion unless an unbalanced force is exerted on the object. 

• Force: The acceleration of an object is dependent on the mass of the object and the force exerted on the object.

• Equal and opposite reaction: When one object exerts a force on another object, the second object exerts an equal and opposite force back. 

When applied to the real world, these laws make engineering possible. Imagine a rocket ship being launched how each of these laws is applicable?

• Inertia: How much thrust should be needed to propel a rocket? How much fuel is required to produce the force needed to give the rocket motion against gravity and enough to ge out of the atmosphere?

• Force: the amount of G force exerted on the rocket as a product of its weight and it speed. If a rocket is not able to withstand the natural forces, it will explode. 

• Equal and opposite reaction: As a rocket travels through the sky, it is met with friction and vibrations. The faster the rocket flies, the more friction it will experience. Is the rocket built strong enough to push through friction? 

The Father(s) of Calculus

Although Newton is more well-known in calculus and is given the most credit for inventing calculus, Gottfried Leibniz is equally responsible for its creation. While Newton was more concerned with applying calculus in physics Leibniz was occupied with notations using symbols like dx for derivatives and the integral symbol shaped like an elongated S. Through his work Leibniz was able to allow upcoming mathematicians to expand upon his work and interpret it in different ways. 

And Beyond… 

Isaac Newton is rightfully called the father of calculus. He is a pioneer of the unknown, an explorer of the dark. He tackled the infinite bounds of the universe and thus gave us the possibility of modern engineering and science. His work represents relentless human curiosity, our yearning to know and understand more. Yet with Newton’s work, what lies in our universe remains a mystery and the idea of infinite bounds is still one we have yet to understand. Are we even meant to fully grasp our world, or are venturing beyond our capacity?