Introduction

The purpose of this report is to identify who should

claim more credit for inventing calculus. It will first discuss who both

Gottfried Leibniz and Isaac Newton were, how they both developed calculus

independently of each other and the controversy caused by who had invented the

mathematical study of change, calculus, first.

Findings

Calculus is one of the most important branches of

mathematics with applications in science, economics and engineering.

Differential calculus is concerned with the study of rates at which quantities change

whilst the integral calculus is concerned with the determination of lengths,

area and volumes.

Both Newton and Leibniz

developed the idea of calculus but neither of them invented calculus. Isaac Barrow

developed a method of determining tangents that closely approached the methods

of calculus, and the first recognised that what became known as the process of integration

and differentiation.

Gottfried Leibniz was

a German philosopher, mathematician and inventor in the field of mechanical

calculators. He developed the binary number system used in digital computers (in

text citation) and developed the idea of calculus independently of sir Isaac

Newton. The binary number system is a number system that only uses two digits:

one and zero to process data in a computer.

Gottfried was born in

1646 in Leipzig, Germany. He pursued a bachelor’s degree at the University of

Leipzig from 1661, obtaining a Master’s degree in philosophy 2 years later. He

then wanted to complete his Doctorate in Law at the same university but unfortunately

because Leibniz was too young the university refused him. Due to this, he

completed his Doctorate in 1667 at the University of Altford.

Throughout his life,

he spent several years in Paris where he made contact with some intellectual

figures of the seventeenth century including philosophers and scientists. His

first publication on calculus was released in 1684, which included his notation

on calculus as well as the rules for differentiation of powers, products and

quotients.

Leibniz’s

contribution in mathematics was in the year 1675, when he discovered the

fundamental principles of infinitesimal calculus. He also contributed in 1672

by inventing a calculating machine that was capable of multiplying, dividing

and extracting roots.

Isaac Newton was an

English mathematician, physicist, astronomer and theologian, born in 1642 in

Lincolnshire, England. He lived on an isolated farm, deprived of parental care

and love, without the friendly companionship and rivalry of brothers and

sisters. His father died three months before he was born and his mother

remarried when Newton was less than two years old. As a consequence, Newton was

turned over to his aged grandmother, making him spend most of his time alone.

Whilst Newton thought of calculus in terms of

motion, Leibniz viewed it in terms of sums and differences. Leibniz introduced

the notation of the elongated

“S”. He also used a differential triangle to discover the slope of a tangent

line to a curve. He was thus able to derive the power, product, quotient and

chain rules.

Sir Isaac

Newton developed calculus, revolutionary form of mathematics, allowed for the

calculation of the area inside a shape with curved sides and to calculate the

rate of change of physical quantities. He also used prisms to show that light

was made up of colours of the rainbow, disproved ancient Greek ideas on light

as well as laws of motion.

The dispute began in

1708, in a political climate, intertwined with tensions dividing the Royal

Court. Newton and Leibniz not only had different views on the nature of and

properties of God, on the structure of the material universe, the concepts of

space and time and the possibility of an “action at a distance”.

Clarke had set out to

discredit Leibniz’s philosophical and theological pre-tensions, as the Royal

Society had apparently succeeded in discrediting his mathematical originality

in Leibniz’s manuscript which was published in 1712.

Analysis and evaluation

Why one and not the other?

Conclusion

Both Leibniz and

Newton discovered calculus at approximately the same time, however the Royal

Society credited Leibniz with the first publication but gave Newton the credit

for the first discovery.