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.
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
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
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
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?
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.