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Hrvoje Dorotić
THE CREATIVE LIFE AND WORK OF ISAAC NEWTON
929:531.5
Essay
Summary
Sir Isaac Newton was mathematician, astronomer and a physicist, sometimes also called a
natural philosopher. His major discoveries are related to numerous fields of studies and
widely are used today. Newton is often recognised as the most influential scientist of all time.
His greatest discoveries are summarised in two of his books: The Optics and
Philosophiæ Naturalis Principia Mathematica. This paper shows a short review of his
life and education. The emphasis is put to his scientific achievements: the invention of
calculus, numerical methods that are still used today, prediction of wave-particle duality long
before it was confirmed and development of axioms of motions followed by the development
of universal gravitation law. This essay is written with a purpose to present his extraordinary
and creative mind. During his scientific career, Isaac Newton was always thinking outside of
the box, creating theories which were sometimes considered scientific heresy.
Key words:
Isaac Newton, Calculus, Optics, Universal law of gravitation
1. Life and education
1.1
Childhood
Sir Isaac Newton (shown on Figure 1) was born on December 25 1642 (Christmas) by
Julian calendar, i.e. January 4 1643 according to Gregorian calendar, in Woolsthorpe Manor.
He was born too early and his mother, Hannah Ayscough told that he could fit in the small
cup. Isaac Newton was named after his father who died 3 months before his birth [1].
His first serious education started at The King’s School in Grantham at age 12 where he
stayed for 5 years. He left The King’s School in the age of 17 and moved with her mother in
Woolsthorpe-by-Colsterworth where she wanted to make a farmer of him. Newton didn’t like
that idea and, luckily, principal of King’s School asked his mother to let him go back to
school. He finished it with great final report [2].
Hrvoje Dorotić
The Life and Work of Isaac Newton
Figure 1 Portrait of Newton in 1689 by Godfrey Kneller
1.2
Years at the Trinity College
Trinity College in Cambridge was his next destination, where he started his partly
student/worker role in June 1661. There, he was getting familiar with the classical teachings
of Aristotle. Newton was fond of mathematics and astronomy: he had no problems in
understanding a work of Descartes, Copernicus, Galileo and Kepler. He acquired most of his
knowledge during his private time. He wasn’t ordinary adolescent. While other students were
having their spare time, he was reading Euclid’s Elements. His professor of mathematics,
Isaac Barrow, noticed his interest in mathematics and encouraged his education. Newton
finished his bachelor in time, with no honours. In that time nobody else was aware of his
talent [1].
It was 1665 when the plague arrived in England and Newton had to leave Cambridge
and go back to Woolsthorpe. The leave lasted for 18 months and during that period, he
managed to make the greatest scientific breakthrough of his lifetime. He laid the foundations
for his mathematical “method of fluxions” (today known as calculus), his theory of light, and
made big progress in planetary motion which he will later on improve and develop the
universal gravitational law. All this achievements will be published in his greatest two books:
The Optics and Philosophiæ Naturalis Principia Mathematica [4]. The first one will present a
model for experimental physics of 18th century and the latter one today presents one of the
greatest scientific works ever published in the history of the mankind [1].
Newton returned to Cambridge in 1667 and enrolled in master studies which he finished
in 1669. This was also the year when he succeeded his mathematics’ professor Isaac Barrow.
Newton didn’t even reached his 27th birthday by that time [5]. This gave him the possibility to
deepen his understanding about light and colour through additional experiments. His first
published paper was a study on the nature of light and colour, which he published just after
his election to Royal Society. This was also a time of his first public debate in which he
confronted brilliant scientist Robert Hooke.
1.3
Getaway to alchemy and development of the gravitational theory
His mother’s death in 1678 left a large impact on him. Some believe he went through
his first emotional breakdown, he cut off the connections with his close friends and started
working on alchemical research, which was in that time considered scientific heresy. It didn’t
suit the laws of classical mechanical properties of that era. The whole scientific community
relied on the physical bond between two material bodies, the only force between them should
be only if they are somehow connected [3]. Newton had other idea. He believed there is some
invisible connection between any two bodies which have the property of mass. In the
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Hrvoje Dorotić
The Life and Work of Isaac Newton
combination with this “alchemist’s idea” and his powerful mathematical tool that he
developed in the earlier stages, he proposed a new fundamental force, called universal
gravitational force. He named it after Latin word for weight, gravitas.
Development of gravitational theory led to publishing another paper about planetary
motion called De Motu (About Motion) and from that he created Principia. It was received
great in the scientific community. After the publishing, his social life flourished [5]. He has
been chosen to represent Cambridge in the Parliament. In London, he became good friends
with John Locke and Nicola Fatio de Duillier. These were also the years of many public
affairs related to the publishing of Principia. He suffered from another nervous disorder and
the reason is still unknown. Many say it was connected to stress caused by many intrigues,
some say it is from overworking or loss of friendship with Duillier. Some speculations claim
that the reason is mercury poisoning from alchemical experiments. The latter could be true,
during the autopsy, an increased amount of mercury has been found in his hair.
1.4
Moving to London
After the recovery, Newton moved to London, where he was appointed a Warden and
afterwards, a Master of the Mint [1]. This new position assured him a social and economic
status. Now, he didn’t have to worry about financing till the rest of his life. But this wasn’t
enough for him. After the death of Robert Hooke he was elected the president of the Royal
Society and he has been re-elected until his death. He published his second major book in
1704 called Opticks which was based on his studies on light and colour. This was his most
wide read work. One year later, 1705, he was knighted. Sir Isaac Newton was the second
scientist in the history to receive this honour, after Sir Francis Bacon.
Although last 20 years represent the twilight of his scientific achievements this doesn’t
mean that he didn’t have any influence. They said that his presidential mandates have been
autocratic and tyrannical. Newton used his position to establish the advantage in his affairs
during the Newton-Leibniz calculus controversy. This wasn’t the case during his debate with
Robert Hooke where he had to act personally. Newton didn’t have a scientific rival until the
end of his life. He dominated the scientific world until his last day, March 20, 1727, i.e.
March 31 by Gregorian calendar [5]. He died in London, peacefully in his bed. He was buried
in Westminster Abbey. His tomb is shown on Figure 2.
Figure 2 Newton grave in Westminster Abbey in London
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Hrvoje Dorotić
The Life and Work of Isaac Newton
2. Scientific accomplishments
2.1
Mathematics
Isaac Newton began exploring the world of mathematics in the early stage of his
education, while he was still undergraduate at Cambridge. He got familiar with Descartes’s
Géométrie and John Wallis' Arithmetica infinitorum etc.
He is mostly known for his “direct and inverse method of fluxions” where he found
general solution of the problem of the rate of change and how to find a value of an area below
the curve. For example, by knowing the velocity over time, we can calculate the acceleration
in the certain time moment (slope of the time-velocity diagram, graphical explanation on
Figure 3 – left) and an overall distance passed in some period of time (surface under the timevelocity diagram, graphical explanation on Figure 3 – right). In the modern era, the terms
derivative and integral are used to describe “direct and inverse method of fluxions”, where
“fluxions” could be any property, such as velocity, mass flow, etc.
Figure 3 Graphical representation of the “direct and inverse method of fluxions”
This was actually one of his most important discoveries. Using this method he was able
to derive his axioms of motions and develop law of universal gravitation. This method is also
known as infinitesimal calculus (lat. calculus means small pebble, used for counting) [1]
where small, infinitesimal particle of matter can be observed and then all of its properties
could be integrated over the surface, volume or time. This are the basics of the physics we
know today, i.e. Isaac Newton with his method wrote the first words of the language we use
to describe all natural observations, from fluid mechanics in the glass of water to motion of
the planets and galaxies.
Today, calculus is linked to one of the most famous scientific disputes. It was between
two great scientists of that time, Isaac Newton and Gottfied Wilhelm Leibniz. The dispute
also goes by the name Leibniz-Newton calculus controversy (Ger. Prioritätsstreit, priority
dispute). It started in 1699 and culminated in 1711. The problem was that both of them during
their scientific career published their work on calculus [3]. The Leibniz main argument was
that he officially published his work before Newton, in 1684. Newton didn’t publish his work
on calculus until the issuing of Principia, in 1687, which is based on that method. Newton
was starting developing his “method of fluxions” while staying in Woolsthorpe during the
plague from 1665 until 1667, but the main problem was that he didn’t publish anything in that
period. So Newton’s main argument was that Leibniz copied his work and rushed with its
publication. During the dispute, Newton was president of the Royal Society which was the
important advantage during this affair. Today is now generally considered that Leibniz and
Newton both developed calculus method independently but the Newton was the first who
started developing it and Leibniz is the first the one who published the results [1].
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Hrvoje Dorotić
The Life and Work of Isaac Newton
Newton also made a big contribution in the analytic geometry and algebra. He classified
cubic plane curves (polynomials of degree three in two variables) and developed generalised
binomial theorem which describes algebraic expansion of powers of a binomial. It can be
illustrated using the Pascal’s triangle (Figure 4).
Figure 4 Pascal's triangle
Using Newton’s theorem it is possible to calculate any power of sum of two numbers,
according to the equation:
n
n
n
n
( x  y ) n     x n k y k    x k y n k
k 0  k 
k 0  k 
(
(1)
He also made a contribution to numerical mathematics used today. He developed
method which can find an unknown solution of a complex equation by using “method of
fluxes”, i.e. by knowing the equation of the tangent line. The process of the method is shown
on the Figure 5-left. The process starts with finding the intersection between an x-axes and a
tangent line of a selected x-point on the curve. Next step is the same as the first one, but this
time selected x-point is the intersection between tangent line and x-axes from the previous
step. This process is continued until the intersection of the tangent line becomes the solution
of the equation. This numerical method is primitive because it doesn’t converge when the
function is highly concave, the example is shown on the Figure 5-right.
Figure 5 Newton method for finding an isolated root of the equation
Besides Newton’s method, he developed a finite difference method which is today
widely used in numerical mechanics. It solves differential equations by replacing them with
differential equations, i.e. finite differences are approximating the derivatives (Figure 6).
Because of it, this method belongs to discretization methods.
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Hrvoje Dorotić
The Life and Work of Isaac Newton
Figure 6 Representation of the finite difference method
2.2
Optics
Isaac Newton started with optic research in Woolsthorpe, while he was absent from
Cambridge, during the plague. His biggest discovery was that white light is actually
composed of spectre of colours. The most important experiment (lat. experimentum crucis,
crucial experiment) which proved his hypothesis was set up as following. The ray of white
light was entering through a small hole in the dark room and passed through a prism, thus
scattering on the spectre of colours in the board. On it was another small hole, so that only
one colour was able pass through it into another prism. From that other prism came out only
one colour and no dispersion happened this time [1]. The experimentum crucis is shown on
Figure 7. Using this result, he concluded that white light is just secondary form of light and it
consists of a spectre of primary colours (from red to violet). This was the discovery that
shocked and intrigued everybody, not just scientific society. His achievements will later on
help Joseph von Fraunhofer to closely look at the spectrum. He will notice that some lines of
the spectrum are missing, later on they will be called “Fraunhofer lines” and thus inventing
the first spectroscope.
Figure 7 Isaac Newton performing his crucial prism experiment - the “experimentum crucis” - in his
Woolsthorpe Manor bedroom
This discovery has broaden his knowledge of light and colour. During that time it was
held that light is travelling in the form of a wave, just like a sound, this was also the opinion
of his greatest critics: Robert Hooke and Christiaan Huygens. Newton was brave enough to
oppose them. His opinion was that light is actually travelling in the form of small particles, so
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Hrvoje Dorotić
The Life and Work of Isaac Newton
he developed the Corpuscular theory of light (lat. corpuscula, particle). He held that light
isn’t homogenous like a wave, it is heterogonous. Newton was imagining the light as a
particle which travels in the straight line almost 200 hundred years before scientist Max
Planck proved that light actually is a particle, which is today called photon.
His ingenuity didn’t stop there. During his correspondence with Hooke he considered
the idea of ethereal substance – the elastic material which is subtle than air which surround us
and provides the propagation of waves and vibrations. That discussion, together with the next
experiment, will make him reconsider the wave theory. The experiment went like this. He was
observing what happens when a light flows through the convex lens which is pressed against
a flat glass plate. He noticed the appearing of black and white stripes. This stripes will later be
named “Newton rings” [6]. This is the first time that he noticed that light behaves
periodically, like a wave. Thomas Young will explain what really happened in this experiment
about 100 years later. He made a similar experiment where a beam of light passed through a
small double-slit. He also noticed black and white stripes appearing on the wall behind the
slit. His explanation was that light is showing the same characteristics as a wave – a
destructive and constructive interference. Figure 8 shows the similarities between Newton
experiments where he achieved black-white rings and Young’s experiment where he got black
and white stripes on the wall. Thomas Young was actually afraid publishing his discovery
because Isaac Newton was representative of a particular theory. These two experiments are
basically the same, they show that light can have wave properties, i.e. constructive and
destructive interference.
Figure 8 Similarities between Newton’s (left) and Young’s (right) experiment
This discovery showed him the periodicity of light, but he always believed in particular
theory. Isaac was the first one who thought of light duality. He didn’t abandon the corpuscular
theory, he just wanted to modify it. It will later on be shown that Newton was right again. The
greatest quantum physicists of 20th century have agreed that light is actually both wave and a
particle, and the theory was called wave-particle duality of a light.
From all this findings he wrote a book, called The Opticks. This was his most wide-read book.
It had 3 editions. The most interesting and also the most provocative part of the book is the
last chapter called “Queries” where he wrote about the nature of a light, colour and matter and
the forces of nature.
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Hrvoje Dorotić
2.3
The Life and Work of Isaac Newton
Mechanics
All scientific findings on mechanics lead to development of universal gravitational
force. The process was lasting and can be devised into three 3 periods [1], it didn’t happen in
one moment after seeing an apple falling from a tree.
The first stage was during his stay in Woolsthorpe while the plague was present in
England. The myth about the apple probably reaches from this period. Maybe he actually get
the idea from it, but in that moment he didn’t have the knowledge about the gravitational
attraction. During that time he was studying the motion of the Moon. He noticed that some
unknown mechanical constraint is holding it in the orbit of the Earth. This was contradictory
to general mechanical belief, because it involved some kind of invisible attraction, action-atthe-distance. During this he assumed the circular orbit. He tried to test his ideas on the Moon,
but the results didn’t match and he abandoned the problem.
Next period of gravitational force development was during 1679 and 1680 when he
exchanged letters with Robert Hooke. Hooke proposed that the planetary motion is due to
some tangential and the attractive motion towards the central body. He also claimed that the
“pull” is falling with the square of the distance between those two bodies. Hooke was really
close to the answer of the problem, but he missed the mathematical tool to prove it. Newton
took the concept from Hooke and improved it by using his mathematical method that he
developed earlier – calculus.
The crucial moment for publishing of the gravitational theory in Principia was Edmond
Halley’s visit to Cambridge. Halley was interested in the problem of planetary motion which
he already discussed with Robert Hooke, but they couldn’t provide a solid answer. Halley
then seek help from Newton. He was interested in the shape of planetary orbit and the relation
between distance and the attraction between two bodies. Isaac Newton already had an answer
ready from him. He showed him the model which he already developed: the orbit has the
shape of an ellipse and the attraction falls with the square of the distance between two bodies.
Newton’s law of the universal gravitation can be written as: the attraction force between
any two bodies is proportional to product of their masses and the reciprocal value of a squared
distance between them. The direction of the force is parallel to the direction of connector
which joins the centres of masses of those bodies. The law can be expressed with the equation
as follows:
(
M m
Fg  G 2
(2)
r
Where Fg represents gravitational force, M and m are masses of the two observed bodies, r is
the distance between them and G is gravitational constant.
Halley was amazed by Newton’s work and he encouraged him to publish his model.
Halley personally invested in the printing of the Principia. It was ready for the press in July
1687.
2.4
Philosophiae Naturalis Principia Mathematica
Principa (shown on Figure 10) is divided in three books. In the first book he set the
definitions and axioms he will used in the next chapters. Here are defined 3 fundamental laws
of motion, which are today called Newton’s laws of motion:
1) In an inertial reference frame, an object either remains at rest or continues to move
at a constant velocity, unless acted upon by a force
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The Life and Work of Isaac Newton
2) In an inertial reference frame, the vector sum of the forces F on an object is equal to
the mass m of that object multiplied by the acceleration a of the object, it could be
written as:
(
d p d ( mv )
d (v )

m
 ma
(3)
dt
dt
dt
Equation above is one of the most known axioms in the scientific history, to honour Isaac
Newton the SI unit for force is called after him, Newton (N)
3) Third law says when one body exerts a force on a second body, the second body
simultaneously exerts a force equal in magnitude and opposite in direction on the
first body.
The second book continues explaining the axioms and definitions given in the first book
by using them to explain the motion of bodies through resisting mediums including the
motion of fluids. Here, he defined the law of viscosity which can be represented with
following equation [7]:
F
 v j vi  
(

    2   v k 



ji
 x x   V 3  x ji
(4)
j 
k
 i
Where Σji is symmetrical tensor of viscous stress, v is velocity, µ is dynamic viscosity.
µV is volumetric viscosity and δji is unit tensor. Equation above says that the force on the fluid
particle is proportional to the gradient of velocity. It is important to say that this connection is
usually linear. Today, the fluids who have linear connection between the stress tensor and
gradient of velocity are called Newtonian fluids, and those which don’t, are called nonNewtonian fluids, shown on Figure 9.

Figure 9 Newtonian and non-Newtonian fluids comparison
Most of this book is dedicated to fluid mechanics and it looks like it doesn’t belong to
the Principia. The reason for that is probably he wanted to merge all the achievements from
the mechanics field in one book. In the last chapters of the second book Newton explains that
the planetary motion model proposed by Descartes, which is based on vortices, isn’t possible.
The proposed vortices won’t be self-sustained.
In the third book of Principia, subtitled the De mundi systemate (On the system of the
world), Newton describes the laws of the motion, introduced in the first book, on the
planetary motion. He develops and demonstrates the law of universal gravitation. In the end,
he is using the law to explain the motion of the planets, asteroids and to predict time of tides
and equinoxes.
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Hrvoje Dorotić
The Life and Work of Isaac Newton
Figure 10 Philosophiae Naturalis Principia Mathematica cover
3. Conclusion
Isaac Newton made crucial discoveries in the field of mathematics, optics and mechanics. He
is recognized today as one of the most brilliant minds in the history of the mankind. Secret of
his scientific achievements is creativity and hard work. He was creative, he always thought
outside of the box, he dared to think differently. Isaac Newton used the knowledge from
others fields of science and combining them together. Doing so, he accomplished great
results. One example is development of gravitational law by using calculus and the idea of
action-at-distance that he got from different field of study, alchemy, which was then
considered heresy. Other example is corpuscular theory of light and even afterwards,
indications of dual theory of light. Nobody was considering that, even as an option. His mind
let him wonder and think of, for that period, unimaginable secrets of nature. By any standards,
he was ahead of his time.
His ideas didn’t occur just by looking at the apple falling from the tree as a myth says. Maybe
he started thinking about it then, preparing his mind for the idea of gravity. But creativity
doesn’t come by itself. He was immersed in his problems, he studied them for many years
until he got “the creative idea”. Hard work and persistence to solve a problem is a key to a
solution. These two can create a solid base for new ideas. Even he once said that: “If I have
seen further, it is by standing on the shoulders of giants”.
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Hrvoje Dorotić
The Life and Work of Isaac Newton
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
http://users.clas.ufl.edu/ufhatch/pages/01-courses/current-courses/08sr-newton.htm [6.2.2017.]
https://www.newton.ac.uk/about/isaac-newton/life [6.2.2017.]
http://scienceworld.wolfram.com/biography/Newton.html [6.2.2017.]
http://www-old.newton.ac.uk/newton.html [6.2.2017.]
http://www.maths.tcd.ie/pub/HistMath/People/Newton/Fontenelle/Fonten.html [6.2.2017]
http://www.animations.physics.unsw.edu.au/jw/light/Newton's-rings.html [6.2.2017.]
https://www.fsb.unizg.hr/hydro/pdf/Nastavni_materijali/MFII_Predavanja.pdf [6.2.2017.]
Defined:
9.1.2017
Delivered
7.2.2017.
Supervised by Kalman Žiha
Hrvoje Dorotić
Faculty of Mechanical Engineering and Naval
Architecture, University of Zagreb,
Ivana Lučića 5, 10002, Zagreb
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