Isaac Newton
1642 - 1727
Nature and nature’s laws lay hid in night,
God said “Let Newton be”, and all was light.
Alexander Pope
Timeline
1642: Born 25 December, Lincolnshire (the year Galileo
died?)
1661: Started at Trinity College, Cambridge
1665: Graduated and returned home after plague closes
the university
1667: Elected a fellow of Trinity College
1669: Became Lucasian Professor of Mathematics at
Cambridge
1672: Became a Fellow of the Royal Society
1696: Became Warden of the Mint - Master 2 years later
1703: Elected President of the Royal Society
1705: Knighted by Queen Anne
1727: Died and was buried in Westminster Abbey
Early life
• Born on Christmas day 1642 – barely survived – at
Woolsthorpe Manor in Lincolnshire
• Father died 3 months before he was born
• Mother married wealthy rector 3 years later
• Newton left to be brought up by his grandmother
• Little known about next 8 years – do know he didn’t
like his stepfather
• Grantham Grammar in his teens – very good education
• Expressed desire, as a teenager, to burn the house
down, with his mother and stepfather in it
• Not regarded as an outstanding scholar at first
Early life
• Mother was very rich, but Newton was a very poor
Scholar – had to wait on other students and Fellows at
Trinity
Plague years – Anni Mirabiles
• In the beginning of the year 1665 I found the
Method of approximating series & the Rule
for reducing any dignity of Binomial into
such a series. The same year in May I found
the method of Tangents of Gregory &
Slusius, & in November had the direct
method of fluxions & the next year in January
had the Theory of Colours & in May following I
had entrance into ye inverse method of
fluxions…
Plague years – Anni Mirabiles
• …And the same year I began to think of
gravity extending to ye orb of the Moon &
(having found out how to estimate the force
with wch [a] globe revolving within a
sphere presses the surface of the sphere)
from Kepler's rule of the periodical times of
the Planets being in sesquialterate
proportion of their distances from the center
of their Orbs must [be] reciprocally as the
squares of their distances from the centers
about wch they revolve…
Plague years – Anni Mirabiles
• & thereby compared the force requisite to
keep the Moon in her Orb with the force of
gravity at the surface of the earth, & found
them answer pretty nearly. All this was in the
two plague years of 1665-1666. For in those
days I was in the prime age for invention &
minded Mathematicks & Philosophy more
than at any time since.
Plague years – Anni Mirabiles
• This period is when the falling apple story took
place
• The prism experiment - spectrum
• Experiments on himself:
‘I push a bodkin betwixt my eye and the bone as
near to the backside of my eye as I can and
pressing my eye with the end of it there appear
several white, dark and coloured circles, which
circles are plainest when I continue to rub my
eye with the point of the bodkin.’
How did he do it?
In his own words:
‘If I am anything, which I highly doubt, I have
made myself so by hard work.’
‘If I have ever made any valuable discoveries, it
has been due more to patient attention, than to any
other talent’
How he came upon his theory of gravity: ‘By
thinking on it continually’
Lucasian Professor of
Mathematics
• Took up the post at the age of 27 in 1669
• Recommended by his predecessor, Isaac
Barrow
• His contemporaries recognised his genius
• Not successful as a lecturer:
‘…so few went to hear him, & fewer yet understood
him, that oftimes he did in a manner, for want of
Hearers, read to ye Walls.’
Key Works
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1664: Writes ‘Certain Philosophical questions’
1669: Writes ‘On Analysis by infinite Series’
1684: Writes ‘On Motion’
1687: ‘Principia Mathematica’ published
1704: ‘Opticks’ published
1707: ‘Arithmetica Universalis’ published
Principia Mathematica
• ‘Perhaps the single most important book in the history of
science’
• He only wrote it because his friend, Edmund Halley,
urged him to do so (1684)
• In the late 1670s he seems to have been obsessed with
studying alchemy and scripture
• Halley pressured him to publish, even paid the
expenses
• Finally published 1687
Principia Mathematica
• Principia Mathematica contains, among other things
Newton’s three laws of motion and his universal law of
gravitation
• He almost certainly used calculus to develop many of
the ideas in Principia, but he expressed the ideas in
Principia in classical geometric terms, rather than
using calculus
• Everything in the world that is mechanical follows
Newton’s laws
• All the physics needed for the space programme is
contained in Principia
“If I have seen further it is by standing on
the shoulders of giants.”
Whose shoulders did he stand on?
Rene Descartes (1596 – 1650)
Galileo Galilei (1564 – 1642)
Robert Hooke? (1635 – 1703)
Gotfried Leibnitz? (1646 – 1716)
Newton and the Binomial
Theorem
• Newton generalised the Binomial Theorem to include
negative and non-integer powers
• He did this intuitively – he pioneered the idea of
‘generalising’
• He did not offer a rigorous proof
• He did verify that it worked
• Verifying binomial expansions of simple expressions
with non-integer or negative powers could be a useful
exercise for A level Maths students
Newton and the Binomial
Theorem – an A level activity
Newton and GCSE Mathematics
Kinematics formulae
• Where 𝑎 is constant acceleration, u is initial
velocity, v is final velocity, s is displacement
from the position when t = 0 and t is time taken:
1)
𝑣= 𝑢+ 𝑎𝑡
2)
𝑠= 𝑢𝑡+ 12𝑎𝑡2
3)
𝑣2= 𝑢2+ 2𝑎𝑠
Obtain 1) and 2) from a velocity vs time graph
Obtain 3) be eliminating t from 2) using 1).
Newton and GCSE Mathematics
velocity
v
u
t
time
Newton and GCSE Mathematics
• New GCSE content - Ratio, proportion and
rates of change
‘interpret the gradient at a point on a curve
as the instantaneous rate of change; apply
the concepts of average and instantaneous
rate of change (gradients of chords and
tangents) in numerical, algebraic and
graphical contexts’
• This idea is what Newton used to develop
differential calculus – what he called fluxions
Newton and A level Mechanics
• Conjecture: If Newton had not been British, we
wouldn’t teach mechanics as a branch of
mathematics
Newton’s laws of motion
Newton’s gravity equation
Newton’s gravity equation
Newton’s gravity equation
An exercise for FM students:
• Given that the Moon’s average distance from
Earth is 384 000 km and the Moon weighs
7.36 X 1022 kg, how long does the Moon take
to orbit the Earth?
• Did you need to know the mass of the Moon?
• What assumptions did you make?
Universal laws
• Newton – building from Galileo – invented
the scientific method
• He used it to develop the three laws of motion
and the law of gravitation
• His great insight was that nature is not
capricious – if you understand its laws, you
can predict how things will behave – simple
laws can explain complicated things –
Newton’s universal law of gravitation fits
planetary orbits because gravity follows an
inverse square law, here on earth and
everywhere in the universe
Feuds: Robert Hooke
• Hooke criticised Newton’s early work on optics, claiming
that some of Newton’s ideas were ideas Hooke had
already had and that others were just plain wrong
• Newton reacted by publishing nothing more on opics until
after Hooke’s death
• Hooke claimed that Newton could not have come up with
his law of gravitation without using some of Hooke’s ideas
• Newton disagreed strongly; he became president of the
Royal Society in 1703, the year of Hooke’s death, and it is
rumoured he worked to erase Hooke’s (considerable)
contributions to science from history
Feuds: Gottfried Leibnitz
Feuds: Gottfried Leibnitz
• Leibnitz claimed he had invented calculus
• Leibnitz published first, in 1684 – Newton didn’t first
publish until 1704 (in an annex to ‘Opticks’)_
• Newton’s work had not been published, but he had
developed calculus (fluxions and fluents) back in the mid
1660s
• Newton’s contemporaries knew of his work and he had
corresponded with Leibnitz, but had not mentioned his
calculus explicitly
• Leibnitz could certainly have seen Newton’s ideas, or
discussed them with others
Feuds: Gottfried Leibnitz
• Leibnitz died 11 years before Newton and Newton’s fame
and influence grew further after Leibnitz’s death
• Newton is, probably correctly, generally credited with
inventing calculus
• It is likely that Leibnitz developed calculus
independently, but at least 10 years later
• Leibnitz’s notation was definitely superior and it is his
notation we use today
Newton and A level calculus
Newton and A level calculus
• Newton is credited with developing the mathematical
theory that underpins the fundamental theorem of
calculus
Newton and A level calculus
• The Newton-Raphson method for approximating roots of
equations is on the A level syllabus – Newton probably
did it first, but Raphson did it independently and
published first (1690), and his method was expressed
more simply and is the one used in A level Maths
• Newton’s estimation of Pi – a beautiful bit of maths,
accessible to A level Maths students and very relevant to
the A level Maths Core content
I do not know what I appear to the world, but
to myself I seem to have been only like a boy
playing on the sea-shore, and diverting myself
in now and then finding smoother pebble or a
prettier shell than ordinary, whilst the great
ocean of truth lay all undiscovered before me.”
Laplace on Newton
‘Newton was the greatest genius
that ever existed and the most
fortunate, for we cannot find more
than once a system for the world
to establish’
Einstein on Newton
‘Nature to him was an open book.
He stands before us strong,
certain and alone’
Newton’s tomb, Westminster Abbey
Newton’s Epitaph
Here is buried Isaac Newton, Knight, who by a strength of mind
almost divine, and mathematical principles peculiarly his own,
explored the course and figures of the planets, the paths of
comets, the tides of the sea, the dissimilarities in rays of light,
and, what no other scholar has previously imagined, the
properties of the colours thus produced. Diligent, sagacious and
faithful, in his expositions of nature, antiquity and the holy
Scriptures, he vindicated by his philosophy the majesty of God
mighty and good, and expressed the simplicity of the Gospel in
his manners. Mortals rejoice that there has existed such and
so great an ornament of the human race!