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The Art of Explanation
A short guide to some of the greatest
contributors to mathematics and science.
Compiled by Anne-Marie Trenholme
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“Mathematics is the art of explanation”
The above quote, by Paul Lockhart, got me thinking about how under appreciated
mathematicians and scientists are. Perhaps it’s because they are the quiet ones at school
and then continue to work away, out of sight of the public in labs and research
departments worldwide. Or perhaps it’s because maths is not “cool” socially and no one
wants to be seen reading about algebra or calculus. Yet most of the modern technology,
gadgets and advances we take for granted are underpinned by mathematics and science.
Our understanding of the world we live in has been shaped by the development of laws
and equations to explain things. Inventors have asked questions, calculated and used
experimentation to find solutions to problems, sometimes with world changing results.
So, here is an e-scrapbook of fifty two mathematics and science innovators, one for each
week of the academic year. You can scan the QR codes on each page to access more in-
formation and resources on each person and his/her work, life and times. You may also
wish to print the pages out as posters. Enjoy!
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Contents
Sylvester 5
Curry 6
Riemann 7
Wilkinson 8
Williams 9
Richardson 10
Wren 11
Jungius 12
Boole 13
Halley 14
Strutt 15
Hubble 16
Franklin 17
Hopper 18
Davidov 19
Ramanujan 20
Babbage 21
Newton 22
Hawking 23
Franklin 24
LaGrange 25
Euclid 26
Yasuaki 27
Rheticus 28
Boltzmann 29
De la Faille 30
Oughtred 31
Einstein 32
Fourier 33
Descartes 34
Napier 35
Wiles 36
Euler 37
Planck 38
Gauss 39
Nightingale 40
Heaviside 41
Copernicus 42
Kemeny 43
Olive 44
Maxwell 45
Poisson 46
Kirchoff 47
Rankine 48
Dee 49
Hooke 50
Youqin 51
Venn 52
Olivier 53
Fermat 54
Fibonacci 55
Coulomb 56
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Sylvester carried out key work on
matrix theory. He discovered the
discriminant of a cubic equation and
first used the name 'discriminant' for
equations of higher order.
Week 1 - September James Joseph Sylvester
1814 - 1897
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Haskell Curry was an American
mathematician and logician who
worked on combinatory logic and most
importantly ENIAC, the first electronic
general purpose computer, whose
existence and success was announced
after the second world war.
Week 2 - September Haskell Brooks Curry
1900 - 1982
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Riemann’s ideas on the geometry of
space had a profound effect on the
development of modern theoretical
physics, leading to the later develop-
ment of the theory of general relativity.
He clarified the notion of integrals by
defining what we now call the Riemann
integral.
Week 3 - September Bernhard Riemann
1826 - 1866
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James Hardy Wilkinson studied the
thermodynamics of ballistics and ex-
plosions, he worked on numerical
methods for solving systems of linear
equations and eigenvalue problems.
He also worked with early computing.
Week 4 - September James Hardy Wilkinson
1919 - 1986
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In 1922, a time of high levels of
discrimination and racial tension,
Williams was the first lecturer in the
USA to accept a non white student for
a PhD. He was also founder of the
Canadian Mathematical Society.
Week 5 - October William Lloyd Garrison Williams
1888 - 1976
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Richardson researched solving the dynamics of
the atmosphere to predict the weather. The result
was “Weather Prediction by Numerical Process” in
1922. His calculations were long and done by
hand, making the procedure impractical for daily
use at the time, but it forms the basis of modern
weather forecasting now that computers can do
the maths in seconds.
Week 6 - October Lewis Fry Richardson
1881 - 1953
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Sir Christopher Wren is most famous
for redesigning St Paul’s Cathedral
after the Great Fire of London. He also
worked on optics, devised an early
method of blood transfusion using
animals and formulated the inverse
square law of gravitational attraction.
Week 7 - October Sir Christopher Wren
1632 - 1723
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Jungius was among the first to use
exponents to represent powers. He decided
to train as a doctor and became an
advocate of the use of mathematical
models and logic in scientific study. He
faced opposition from the established
church at a time when a lot of things were
still explained spiritually.
Week 8 - October Joachim Jungius, aka Jung
1587 - 1657
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Known best for incorporating logic
into mathematics, resulting in Boolean
algebra, Boole did a lot of work on
probability and received 2 honorary
degrees. He was born in Lincoln.
Week 9 - October George Boole
1815 - 1864
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Halley was a friend and supporter of
Newton and shared many of his
research interests. He is famous for
calculating the orbit and predicting
the return pattern of the comet now
known as Halley’s comet.
Week 10 - November Edmund Halley
1656 - 1742
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Lord Rayleigh overcame health problems in
childhood to study physics. His initial studies
looked at optics and vibrating systems but
he later covered many areas including sound
waves, light waves, gases and elasticity - he
explained for the first time why the sky is
blue and won a Nobel prize in 1904 for the
discovery of Argon.
Week 11 - November John William Strutt (Lord Rayleigh)
1842 - 1919
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Edwin Hubble was an American
astronomer who first discovered that
the universe is expanding and what
exactly galaxies are. He is said to be
the father of modern cosmology. The
famous telescope is named after him.
Edwin Powell Hubble
1889 - 1953
Week 12 - November
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Christine Franklin waited 47 years for her
PhD due to rules which barred women
from receiving the award at the time she
produced her thesis on the algebra of
logic in 1887. She then worked on colour
vision at Gottingen University, Germany
despite not being allowed to attend
lectures within the same department!
Week 13 - November Christine Ladd-Franklin
1847 - 1930
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Thought to be the only mathematician to
have a warship named after her, Grace
Hopper was a pioneer of computing in the
USA and was on the team that supposedly
discovered the first computer “bug” – a moth
that shorted one of the 17,000 relays in the
machine. The team also developed the first
English language data processing compiler
and promoted standardisation.
Week 14 - December Grace Brewster Murray Hopper
1906 - 1992
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Davidov worked in Moscow on theories
of fluids, most notably capillary action
and the equilibrium of floating bodies.
He also studied elliptical functions
and application of probability to
statistics, as well as writing a number
of textbooks for secondary schools. He
co founded the Moscow Mathematical
Society.
Week 15 - December August Yulevich Davidov
1823 - 1885
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Ramanujan was largely self taught having
had a basic education as a child. His work
focussed greatly on series and sequences and
he independently discovered results normally
attributed to Euler, Riemann and others. His
findings led to bigger developments and
more research in the field of hypergeometric
series. 2012 was National Mathematics year
in India in his honour.
Week 16 - December Srinivasa Aiyangar Ramanujan
1887 - 1920
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Babbage invented a mechanical calculating
machine, operated by punched cards which is
remarkably similar in concept to modern
computers. Although the machine was never
built successfully in his lifetime, his vision
of calculations being performed quickly by
machinery was revolutionary and paved the
way for what we now take for granted.
Week 17 - December Charles Babbage
1791 - 1871
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Sir Isaac Newton is famous for so much but
some of his key achievements were in the
development of calculus, work on gravity
and the laws of motion that have been
applied to many branches of science since.
His date of birth was originally recorded
as Christmas day because the Gregorian
calendar we use today had not yet been
introduced.
Week 18 - January Sir Isaac Newton
1643 - 1727
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Hawking is a world renowned
physicist and cosmologist and the
author of “A brief history of time”. In
1974 he predicted the existence of a
type of radiation that now carries his
name. It was observed for the first
time in 2010.
Week 19 - January Stephen William Hawking
1942 -
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Well known for many things including
his work with electricity and his role in
the American revolution but Franklin
was fascinated by number patterns and
invented a form of magic square, now
known as the Franklin magic square.
Week 20 - January Benjamin Franklin
1706 - 1790
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LaGrange’s mathematical abilities covered a
wide variety of areas. He used experiments
with a tautochrone to develop ideas in
calculus, thinking in terms of motion of an
object. He also produced papers on kinetic
energy, vibrating strings, probability and
more. The lagrangian function is named
after him in recognition of his contribution
to science.
Week 21 - January Joseph Louis LaGrange
1736 - 1813
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Little is really known about Euclid but his
most famous work is “The Elements”. The
book was a compilation of knowledge that
became the centre of mathematical teaching
for 2000 years. It contains key definitions of
concepts such as equality and geometrical
facts that underpinned all subsequent
mathematical developments.
Week 22 - January Euclid of Alexandria
325BC – 265BC
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Aida compiled “Sampo tensi shinan” which
appeared in 1788. The book contains his work
on geometry problems and algebra. It gives
formulae for ellipses, spheres, circles etc. He
explained the uses and construction of
equations. He also worked on number theory
and studied continued fractions. He worked
as an engineer in what is now Tokyo in 1770.
Week 23 - February Aida Yasuaki
1747 - 1817
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Rheticus keenly studied “the science of
triangles” and in 1541 published the
trigonometrical sections of Copernicus's
“De Revolutionibus“, adding tables of
his own. These gave what we now call
sines and cosines It was the first time
cosines had been published and was
therefore a major step forward in the
field of trigonometry.
Week 24 - February Georg Joachim von Lauchen Rheticus
1514 - 1574
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The inventor of “Statistical mechanics”
which models a system in terms of the
average behaviour of the large numbers
of atoms and molecules making up the
system. He was among the first to
recognise the importance of Maxwell’s
electromagnetic theory and Boltzmann’s
constant is named after him.
Week 25 - February Ludwig Boltzmann
1844 - 1906
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La Faille taught mathematics and
military engineering in Madrid. He was
the first to determine the centre of gravity
of the sector of a circle. Centres of gravity
are widely used in structural engineering.
His family were very wealthy and paid
for him to be painted by Van Dyck.
Week 26 - February Jan-Karel della Faille
(or Jean-Charles de La Faille)
1597 - 1652
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William Oughtred
1574 - 1660
Oughtred introduced the symbol X to
indicate multiplication and first used
the symbol π, though it represented the
circumference of a circle rather than its
modern use. He is credited with inventing
an early form of slide rule in 1622,
which made calculations much easier
and quicker.
Week 27 - March
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Possibly the most well known scientist
in history, Einstein did not excel at
school and began to study mathematics
and physics after failing to qualify as
an engineer! He is best known for his
theory of general relativity but received
a Nobel prize in 1921 for his work on the
photoelectric effect. He also studied the
interaction of waves and matter.
Albert Einstein
1879 - 1955
Week 28 - March
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Best known for the Fourier series, a
mathematical method of analysing
the components of waveforms. It is
widely used in modern engineering.
He also worked on trigonometry and
the theory of heat. He narrowly
escaped execution during the French
revolution.
Week 29 - March Jean Baptiste Joseph Fourier
1768 - 1830
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René Descartes was a French philosopher.
His book, “La géométrie,” included a new
application of algebra to geometry
which resulted in Cartesian geometry.
Other mathematicians and philosophers
were greatly influenced by his work and
we still use Cartesian graphs etc. today.
Week 30 - March Rene Descartes
1596 - 1650
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Napier invented logarithms. They
were initially distrusted, rather like
computers were in the 1950’s/60’s.
Napier’s logarithms would later be
developed further by Kepler, and his
work was then used by Sir Isaac
Newton to derive his now famous
theory of universal gravitation.
Week 31 - April John Napier
1550 - 1617
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Andrew John Wiles
1953 -
Andrew Wiles was able to prove
Fermat’s last theorem in 1994. It was a
mathematical feat that had evaded all
who tried for over 300 years!
Week 32 - April
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Euler was a Swiss mathematician who made
enormous contributions to a wide range of
mathematics including geometry, trigonometry,
geometry, calculus and number theory. The
familiar notations f(x) for a function, e for the
base of natural logs, i for the square root of -1,
π for pi, ∑ for the sum of, Δy and Δ2y for finite
differences and many others were the results of
Euler’s work and he is considered by some to be
the greatest mathematician to have lived.
Week 33 - April Leonhard Euler
1707 - 1783
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Max Planck studied thermodynamics, in
particular looking at the distribution of
energy according to wavelength. In October
1900 Planck announced a formula now
known as Planck's radiation formula. Planck
made a complete theoretical deduction of his
formula, renouncing classical physics and
introducing the quanta of energy. Planck was
awarded the Nobel Prize for Physics in 1918
for his achievement and Planck’s constant is
named after him.
Week 34 - April Max Karl Ernst Ludwig Planck
1858 - 1947
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Gauss worked in a wide variety of fields in
both mathematics and physics. His work
included number theory, analysis, differen-
tial geometry, geodesy, magnetism
(alongside Weber), astronomy and optics.
His work has had an immense influence in
many areas. He was the inventor of the
heliotrope and the normal or Gaussian
distribution is named after him.
Week 35 - April Johann Carl Friedrich Gauss
1777 - 1855
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Florence Nightingale is usually best
remembered as a nurse, but was also a
pioneering statistician. She proved the causes
of mortality in military hospitals, leading
to massive improvements in conditions and
consequently better survival rates for
casualties (40% to 97.8% in a year).
Week 36 - May Florence Nightingale
1820 - 1910
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Heaviside did a lot of work on electromagnetics
and transmission lines following his job as a
telegrapher. Using modern techniques, he reworked
Maxwell’s 20 equations, reducing them down to 4.
He proposed the existence of the ionosphere, which
was proved in 1923. He patented the idea behind
coaxial cable and is responsible for the terms
admittance, conductance, impedance, inductance,
permeability, permittance (later susceptance) and
reluctance.
Week 37 - May Oliver Heaviside
1850 - 1925
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Copernicus was a Polish astronomer and
mathematician who discovered that the earth
rotates about its own axis and is in yearly
motion around the sun. This theory profoundly
altered later workers' view of the universe and
set the scene for what is now accepted as fact.
It was however rejected by the Catholic church,
and caused serious problems for Copernicus in
a world where the church held great authority.
Week 38 - May Nicolaus Copernicus
1473 - 1543
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Week 39 - May
Best known as co-inventor of the computer
programming language BASIC, designed to
improve access to computing for his students,
John Kemeny also worked as Albert Einstein’s
mathematical assistant while studying for a PhD.
He became a keen advocate of teaching more
modern and applicable mathematics such as
matrices, logic and probability because in his
words, maths was “the only subject you can study
for 14 years and not learn a single thing that has
been done since 1800 “.
John Kemeny
1926 - 1992
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Week 40 - June
Gloria Olive was a female PhD at a time when mathematics
departments were still very much a male domain. She
became well known in the mathematics community for her
work on binomial functions and matrices. She argued that
teaching should be student centred before such an idea was
fashionable or current practice. She was also the convenor
of the New Zealand National Society for Mathematics and
decided to leave her body to medical science following her
death in 2006.
Gloria Olive
1923 - 2006
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Week 41 - June
James Clerk Maxwell did revolutionary
work on electricity and magnetism and on
the kinetic theory of gases. He extended the
work of Faraday on electrical and
magnetic fields and their interrelation.
Maxwell’s equations (later simplified by
Heaviside) describe this work in what at the
time was a concise and easy to use form.
James Clerk Maxwell
1831 - 1879
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Week 42 - June Simeon Denis Poisson
1781 - 1840
Poisson worked on differential
equations, heat (in competition with
Fourier), electricity and magnetism,
and probability. In statistics, the
Poisson distribution is named after
him as is Poisson’s ratio .
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Week 43 - June Gustav Robert Kirchoff
1824 - 1887
The very famous current and voltage
laws are named after him. These
started as an extension of the work
of Ohm. Kirchoff developed the
method of circuit analysis known as
network analysis and carried out
more research into the velocities of
currents in conductors.
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Week 44 - July William John Macquorn Rankine
1820 - 1872
Rankine was an engineer who developed
the Rankine method for laying out rail-
way curves, the Rankine cycle for the
analysis of the ideal heat engine and
the Rankine temperature scale. He also
founded the Institution of Engineers in
Scotland and was an opponent of the
metric system of measurement.
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Week 45 - July John Dee
1527 - 1609
Dee was in modern terms an astrologer but as
a result of his observations he proposed the
idea of objects emitting rays of force which act
on other object – a forerunner of the theory of
gravitation. In a bid to stay in favour with the
monarchy at a time of religious turmoil he
started a library, aimed at bringing together the
finest knowledge and preserving learning. His
studies of the planets led him to recommend
the adoption of the Gregorian Calendar in 1583
but for political reasons the reform did not
take place until 1752!
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Week 46 - July Robert Hooke
1635 - 1703
Hooke was not formally educated as a young
child but spent time observing things around
him and forming theories as to how things
worked. Later in life, in better health and hav-
ing been to school, the main work for which he
is remembered is the formulation of Hooke’s
law, discovered while trying to build spring
driven clocks for use at sea. Hooke was also a
good artist and made drawings of mars using
a home built telescope.
Hooke was never painted in his lifetime. This picture
depicts how he may have looked.
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Week 47 - July Zhao Youqin
1271 - 1335
Zhao Youquin spent some time as a Daoist
hermit. He studied the universe as best as he
could with the available technology at the
time. He developed various instruments to
help him with his studies and is known to
have worked with a camera obscura. But, his
most influential work was his calculation of
pi. This has been an area of interest for mathe-
maticians for thousands of years because it
is a value that occurs in so many phenomena. There is no known picture of Zhao Youqin
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Week 48 - July John Venn
1834 - 1923
Venn extended Boole's mathematical logic
and is best known to mathematicians and
logicians for his diagrammatic way of
representing sets, and their unions and
intersections. He lectured in Moral Science
at Cambridge University and taught logic
and probability theory.
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Week 49 - August Théodore Olivier
1793 - 1853
Olivier was involved in the training of early
engineers as we now know it, with thorough
grounding in mathematics, science and industry.
He found fame for his mathematical models
that were used as teaching aids in Geometry
and helped students visualise what he was
saying. In an age of “chalk and talk” lectures
this was revolutionary. His models are now
held at Union College in Schenectady, east-
central New York, USA.
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Week 50 - August Pierre de Fermat
1601 - 1665
Fermat is best known for his work on number
theory and came up with a number of theorems
which have intrigued mathematicians for years.
He did not include much evidence of how his
conclusions had been reached and so people
tried to prove or disprove them, making many
important discoveries as they did so. Fermat’s
last theorem was only proved in 1995.
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Week 51 - August Leonardo Fibonacci
1170 - 1250
Fibonacci spent his early years in
Algeria and studied from there. He is
credited with the introduction of the
Arabic numbering system to Europe. It
is much easier to work with then the
Roman system that was in use at the
time and has persisted ever since. The
Fibonacci series was also brought to
Europe by Fibonacci and it appears in
may biological processes.
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Week 52 - August Charles Augustin de Coulomb
1736 - 1806
Coulomb ’s early career was spent as a military
engineer where he was involved in designing
structures and fortifications in the French colonies.
His theory of earth pressure and the generalized
wedge theory of soil mechanics is still used today.
But he is best remembered for the law which was
named after him, concerning the force between
charged particles. The unit of electrical charge is
the Coulomb in his honour. All subsequent work
and developments in electromagnetism were based
on Coulomb’s discovery.
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I hope you have enjoyed this resource and found it useful. All images and links are
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copyright and do not reproduce them without permission. If you are the owner of any
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Anne-Marie Trenholme
(Last updated 2015)
Please feel free to email me your questions, comments and feedback.
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