The Art of Explanation

A short guide to some of the greatest

contributors to mathematics and science.

Compiled by Anne-Marie Trenholme

“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!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 -

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 .

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.

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.

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!

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.

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

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.

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.

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.

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.

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.

I hope you have enjoyed this resource and found it useful. All images and links are

provided for research and entertainment purposes only, please respect their owners'

copyright and do not reproduce them without permission. If you are the owner of any

of the selected images or links and believe that I have infringed your copyright please

let me know so the item in question can be removed or suitably credited.

Anne-Marie Trenholme

(Last updated 2015)

Please feel free to email me your questions, comments and feedback.