The Art of Explanation Compiled by Anne-Marie Trenholme
A short guide to some of the greatest contributors to mathematics and science.
“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 information 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
Hopper
18
Einstein
32
Poisson
46
Sylvester
5
Davidov
19
Fourier
33
Kirchoff
47
Curry
6
Ramanujan
20
Descartes
34
Rankine
48
Riemann
7
Babbage
21
Napier
35
Dee
49
Wilkinson
8
Newton
22
Wiles
36
Hooke
50
Williams
9
Hawking
23
Euler
37
Youqin
51
Richardson
10
Franklin
24
Planck
38
Venn
52
Wren
11
LaGrange
25
Gauss
39
Olivier
53
Jungius
12
Euclid
26
Nightingale
40
Fermat
54
Boole
13
Yasuaki
27
Heaviside
41
Fibonacci
55
Halley
14
Rheticus
28
Copernicus
42
Coulomb
56
Strutt
15
Boltzmann
29
Kemeny
43
Hubble
16
De la Faille
30
Olive
44
Franklin
17
Oughtred
31
Maxwell
45
Week 1 - September
James Joseph Sylvester 1814 - 1897
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 2 - September
Haskell Brooks Curry 1900 - 1982
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 3 - September
Bernhard Riemann 1826 - 1866
Riemann’s ideas on the geometry of space had a profound effect on the development of modern theoretical physics, leading to the later development of the theory of general relativity. He clarified the notion of integrals by defining what we now call the Riemann integral.
Week 4 - September
James Hardy Wilkinson 1919 - 1986
James Hardy Wilkinson studied the thermodynamics of ballistics and explosions, he worked on numerical methods for solving systems of linear equations and eigenvalue problems. He also worked with early computing.
Week 5 - October
William Lloyd Garrison Williams 1888 - 1976
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 6 - October
Lewis Fry Richardson 1881 - 1953 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 7 - October
Sir Christopher Wren 1632 - 1723
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 8 - October
Joachim Jungius, aka Jung 1587 - 1657
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 9 - October
George Boole 1815 - 1864
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 10 - November
Edmund Halley 1656 - 1742
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 11 - November
John William Strutt (Lord Rayleigh) 1842 - 1919
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 12 - November
Edwin Powell Hubble 1889 - 1953
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.
Week 13 - November
Christine Ladd-Franklin 1847 - 1930
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 14 - December
Grace Brewster Murray Hopper 1906 - 1992 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 15 - December
August Yulevich Davidov 1823 - 1885
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 16 - December
Srinivasa Aiyangar Ramanujan 1887 - 1920
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 17 - December
Charles Babbage 1791 - 1871
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 18 - January
Sir Isaac Newton 1643 - 1727
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 19 - January
Stephen William Hawking 1942 -
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 20 - January
Benjamin Franklin 1706 - 1790
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 21 - January
Joseph Louis LaGrange 1736 - 1813
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 22 - January
Euclid of Alexandria 325BC – 265BC 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 23 - February
Aida Yasuaki 1747 - 1817
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 24 - February
Georg Joachim von Lauchen Rheticus 1514 - 1574
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 25 - February
Ludwig Boltzmann 1844 - 1906
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 26 - February
Jan-Karel della Faille (or Jean-Charles de La Faille) 1597 - 1652
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 27 - March
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 28 - March
Albert Einstein 1879 - 1955
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.
Week 29 - March
Jean Baptiste Joseph Fourier 1768 - 1830
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 30 - March
Rene Descartes 1596 - 1650
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 31 - April
John Napier 1550 - 1617
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 32 - April
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 33 - April
Leonhard Euler 1707 - 1783 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 34 - April
Max Karl Ernst Ludwig Planck 1858 - 1947 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 35 - April
Johann Carl Friedrich Gauss 1777 - 1855 Gauss worked in a wide variety of fields in both mathematics and physics. His work included number theory, analysis, differential 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 36 - May
Florence Nightingale 1820 - 1910
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 37 - May
Oliver Heaviside 1850 - 1925 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 38 - May
Nicolaus Copernicus 1473 - 1543 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 39 - May
John Kemeny 1926 - 1992 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 “.
Week 40 - June
Gloria Olive 1923 - 2006 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.
Week 41 - June
James Clerk Maxwell 1831 - 1879
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.
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 railway 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 having 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 mathematicians for thousands of years because it
There is no known picture of Zhao Youqin
is a value that occurs in so many phenomena.
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, eastcentral 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.
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Anne-Marie Trenholme
(Last updated 2015)
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