George Green (mathematician)
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George Green (14 July 1793 – 31 May 1841) was a British
mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...
who wrote '' An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism'' in 1828. The essay introduced several important concepts, among them a theorem similar to the modern
Green's theorem In vector calculus, Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by . It is the two-dimensional special case of Stokes' theorem. Theorem Let be a positively orient ...
, the idea of
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
functions as currently used in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, and the concept of what are now called
Green's function In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential ...
s. Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
, William Thomson, and others. His work on
potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravi ...
ran parallel to that of
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
. Green's life story is remarkable in that he was almost entirely self-taught. He received only about one year of formal schooling as a child, between the ages of 8 and 9.


Early life

Green was born and lived for most of his life in the English town of
Sneinton Sneinton (pronounced "Snenton") is a suburb of Nottingham, England. The area is bounded by Nottingham city centre to the west, Bakersfield to the north, Colwick to the east, and the River Trent to the south. Sneinton lies within the unitary au ...
, Nottinghamshire, now part of the city of
Nottingham Nottingham ( , East Midlands English, locally ) is a city status in the United Kingdom, city and Unitary authorities of England, unitary authority area in Nottinghamshire, East Midlands, England. It is located north-west of London, south-east ...
. His father, also named George, was a baker who had built and owned a brick
windmill A windmill is a structure that converts wind power into rotational energy using vanes called windmill sail, sails or blades, specifically to mill (grinding), mill grain (gristmills), but the term is also extended to windpumps, wind turbines, and ...
used to grind grain. In his youth, Green was described as having a frail constitution and a dislike for doing work in his father's bakery. He had no choice in the matter, however, and as was common for the time he likely began working daily to earn his living at the age of five.


Robert Goodacre's Academy

During this era it was common for only 25–50% of children in Nottingham to receive any schooling. The majority of schools were Sunday schools, run by the Church, and children would typically attend for one or two years only. Recognizing the young Green's above average intellect, and being in a strong financial situation due to his successful bakery, his father enrolled him in March 1801 at Robert Goodacre's Academy in Upper Parliament Street. Robert Goodacre was a well-known science populariser and educator of the time. He published ''Essay on the Education of Youth'', in which he wrote that he did not "study the interest of the boy but the embryo Man". To a non-specialist, he would have seemed deeply knowledgeable in science and mathematics, but a close inspection of his essay and curriculum revealed that the extent of his mathematical teachings was limited to algebra, trigonometry and logarithms. Thus, Green's later mathematical contributions, which exhibited knowledge of very modern developments in mathematics, could not have resulted from his tenure at the Robert Goodacre Academy. He stayed for only four terms (one school year), and it was speculated by his contemporaries that he had exhausted all they had to teach him.


Move from Nottingham to Sneinton

In 1773 George's father moved to
Nottingham Nottingham ( , East Midlands English, locally ) is a city status in the United Kingdom, city and Unitary authorities of England, unitary authority area in Nottinghamshire, East Midlands, England. It is located north-west of London, south-east ...
, which at the time had a reputation for being a pleasant town with open spaces and wide roads. By 1831, however, the population had increased nearly five times, in part due to the budding
industrial revolution The Industrial Revolution was the transition to new manufacturing processes in Great Britain, continental Europe, and the United States, that occurred during the period from around 1760 to about 1820–1840. This transition included going f ...
, and the city became known as one of the worst slums in England. There were frequent riots by starving workers, often associated with special hostility towards bakers and millers on the suspicion that they were hiding grain to drive up food prices. For these reasons, in 1807, George Green senior bought a plot of land in Sneinton. On this plot of land he built a "brick wind corn mill", now referred to as Green's Windmill. It was technologically impressive for its time, but required nearly twenty-four-hour maintenance, which was to become Green's burden for the next twenty years.


Adult life


Miller

Just as with baking, Green found the responsibilities of operating the mill annoying and tedious. Grain from the fields was arriving continuously at the mill's doorstep, and the sails of the windmill had to be constantly adjusted to the windspeed, both to prevent damage in high winds, and to maximise rotational speed in low winds. The
millstone Millstones or mill stones are stones used in gristmills, for grinding wheat or other grains. They are sometimes referred to as grindstones or grinding stones. Millstones come in pairs: a convex stationary base known as the ''bedstone'' and ...
s that would continuously grind against each other, could wear down or cause a fire if they ran out of grain to grind. Every month the stones, which weighed over a ton, would have to be replaced or repaired.


Family life

In 1823 Green formed a relationship with Jane Smith, the daughter of William Smith, hired by Green Senior as mill manager. Although Green and Jane Smith never married, Jane eventually became known as Jane Green and the couple had seven children together; all but the first had Green as a baptismal name. The youngest child was born 13 months before Green's death. Green provided for his common-law wife and children in his will.


Nottingham Subscription Library

When Green was thirty, he became a member of the
Nottingham Subscription Library Bromley House Library (originally the Nottingham Subscription Library) is a subscription library in Nottingham. Premises The library is situated in Bromley House, a Georgian townhouse in Nottingham city centre. This building is grade II* lis ...
. This library exists today, and was likely the main source of Green's advanced mathematical knowledge. Unlike more conventional libraries, the subscription library was exclusive to a hundred or so subscribers, and the first on the list of subscribers was the Duke of Newcastle. This library catered to requests for specialised books and journals that satisfied the particular interests of their subscribers.


1828 essay

In 1828, Green published '' An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism'', which is the essay he is most famous for today. It was published privately at the author's expense, because he thought it would be presumptuous for a person like himself, with no formal education in mathematics, to submit the paper to an established journal. When Green published his ''Essay'', it was sold on a subscription basis to 51 people, most of whom were friends who probably could not understand it. The wealthy landowner and mathematician Sir Edward Bromhead bought a copy and encouraged Green to do further work in mathematics. Not believing the offer was sincere, Green did not contact Bromhead for two years.


Mathematician

By the time Green's father died in 1829, the senior Green had become one of the
gentry Gentry (from Old French ''genterie'', from ''gentil'', "high-born, noble") are "well-born, genteel and well-bred people" of high social class, especially in the past. Word similar to gentle imple and decentfamilies ''Gentry'', in its widest ...
due to his considerable accumulated wealth and land owned, roughly half of which he left to his son and the other half to his daughter. The young Green, now thirty-six years old, consequently was able to use this wealth to abandon his
miller A miller is a person who operates a Gristmill, mill, a machine to grind a grain (for example corn or wheat) to make flour. Mill (grinding), Milling is among the oldest of human occupations. "Miller", "Milne" and other variants are common surname ...
duties and pursue mathematical studies.


Cambridge

Members of the Nottingham Subscription Library who knew Green repeatedly insisted that he obtain a proper University education. In particular, one of the library's most prestigious subscribers was Sir Edward Bromhead, with whom Green shared many correspondences; he insisted that Green go to Cambridge. In 1832, aged nearly forty, Green was admitted as an undergraduate at
Gonville and Caius College, Cambridge Gonville and Caius College, often referred to simply as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348, it is the fourth-oldest of the University of Cambridge's 31 colleges and one of th ...
. He was particularly insecure about his lack of knowledge of
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
and
Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
, which were prerequisites, but it turned out not to be as hard for him to learn these as he had envisaged, as the degree of expected mastery was not as high as he had expected. In the mathematics examinations, he won the first-year mathematical prize. He graduated with a BA in 1838 as a 4th Wrangler (the 4th highest scoring student in his graduating class, coming after
James Joseph Sylvester James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership ro ...
who scored 2nd).


College fellow

Following his graduation, Green was elected a fellow of the
Cambridge Philosophical Society The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ...
. Even without his stellar academic standing, the Society had already read and made note of his Essay and three other publications, so Green was welcomed. The next two years provided an unparalleled opportunity for Green to read, write, and discuss his scientific ideas. In this short time he published an additional six publications with applications to hydrodynamics, sound, and optics.


Final years and posthumous fame

In his final years at Cambridge, Green became rather ill, and in 1840 he returned to
Sneinton Sneinton (pronounced "Snenton") is a suburb of Nottingham, England. The area is bounded by Nottingham city centre to the west, Bakersfield to the north, Colwick to the east, and the River Trent to the south. Sneinton lies within the unitary au ...
, only to die a year later. There are rumours that at Cambridge, Green had "succumbed to alcohol", and some of his earlier supporters, such as Sir Edward Bromhead, tried to distance themselves from him. Green's work was not well known in the mathematical community during his lifetime. Besides Green himself, the first mathematician to quote his 1828 work was the Briton
Robert Murphy Robert, Rob, Bob or Bobby Murphy may refer to: Sports Ice hockey *Robert Ronald Murphy or Ron Murphy (1933–2014), Canadian ice hockey player * Bob Murphy (ice hockey) (born 1951), Canadian retired professional ice hockey player * Rob Murphy (ice ...
(1806–1843) in his 1833 work. In 1845, four years after Green's death, Green's work was rediscovered by the young William Thomson (then aged 21), later known as
Lord Kelvin William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...
, who popularised it for future mathematicians. According to the book "George Green" by D.M. Cannell, William Thomson noticed Murphy's citation of Green's 1828 essay but found it difficult to locate Green's 1828 work; he finally got some copies of Green's 1828 work from
William Hopkins William Hopkins Fellow of the Royal Society, FRS (2 February 179313 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate University of Cambridge, Cambridge mathematicians, earning h ...
in 1845. In 1871
N. M. Ferrers Norman Macleod Ferrers D.D. (11 August 1829 – 31 January 1903) was a British mathematician and university administrator and editor of a mathematical journal. Career and research Ferrers was educated at Eton College before studying at Gonvill ...
assembled ''The Mathematical Papers of the late George Green'' for publication. Green's work on the motion of waves in a canal (resulting in what is known as Green's law) anticipates the
WKB approximation In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mecha ...
of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, while his research on light-waves and the properties of the Aether produced what is now known as the Cauchy-Green tensor.
Green's theorem In vector calculus, Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by . It is the two-dimensional special case of Stokes' theorem. Theorem Let be a positively orient ...
and functions were important tools in classical mechanics, and were revised by Schwinger's 1948 work on
electrodynamics In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
that led to his 1965 Nobel prize (shared with
Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
and
Tomonaga Tomonaga is both a masculine Japanese given name and a Japanese surname. Possible writings Tomonaga can be written using different combinations of kanji characters. Here are some examples: *友永, "friend, eternity" *友長, "friend, long/lead ...
). Green's functions later also proved useful in analysing
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
. On a visit to Nottingham in 1930,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
commented that Green had been 20 years ahead of his time. The theoretical physicist
Julian Schwinger Julian Seymour Schwinger (; February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist. He is best known for his work on quantum electrodynamics (QED), in particular for developing a relativistically invariant ...
, who used Green's functions in his ground-breaking works, published a tribute entitled "The Greening of Quantum Field Theory: George and I" in 1993. The George Green Library at the
University of Nottingham The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...
is named after him, and houses the majority of the university's science and engineering Collection. ''The George Green Institute for Electromagnetics Research'', a research group in the
University of Nottingham The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...
engineering department, is also named after him. In 1986, Green's Windmill was restored to working order. It now serves both as a working example of a 19th-century
windmill A windmill is a structure that converts wind power into rotational energy using vanes called windmill sail, sails or blades, specifically to mill (grinding), mill grain (gristmills), but the term is also extended to windpumps, wind turbines, and ...
and as a museum and science centre dedicated to Green.
Westminster Abbey Westminster Abbey, formally titled the Collegiate Church of Saint Peter at Westminster, is an historic, mainly Gothic church in the City of Westminster, London, England, just to the west of the Palace of Westminster. It is one of the United ...
has a memorial stone for Green in the nave adjoining the graves of
Sir Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the great ...
and Lord Kelvin. His work and influence on 19th-century applied physics had been largely forgotten until the publication of his biography by Mary Cannell in 1993.


Source of knowledge

It is unclear to historians exactly where Green obtained information on current developments in mathematics, as Nottingham had little in the way of intellectual resources. What is even more mysterious is that Green had used "the Mathematical Analysis," a form of calculus derived from
Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibniz being a contemporary of
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...
who had his own methods that were championed in England). This form of calculus, and the developments of mathematicians such as the French mathematicians
Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
, Lacroix and Poisson were not taught even at Cambridge, let alone Nottingham, and yet Green not only had heard of these developments, but improved upon them. It is speculated that only one person educated in mathematics,
John Toplis John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second ...
, headmaster of
Nottingham High School , motto_translation = Praise to the end , address = Waverley Mount , city = Nottingham , county = Nottinghamshire , postcode = NG7 4ED , country = England , coordinates = , type = Independent day school , established = , closed = , religious ...
1806–1819, graduate from Cambridge as 11th Wrangler and an enthusiast of French mathematics, lived in Nottingham at the time.


List of publications

* '' An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism''. By George Green, Nottingham. Printed for the Author by T. Wheelhouse, Nottingham. 1828. (Quarto, vii + 72 pages.) * Presented 12 November 1832. * Presented 6 May 1833. * Presented 16 December 1833. * Presented 11 December 1837. * Presented 15 May 1837. * Presented 11 December 1837. * Presented 18 February 1839. * Presented 6 May 1839. * Presented 20 May 1839.


Notes


References

*
Ivor Grattan-Guinness Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bac ...
, 'Green, George (1793–1841)', ''Oxford Dictionary of National Biography'', Oxford University Press, 200
accessed 26 May 2009
* D. M. Cannell, "George Green mathematician and physicist 1793–1841", The Athlone Press, London, 1993. * (Note: This was the first quotation of Green's 1828 work by somebody other than Green himself.) * * – An excellent on-line source of George Green information * * * *


External links



* * {{DEFAULTSORT:Green, George 19th-century English mathematicians English physicists Mathematical analysts Alumni of Gonville and Caius College, Cambridge Fellows of Gonville and Caius College, Cambridge People from Sneinton 1793 births 1841 deaths Tourist attractions in Nottinghamshire Nottingham