George Green
George Green  

Born  Sneinton, Nottinghamshire, England 
14 July 1793
Died  31 May 1841 Nottingham, Nottinghamshire, England 
(aged 47)
Alma mater  University of Cambridge 
Known for  Green measure Green's functions Green's identities Green's matrix Green's theorem 
Influenced  Lord Kelvin Julian Schwinger 
George Green (14 July 1793 – 31 May 1841) was a British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Green, 1828).^{1}^{2} The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. 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, William Thomson, and others. His work on potential theory ran parallel to that of Carl Friedrich Gauss.
Green's life story is remarkable in that he was almost entirely selftaught. He received only about one year of formal schooling as a child, between the ages of 8 and 9.
Contents
Early life
This section does not cite any references or sources. (April 2013) 
Green was born and lived for most of his life in the English town of Sneinton, Nottinghamshire, now part of the city of Nottingham. His father, also named George, was a baker who had built and owned a brick windmill used to grind grain.^{3}
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
Roughly 25–50% of children in Nottingham received any schooling in this period. 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 wellknown 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 nonspecialist, he would have seemed deeply knowledgeable in science and maths, 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 maths, 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 probably exhausted all they had to teach him.
Move from Nottingham to Sneinton
In 1773 George's father moved to Nottingham, 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, 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, a small town about a mile away from Nottingham. On this plot of land he built a "brick wind corn mill", now famously referred to as Green's Windmill. It was technologically impressive for its time, but required nearly twentyfour hour maintenance, which was to become George 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 millstones 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 commonlaw wife and children in his will.^{4}
Nottingham Subscription Library
When Green was thirty, he became a member of the Nottingham Subscription Library. This library exists today, and was likely one of the only sources 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 and probably could not understand it.
The wealthy landowner and mathematician 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 1829, the time when Green's father died, the senior Green had become one of the gentry 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 thirtysix years old, consequently was able to use this wealth to abandon his miller 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.^{5} He was particularly insecure about his lack of knowledge of Greek and Latin, which were prerequisites, but it turned out not to be as hard for him to learn as he believed, as the expected mastery was not as high as he had expected. In the mathematics examinations, he won the firstyear mathematical prize. He graduated BA in 1838 as a 4th Wrangler (the 4th highest scoring student in his graduating class, coming after James Joseph Sylvester who scored 2nd).^{5}
College fellow
Following his graduation, Green was elected a fellow of the Cambridge Philosophical Society. Even without his stellar academic standing, the Society had already read and made note of his Essay and three other publications, and so Green was warmly 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, 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 (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, 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 in 1845.
Green's work on the motion of waves in a canal anticipates the WKB approximation of quantum mechanics, while his research on lightwaves and the properties of the ether produced what is now known as the CauchyGreen tensor. Green's theorem and functions were important tools in classical mechanics, and were revised by Schwinger's 1948 work on electrodynamics that led to his 1965 Nobel prize (shared with Feynman and Tomonaga). Green's functions later also proved useful in analysing superconductivity. On a visit to Nottingham in 1930, Albert Einstein commented that Green had been 20 years ahead of his time. The theoretical physicist, Julian Schwinger, who used Green's functions in his groundbreaking works, published a tribute, entitled "The Greening of Quantum Field Theory: George and I", in 1993.^{6}
The George Green Library at the University of Nottingham 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 engineering department, is also named after him.^{7} In 1986, Green's Windmill was restored to working order. It now serves both as a working example of a 19thcentury windmill and as a museum and science centre dedicated to Green.
Westminster Abbey has a memorial stone for Green in the nave adjoining the graves of Sir Isaac Newton and Lord Kelvin.^{8}
Source of knowledge
This section does not cite any references or sources. (October 2012) 
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 that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibniz being a contemporary of Newton who had his own methods that were thus championed in England). This form of calculus, and the developments of mathematicians such as Laplace, Lacroix and Poisson were not taught even at Cambridge, let alone Nottingham, and yet Green had not only heard of these developments, but also improved upon them.
It is speculated that only one person educated in mathematics, John Toplis, headmaster of Nottingham High School 1806–1819, graduate from Cambridge and an enthusiast of French mathematics, is known to have 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.)
 Mathematical Investigations concerning the Laws of the Equilibrium of Fluids analogous to the Electric Fluid, with other similar Researches. By George Green, Esq., Communicated by Sir Edward Ffrench Bromhead, Bart., M.A., F.R.S.L. and E. (Cambridge Philosophical Society, read 12 November 1832, printed in the Transactions 1833. Quatro, 64 pages.) Vol. III, Part I.
 On the Determination of the Exterior and Interior Attractions of Ellipsoids of Variable Densities. By George Green, Esq., Caius College. (Cambridge Philosophical Society, read 6 May 1833, printed in the Transactions 1835. Quarto, 35 pages.) Vol. III, Part III.
 Researches on the Vibration of Pendulums in Fluid Media. By George Green, Esq., Communicated by Sir Edward Ffrench Bromhead, Bart., M.A., F.R.S.S. Lond. and Ed. (Royal Society of Edinburgh, read 16 December 1833, printed in the Transactions 1836, Quarto, 9 pages.) Vol. III, Part I.
 On the Motion of Waves in a Variable Canal of Small Width and Depth. By George Green, Esq., BA, of Caius College. (Cambridge Philosophical Society, read 15 May 1837, printed in the Transactions 1838. Quarto, 6 pages.) Vol. VI, Part IV.
 On the Reflexion and Refraction of Sound. By George Green, Esq., BA, of Caius College, Cambridge. (Cambridge Philosophical Society, read 11 December 1837, printed in the Transactions 1838. Quarto, 11 pages.) Vol. VI, Part III.
 On the Laws of Relexion and Refraction of Light at the common Surface of two noncrystallized Media. By George Green, Esq., BA, of Caius College. (Cambridge Philosophical Society, read 11 December 1837, printed in the Transactions 1838. Quarto, 24 pages.) Vol. VII, Part I.
 Note on the Motion of Waves in Canals. By George Green, Esq., BA, of Caius College. (Cambridge Philosophical Society, read 18 February 1839, printed in the Transactions 1839. Quarto, 9 pages.) Vol. VII, Part I.
 Supplement to a Memoir on the Reflexion and Refraction of Light. By George Green, Esq., BA, of Caius College. (Cambridge Philosophical Society, read 6 May 1839, printed in the Transactions 1839. Quarto, 8 pages.) Vol. VII, Part I.
 On the Propagation of Light in Crystallized Media. By George Green, BA, Fellow of Caius College. (Cambridge Philosophical Society, read 20 May 1839, printed in the Transactions 1839. Quarto, 20 pages.) Vol. VII, Part II.
See also
Notes
 ^ This 1828 essay can be found in Mathematical papers of the late George Green, edited by N. M. Ferrers. The website for this is given below.
 ^ Cannell, D.M. (1999) George Green: An Enigmatic Mathematician, American Mathematical Monthly 106(2), 136–151.
 ^ Greens biography
 ^ Cannel, D. M. and Lord, N. J.; Lord, N. J (March 1993). "George Green, mathematician and physicist 1793–1841". The Mathematical Gazette (The Mathematical Gazette, Vol. 77, No. 478) 77 (478): 26–51. doi:10.2307/3619259. JSTOR 3619259.
 ^ ^{a} ^{b} "Green, George (GRN832G)". A Cambridge Alumni Database. University of Cambridge.
 ^ http://arxiv.org/abs/hepph/9310283
 ^ "George Green Institute for Electromagnetics Research". Retrieved 17 February 2014.
 ^ http://www.westminsterabbey.org/ourhistory/people/georgegreen
References
 I. GrattanGuinness, ‘Green, George (1793–1841)’, Oxford Dictionary of National Biography, Oxford University Press, 2004 accessed 26 May 2009
 D.M. Cannell, "George Green mathematician and physicist 1793–1841", The Athlone Press, London, 1993.
 Robert Murphy, "On the inverse method of definite integrals", Transactions of the Cambridge Philosophical Society, vol. 4 (1833), pp. 353–408. (Note: This was the first quotation of Green's 1828 work by somebody other than Green himself.)
 O'Connor, John J.; Robertson, Edmund F., "George Green", MacTutor History of Mathematics archive, University of St Andrews.
 "George Green". – An excellent online source of George Green information
 Green, George (1828). "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism". arXiv:0807.0088 physics.histph.
 "Mathematical papers of the late George Green ... Ed. by N. M. Ferrers.".
 Cannel, D. M. and Lord, N. J.; Lord, N. J (March 1993). "George Green, mathematician and physicist 1793–1841". The Mathematical Gazette (The Mathematical Gazette, Vol. 77, No. 478) 77 (478): 26–51. doi:10.2307/3619259. JSTOR 3619259.
 Challis, L. and Sheard, F.; Sheard, Fred (December 2003). "The Green of Green Functions". Physics Today 56 (12): 41–46. Bibcode:2003PhT....56l..41C. doi:10.1063/1.1650227.
 "Green's Mill and Science Centre" (Web page). Retrieved 22 November 2005.
 Schwinger, Julian (1993). The Greening of quantum Field Theory: George and I. p. 10283. arXiv:hepph/9310283. Bibcode:1993hep.ph...10283S.
External links
 List of References for George Green
 Quotations related to George Green at Wikiquote
 Bowley, Roger. "George Green & Green's Functions". Sixty Symbols. Brady Haran for the University of Nottingham.

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