George Green (14 July 1793 – 31 May 1841) was a British mathematician and physicist, who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Green, 1828).[1] The essay introduced several important concepts, among them a theorem similar to 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. George Green was the first person to try to explain a mathematical theory of the theories of electricity and magnetism which formed the basis for other scientists such as James Clerk Maxwell, William Thomson, and others. His work ran parallel to that of the great mathematician Gauss (potential theory).
Green's life story is remarkable in that he was almost entirely self-taught. He was born and lived for most of his life in the English town of Sneinton, Nottinghamshire, nowadays 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. The younger Green only had about one year of formal schooling as a child, between the ages of 8 and 9.
Family
Most of George Green's extended family, either through business savvy or good fortune, gained considerable wealth throughout the 1800s. This played an important role in George's contribution to math and physics, as in his times, these were activities of leisure that could not be undertaken by the working class.
The Green family tree. It is not shown, but George Green has many living descendants as of 2009
Father — George Green Senior
George Green senior (1758 - 1829) was the youngest of three sons born to family that farmed the land at Saxondale. When he was fifteen, both of his parents died, and the family farm was no longer able to support the three sons and George Green senior was sent to Nottingham to learn bakery as an apprentice.
He worked as an assistant baker until 1791 when he married the daughter of William Butler (also a baker, and possibly George Green senior's employer), Sarah Butler. At that point he opened his own bakery, and a year later bought land on which was built sixteen houses. He and Sarah had two children, George (junior) and Ann, born in 1793 and 1795 respectively. Over the next twenty years his business prospered so well that he became a gentleman, which was a significant improvement in social status (over being merely a baker), and it was instrumental in helping his son eventually connect with the intellectual elite that later popularized his writings. George Green senior left his considerable resources to his children when he died, a fact that was also important in aiding his son's mathematical development, as it meant his son would no longer have to work.
Mother — Sarah Butler
Little is known about George Green's mother, Sarah Butler (1770-1826), who became Sarah Green in 1791. Her father, William Butler, had become a prosperous land owner by the time she married George Green senior.
Sister — Ann
Like his mother, little is known about Ann Green besides her marriage and the business transacations of her husband. She married William Tomlin in 1816, which was fortunate, as he became very wealthy through property, and later, railway investment.
Romantic partner — Jane Smith
Jane Smith (1802-1877) was a lace-dresser with whom George Green fathered seven children, all outside of marriage. There exists speculation as to why George never married Jane. One possibility is that there was a risk of losing the hard-earned 'gentleman' social status if George was to marry a lace dresser. The other possibility is that George had an eye on enrolling in Cambridge, for which celibacy was required. After George Green's death, Jane Smith finally was known as Mrs Jane Green, and she lived among the gentry, indicating that her social status had since improved.
Children
George and Jane had their first child, also named Jane, when George was 31 and Jane (senior) was 22. The following six children were named Mary Ann (born 1827), George (born 1829), John (born 1831), Catherine, Elizabeth and Clara (born 1840). Nothing is known about the interaction of George Green and his seven children, other than that he supported them financially throughout his life.
Early life
In his youth, George 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 well-known science popularizer and educator of the time. He published Essay on the Education of Youth, in which he made such 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 math, but a close inspection of his essay and curriculum revealed that the extent of his mathematical teachings were limited to algebra, trigonometry and logarithms. Thus, George Green's later mathematical contributions, which exhibited knowledge of very modern developments in math, could not have resulted from his tenure at the Robert Goodacre Academy. He stayed for only four terms (one year), and it was speculated by his contemporaries that he probably exhausted all they had to teach him.
Move from Nottingham to Sneinton
At the time when George's father moved there, 1773, Nottingham 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 Nottingham 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", the wind-mill now famously referred to as Green's Windmill. It was technologically impressive for its time, but required nearly twenty-four hour maintenance, which was to become George Green's burden for the next twenty years.
Adult life
Life as a miller
Just as with baking, George Green found the responsibilities of operating the mill annoying and tedious. Grain from the fields was arriving continuously at the mill's doorstep, and one had to constantly adjust the sails of windmill to the windspeed (either to prevent damage, in high winds, or to maximize rotational speed in low winds). The mill-stones that would continuously grind against each other, could wear down or cause a fire (due to friction) if they ran out of grain to grind. Every month the stones, which weighed over a ton, would have to be replaced or repaired.
Membership to the Nottingham Subscription Library
When George Green was thirty, he became a member to 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 (i.e., the first on the list of subscribers was the Duke of Newcastle). This library catered to requests for specialized books and journals that satisfied the particular interests of their subscribers.
The title page to George Green's original essay on what is now known as Green's theorem. 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.
The 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. 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.
From miller to mathematician
By 1829, the time when George Green's father died, the senior George 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 George Green, now thirty-six years old, consequently was able to use this wealth to abandon his miller duties and pursue mathematical studies.
Undergraduate at Cambridge
Members of the Nottingham Subscription Library who knew George Green repeatedly insisted that he obtain a proper University education. In particular, the next-most prestigious subscriber (after the Duke of Newcastle) was Sir Edward Bromhead, with whom George Green shared many correspondences, insisted that he go to Cambridge.
So, in 1833, at the age of forty, Green was admitted as an undergraduate at Gonville and Caius College, Cambridge. He was particularly insecure about his lack of knowledge of Greek or Latin, which was prerequisite knowledge, but it turned out not to be so hard for him to learn as he had expected (and the expected mastery was not so high as he expected). In the mathematics examinations, he won the first year mathematical prize. He graduated in 1838 as a 4th Wrangler (the 4th highest scoring student in his graduating class).
College fellow
Following his graduation, George Green was elected as 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 as a fellow. The next to years provided an unparalleled opportunity for George 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, George Green became rather ill, and in 1840 he returned to Sneinton, only to die a year later. There are rumors that at Cambridge, Green had "succumbed to alcohol", and some of his earlier supporters, such as Sir Edward Bromstead, 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 British mathematician 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 (age 21 in 1845), 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. So George Green died without any idea of his post-humous fame.
Green's work on the motion of waves in a canal anticipates the WKB approximation of quantum mechanics, while his research on light waves and the properties of the ether produced what is now known as the Cauchy-Green 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 analyzing superconductivity. On a visit to Nottingham in 1930, Albert Einstein commented that Green had been twenty years ahead of his time. The theoretical physicist, Julian Schwinger, 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 is named after him, and houses the majority of the University's Science and Engineering Collection. In 1986, Green's Windmill was restored to working order. It now serves both as a working example of a 19th century windmill and as a museum and science centre dedicated to George Green.
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 non-crystallized 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.
Mystery of his mathematical 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, George Green had used "the Mathematical Analysis", a form of calculus derived from Leibnitz that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibnitz 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 George Green had not only heard of these developments, he 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.
See also
References
- ^ 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.
- I. Grattan-Guinness, ‘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 .
- "George Green". http://www.the-ba.net/the-ba/InYourArea/East+Midlands/GeorgeGreen/. - An excellent on-line source of George Green information
- Green, George (1828). An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. http://arxiv.org/abs/0807.0088.
- "Mathematical papers of the late George Green ... Ed. by N. M. Ferrers.". http://name.umdl.umich.edu/AAN8197.0001.001.
- Cannel, D. M. and Lord, N. J. (March 1993). "George Green, mathematician and physicist 1793-1841". The Mathematical Gazette 77: 26–51. doi:10.2307/3619259.
- Challis, L. and Sheard, F. (December 2003). "The Green of Green Functions". Physics Today 56 (12): 41–46. doi:10.1063/1.1650227.
- "Green's Mill and Science Centre" (Web page). http://www.greensmill.org.uk/. Retrieved on November 22 2005.
- Schwinger, Julian (1993). "The Greening of quantum Field Theory: George and I". http://arxiv.org/abs/hep-ph/9310283.
