George Green, Mathematician. 1793—1841.


I wish to acknowledge my indebtedness to the Rev. F. C. Finch, M.A., formerly Vicar of S. Alban's, Nottingham, for drawing my attention to the mathematician of Sneinton, and for information concerning Green which he gave to me ; also to Dr. Piaggio, Professor of Mathematics, University College, Nottingham, for writing the concluding paragraph of this article, and for the loan from his departmental library of a copy of Green's Mathematical Papers.

THERE is one outstanding mystery connected with the education of Nottingham in the early 19th century of which the complete elucidation will probably never be reached. As the traveller enters Nottingham by the Midland railway line from the north-east, he catches a glimpse of a grey old windmill, standing away on an eminence on his right, a solitary survivor of bygone days, now almost hidden by rows of modern villas. There, in the days when Sneinton, remote from the busy life of the town, was a peaceful village of old-world cottages and little homesteads nestling together on the wind-swept hillside overlooking the wide vale of Trent, was spent the youth and early manhood of one of the most original mathematicians of the 19th century, George Green, who has been described as "standing head and shoulders above all his companions in and outside the University. George Green was born in 1793, at Sneinton, where his father, a miller of considerable property, lived at the mill already mentioned, then the easternmost of three mills situated on the hill; he also carried on business as a baker in Nottingham. George worked with his father, until the death of the latter in 1829. It may be assumed that the younger Green was a man of considerable general education, for in 1823 he became a member of the Nottingham Subscription Library, already located in Bromley House.1 In 1828, there was published in Nottingham, by private subscription, the work which ultimately made Green's name famous for all time, An essay on the application of mathematical analysis to the theories of Electricity and Magnetism, which Dr. Ferrers referred to as "perhaps the most important of Green's papers." In this work the term potential was introduced to denote the result obtained by adding together the masses of all the particles of a system, each divided by its distance from a given point. The essay, which consists of three parts, considers in the first the properties of this function, and in the second and third parts applies them to the theories of magnetism and electricity respectively.2 It is clear from the preface which Green himself wrote to this work that he had access to the writings of French mathematicians; for he refers to "two memoirs of singular elegance, relative to the distribution of electricity on the surface of conducting spheres previously electrified and put in the presence of each other," presented in 1812 to the French Institute by M. Poisson; further on he refers to other "memoirs" of the same writer, also to observations made by M. Arago; he acknowledges familiarity with the investigations of M. Fourier, with work jointly carried out by MM. Cauchy and Poisson; and he makes mention of the work of the English mathematicians, Cavendish and Dr. T. Young.3 How did Green, the son of a miller and baker, following his father's calling, living his life on the outskirts of a provincial town, in the early days of the 19th century when means of intercommunication between different parts of the country-side were largely undeveloped, become acquainted with the works of French mathematicians? Such works were not to be found in Bromley House Library. Dr. Ferrers describes Green as "an almost entirely self-taught mathematical genius." But what was the starting point of his investigations? Who were the friends who were able to appreciate the power shown in his first Paper, and who assisted in the publication of it in Nottingham in 1828? Green certainly became connected in some way with Sir Edward Ffrench Bromhead, whose family seat lay at Thurlby Hall, between Newark and Lincoln, and who took his degree at Cambridge in 1812. How a friendship sprang up between the two men remains unexplained. It has been suggested that Sir E. F. Bromhead lent books to Green,4 and he seems to have encouraged him to go to Cambridge.5 There Green entered Caius, Sir E. F. Bromhead's own College. Green, in his Preface to his Essay published in 1828, wrote that he had been obliged to obtain the little knowledge which he possessed at such intervals and by such means as other indispensable avocations, which offered but few opportunities of mental improvement, afforded.6 The existing Register of the Free Grammar School for Boys dates only from 1809; it is impossible, therefore, to say whether Green attended the Grammar School in Stoney Street, or not. It is probable, however, that he did not, for with the exception of the private pupils of the head master, the pupils of the school were almost entirely sons of the burgesses of Nottingham,7 and Sneinton, in the days of Green's boyhood, was far outside the borough. After his father's death in 1829, Green disposed of the business and prepared to go to Cambridge. In 1832, a Paper entitled On the Laws of the Equilibrium of Fluids analogous to the Electric Fluid, written by Green, was laid before the Cambridge Philosophical Society by Sir Edward Ffrench Bromhead, and later, another On the determination of the attractions of Ellipsoids of variable Densities, before the same Society, by the same friend of the author.8 A copy of the former was presented by Green to the Nottingham Subscription Library in 1833.9 In that year he contributed to the Royal Society of Edinburgh a Paper On the Vibrations of Pendulums in Fluid Media? Green, then a man of middle life, commenced residence in Cambridge, in October, 1833. In 1837 he was Fourth Wrangler in the mathematical tripos; although only Fourth, Green was considered the best man of his year, but "want of familiarity with boy's mathematics prevented him from coming to the top in a time-race."10 In that year he read his Paper On the Motion of Waves in a variable canal of small depth and width, to the Cambridge Philosophical Society. He continued his studies and did much valuable work on the Theory of Sound and the Dynamical Theory of Light, producing Papers On the Reflexion and Refraction of Sound and On the Reflexion and Refraction of Light at the common surface of two non-crystallized media. In 1839 he was elected a Perse Fellow of Caius College, and in the same year he wrote On the Propagation of Light in Crystalline Media?

It seems reasonable to suppose that throughout his years of residence at Cambridge, Green from time to time visited Sneinton, for when his health gave way he settled there in Notintone Place, in those days still a superior residential quarter, within five minutes' walk of the old mill. There, on May 31st, 1841, he died. A plain, flat stone slab marks the spot where his body was laid to rest in S. Stephen's churchyard. In the forties of last century, Nottingham was the home of few mathematicians, and so little was the importance of Green's work appreciated locally, that beyond a short obituary notice of some fourteen words, the local newspaper made no further reference to him at the time of his death. His fame, however, is no doubt much greater now than in his life, and his ideas have proved much more fruitful as years passed than they probably appeared to his contemporaries. Green's most valuable researches were fated for long to escape the notice not only of foreign, but also of British mathematicians, and "it is a singular fact in the history of science that all his general theorems were rediscovered by Lord Kelvin, Chasles and Sturm, and Gauss."

Of Green's direct descendants, who might presumably be able to throw light on the mathematician's early history, none are known to be living. While still a young man, Green fell in love with Miss Jane Smith, but his father is said to have threatened to disinherit him if he married her. She became, however, the mother of his seven children. One son, another George Green, went to St. John's College, Cambridge. The Register of the College gives 12th July, 1829, as the date of his birth, omits his father's name, but gives his mother's name as Jane Smith, and shows him to have been recommended by the Rev. W. H. Wyatt, M.A., Vicar of Sneinton. A surviving member of Green's year describes the mathematician's son in the following terms:—"He was by far the most impressive in his appearance of all the freshmen of his year. He had a broad and lofty forehead and a grave and dignified manner. He must have been about 30 years of age and had been a schoolmaster before he came up." This George Green was 3rd Senior Optime in 1859. One or two of his contemporaries recollect him as very reserved, not seeking companionship and keenly disappointed with his degree, as he hoped to be a wrangler. Apparently none of his Cambridge acquaintances kept in touch with him or heard what became of him after he left Cambridge. For a time he seems to have lived with his sisters at Sneinton.11 The name of this George Green appears on the stone which marks the family grave in S. Stephen's churchyard at Sneinton; the year 1870 is there given as the date of his death.

Clara,12 the youngest child of the mathematician, the last survivor of her family, died in 1919. Papers, books and mathematical instruments, formerly the property of her distinguished father, are said to have been in Miss Green's possession at the time of her death, but they have mysteriously disappeared. As Miss Green died intestate, the old mill-house and some acres of surrounding land became the property of the Crown. This was offered for sale and purchased in November, 1921, by Mr. Oliver W. Hind, who intends to preserve the mill, the brickwork of which is in remarkably good condition, and to portion out into gardens the part of the land previously uncultivated.

The extinction of the family of the great mathematician, and the disappearance within the last few years of his books and papers, have finally destroyed the hope of discovering either the sources whence Green drew his early inspiration or the means by which his mathematical genius was brought to light and developed.

The importance of Green's work seems to increase rather than diminish, with the lapse of time. In Potential, Electricity and Hydrodynamics, Green's Theorem connecting surface- and volume-integrals, takes a prominent place.13 Green's Lemma (also called Green's Theorem in two dimensions) connecting line- and surface-integrals is important in the Theory of Functions.14 Recent works on the Conduction of Heat, Differential Equations and Integral Equations, introduce Green's Functions.15 But in this connection Green's ideas were neglected until fairly recently, so that they still appear too novel for their importance to be fully appreciated.

(1) Minute Book, N.S.L.
(2) Geo. Green, Mathematical Papers, Preface, p. 6
(3) Geo. Green, Mathematical Papers, pp. 1—8.
(4) Manuscript Notes of the Rev. F. C. Finch, M.A.. formerly Vicar of St. Alban's, Sneinton.
(5) Letter of Mr. R. F. Scott, M.A., Master of S.  John's College, Cambridge, Aug. 17th, 1920.
(6) Geo. Green, op. cit., p. 8.
(7) S. Corner. The Forester. July, 1905, p. 67 and p. 68.
(8) N. M. Ferrers, Preface to Mathematical Papers of the late George Green, pp. 6, 7.
(9)  Minute-book of Nottingham Subscription Library.
(10) Dictionary of National Biography.
(11) Recollections of an old Sneinton resident.
(12) At one time, governess in the family of the Rev. W. H. Wyatt.
(13) For this and some other work due to Green, such as Green's Equivalent Layer, Green's Theorem on the discontinuity in field on crossing a boundary with a surface distribution, Green's method of solving condenser problems, etc.; see Routh's Analytical Statics, Vol. II.
(14) See Goursat's or De la Valtee Poussin's Cours d'Analyse.
(15) See Carshaw's Mathematical Theory of the Conduction of Heat.