GEORGE GREEN
Miller and Mathematician |
These notes on Green's life are taken from George
Green, Miller and Mathematician by D M Cannell which is available from the
Green's Mill Shop
For a short account of the life of George Green in
French
or in
Dutch
School
In 1801, at the age of eight years, young George Green started school at Mr
Goodacre's Academy in Nottingham. George's father was a baker in the town and
the school fees must have been a considerable expense for him. Perhaps George
was already showing signs of the genius for mathematics that became evident in
his later life. His cousin, William Tomlin, writing after George Green's death,
said that
'at a very early age . . . he pursued with undeviating
constancy the same as in his mature years an intense application to
mathematics.'
Mr Goodacre was a noted teacher and one who encouraged scientific enquiry,
equipping the school with such instruments as a barometer, thermometer, air
pump, an orrery to show the motion of the moon and planets and astronomical
telescopes. George flourished at the school and William Tomlin tells us that
George's 'profound knowledge in the mathematics' soon exceeded his
schoolmaster's. However, George attended the Academy for only four terms,
leaving at the age of nine years to work in his father's bakery.
A Working Miller
The bakery prospered and in 1807 Mr Green bought a plot of land in
Sneinton, then a village outside of the town of Nottingham, where he built the
fine brick windmill which still stands to this day. Later the family moved out
of the town to a splendid new house next to the mill. At some time Mr Green
appointed as mill manager William Smith who took residence in the cottage built
onto the side of the mill. He had a daughter Jane who, at the age of twenty two,
bore George Green a daughter. Jane and George never married although over a
relationship lasting some sixteen years they had seven children in all. Perhaps
old Mr Green did not approve of his son marrying the daughter of an employee. Or
perhaps it has something to do with George's other life as a mathematician. As
we shall see George eventually became a Fellow at Cambridge University, a
condition of which at that time was that one had to be unmarried.
Intellectual opportunity
In 1823 George Green joined the Bromley House Library in Nottingham. At a
time before the establishment of a University in Nottingham, Bromley House was
the meeting place of intellectuals and academics, the setting for cultural
activities, lectures and exhibitions. The library gave George access to some
scientific publications, for example the Transactions of the Royal Society, and
his introduction to the world of learning wherein he was later to achieve so
much. The library still exists in Nottingham, an oasis of calm in the bustle of
the busy city centre.
The President of the library at that time was the Rev. Robert White Almond,
a mathematics graduate and probably someone who encouraged George's interests.
Another notable local mathematician who almost certainly helped George was the
Rev. John Toplis, Headmaster of the Free Grammar School. Toplis was very
dissatisfied with the style of mathematics taught in England at that time, a
style which still used the old Newtonian notation. Toplis championed the work of
Leibnitz, a German contemporary of Newton, who used a different way of writing
mathematics, one which is used to this day. Scientists on the Continent had made
great advances in applying mathematics to the understanding of problems in
physics but little of this had become known in England. Toplis tried to remedy
this, for example with his translation of the Mécanique Céleste by
LaPlace. George Green and his family lived around the corner from Toplis for
some time and, despite direct evidence, it is inconceivable that the two men,
with such a particular interest in common and in such a small society, did not
have much to share.
The Essay of 1828
What we do know is that in 1828, at the age of thirty five years, George
published his greatest work 'An Essay on the Application of Mathematical
Analysis to the Theories of Electricity and Magnetism'. Published at the
author's expense, it had fifty-one subscribers, about half of whom were members
of Bromley House Library. They each paid the large sum of seven shillings and
sixpence for their copy though few could have understood any part of it nor have
had any idea of the significance of the event. The ideas and concepts in it
were in advance of their time, written in the unfamiliar Continental notation
and containing ideas and techniques which are known to this day as Green's
functions and Green's Theorem.
In the Essay Green applied mathematical analysis or calculation to the
contemporary theories of electricity and magnetism. It was one of the first
attempts to apply mathematical theory to electrical phenomena and was of such
importance that it has been described as 'the beginning of mathematical physics
in England' and 'a major work of striking originality' whose publication was the
'most significant event in the intellectual history of Nottingham'.
Yet, despite the astonishing achievement that the Essay is now seen to be,
it went unregarded at the time. Green, busy by day with his milling business,
had laboured long over the work in, as he put it, 'the hours stolen from my
sleep'. Yet to no avail, it seemed. George put aside mathematics and turned his
attentions to the mill, his business interests and his growing family.
Genius discovered
That might have been the end of the story, the Essay standing as the single
achievement of this remarkable man. However, one of the subscribers to the Essay
was Sir Edward Bromhead of Thurlby Hall near Lincoln. Bromhead, a landowner,
magistrate and High Steward of Lincoln, was also a gifted mathematician who
recognised the potential of Green's work. He made inquiries about Green from an
acquaintance in Nottingham who replied
10 May 1828
Sir,
I learn from Nottingham that Mr G Green is the
Son of a Miller, who has had only a common education in the Town, but has been
ever since his mind could appreciate the value of learning immoderately fond of
Mathematical pursuits, and which attainments have been acquired wholly by his
own perseverance unassisted by any Tutor or Preceptor; he is now only 26 or 27
years of age of rather reserved habits attends the business of the Mill, yet
finds time for his favourite Mathematical reading-
Your obt. servant
Thos
Fisher
A rare glimpse of the personality of George Green - who was actually 35
years old at the time!
Yet it was some two years before good fortune put George Green in
communication with Bromhead. He invited Green to Thurlby Hall, thus starting a
remarkable relationship between the Nottingham miller and the baronet.
Bromhead encouraged Green to write three further 'memoirs', two of which
Bromhead caused to be published by the Cambridge Philosophical Society. One was
'Mathematical Investigations Concerning the Laws of Equilibrium of Fluids
analogous to the Electric Fluid' and the other 'On the Determination of Exterior
and Interior Attractions of Ellipsoids of Variable Densities'.
At the same time Green was working on hydrodynamics and his paper
'Researches on the Vibrations of Pendulums in Fluid Media' was sent by Bromhead
to the Royal Society of Edinburgh, of which he was a Fellow. Green now had a
growing reputation and could perhaps have taken his place amongst the eminent
men of science of his time. However, he was still aware that he was a working
miller whereas the acquaintances of Bromhead were very much gentlemen.
Bromhead's friends at Cambridge had included Charles Babbage who later did so
much on 'calculating engines', John Herschel, son of the Astronomer Royal
William Herschel and himself to become a noted astronomer and George Peacock,
later to be a Professor of Astronomy.
In 1833 Bromhead invited Green to meet some of his old friends at
Cambridge. Green replied 'You were kind enough to mention a journey to
Cambridge on June 24th to see your friends Herschel, Babbage and others who
constitute the Chivalry of British Science. Being as yet only a beginner I think
I have no right to go there and must defer that pleasure until I shall have
become tolerably respectable as a man of science should that day ever arrive.'
Cambridge
The possibility of his going to Cambridge as a student had already been
mentioned by Green earlier that year '. . . you are aware that I have an
inclination for Cambridge if there was a fair prospect of success. Unfortunately
I possess little Latin and less Greek and have seen too many winters, and am
thus held in a state of suspense by counteracting motives.' Bromhead
recommended his own college of Gonville and Caius where he had influence. Green
leased the milling business and the family house, resigned from Bromley House
Library and in October 1833 was admitted as an undergraduate to Caius College.
He was forty years old.
Many of the undergraduates at the college did not come for the higher
learning that the University could offer. They were sent by their families to
complete their education and there were many temptations placed before them. The
poet Byron, there in 1807, has written to a friend 'This place is wretched
enough - a villainous chaos of sin and drunkenness: nothing but Hazard and
Burgundy, hunting, mathematics and Newmarket, riot and racing . . . We have
several parties here and this evening a large assortment of jockeys, gamblers,
boxers, authors, parsons and poets, sup with me - a precious mixture but they
get on well together.'
Whilst such a life may have suited Byron it is likely that Green spent his
time more industriously for, as well as studying mathematics, he had to pass
examinations in Latin, Greek and Ecclesiastical History. Green was listed as
Fourth Wrangler in the Senate House examination in January 1837 and his
reputation stood high. He was awarded the Perse Fellowship at Caius which gave
him a very modest allowance of ten pounds per annum, presumably enough to allow
him to continue his studies. Green published further papers, this time on wave
theory: two on hydrodynamics of wave motion, two on the reflection and
refraction of sound waves and two upon the reflection and refraction of light.
Bishop Harvey Goodwin, at that time an undergraduate at Cambridge, later
wrote of Green that
'He stood head and shoulders above all his contemporaries inside and outside
the University.'
photo: Ian Crosby
Alas, only six months after his election to the Fellowship, in 1840, Green
returned to Nottingham for the last time. In the words of his cousin William
Tomlin
'He returned, indisposed after enjoying many years of excellent
health in Sneinton, Alas, with the opinion that he should never recover from his
illness and which became verified in little more than a year's time by his
decease on 31st May 1841.'
Green's obituary in the Nottingham Review reveals the lack of recognition
of his achievements at that time.
In our obituary of last week, the
death of Mr Green was announced; we believe he was the son of a miller,
residing near to Nottingham but having a taste for study, he applied his gifted
mind to the science of of mathematics, in which he made rapid progress. In Sir
Edward Ffrench Bromhead, Bart., he found a warm friend, and to his influence he
owed much, while studying at Cambridge. Had his life been prolonged he might
have stood eminently high as a mathematician.