# Mary Cannell's book on George Green

Mary Cannell published

*George Green: Mathematician and Physicist 1793-1841: The Background to His Life and Work*in 1993. A second edition was in the process of being published when she died and it appeared in 2001. We give below information about these two editions including extracts from Prefaces, and extracts from reviews.**From the Publisher of the First Edition.**

George Green was a pioneering 19th-century mathematical physicist, whose work influenced modern physics. He was by trade a miller, of scant formal education until most his finest work was complete. Then, at the age of 40, he went to Caius College, Cambridge, to read for a degree in mathematics. He was without public recognition during his lifetime, and it was Kelvin who saw the importance of his work and gave it wide publicity. Today, Green's function technique has been adapted to quantum mechanical problems in areas as diverse as nuclear physics, quantum electrodynamics and superconductivity. This biography's publication coincides with the bicentenary of Green's birth.

**From the Preface to the First Edition.**

This is a story written to interest the lay reader as much as the scientific specialist. Detailed discussion of Green's published papers has therefore been avoided, with the exception of the Essay of 1828, the main points of which are discussed in Appendix I.

The facts relating to George Green and the history of his family have already been detailed in two publications. The first was the monograph of 1945 by the late H Gwynedd Green, who was the pioneer in researching the life of George Green. As a graduate of Caius College Cambridge he developed a lifelong interest in Green, which he pursued during the thirty-three years he spent in the Mathematics Department of Nottingham University, and until his death in 1977. I am very grateful to H G Green's daughter, Mrs H M Bacon, for permission to make unrestricted use of her father's work.

The second account of the Green family may be found in the middle section of the Nottingham Museum booklet George Green, Miller, Snienton, published in 1976. This was written by the then Senior Archivist of the Nottinghamshire Record Office, Mrs Freda Wilkins-Jones, who was able to trace a more detailed picture of the family history from its Saxondale origins through to its apparent extinction this century. I am glad to acknowledge her important contribution to the history of the Green family and the additional information she kindly allowed me to use in my previous publication. The account of Green's relations with Sir Edward Bromhead would not have been possible without reference to the correspondence originally discovered by Dr J M Rollett and painstakingly transcribed and published in the last section of the Castle booklet by its editor, Mr David Phillips, then Keeper of Art at the Castle Museum. I am indeed grateful to Mr Phillips for his generous and spontaneous agreement to my use of this material, as I am for the guidance given in his account when I retraced his steps on visits to Gonville and Caius College Cambridge.

As these two publications were out of print, it was thought desirable to republish this valuable material, and incorporate it into a narrative which would also aim to fill in some of the background to episodes in George Green's life, in a form which would appeal to the general public. The time was appropriate, since the restoration of Green's Mill has brought many visitors to Nottingham, curious to know more of the life of the mathematician. There was also the fact that the bicentenary of George Green's birth is due to be celebrated in 1993.

In researching Green's background, I was given invaluable help by a number of people. One of the first of many kind friends was Dr ] M Rollett who, having previously located the Bromhead correspondence, readily and generously shared his findings on Bromhead and Cambridge, and later his genealogical researches on the Green descendants. Mrs Anne German (nee Bromhead) offered a warm welcome on my visits to Thurlby to discuss the history of her family. I am indebted to her and to her husband, Mr Robin German, and also to Mr James Hall and his sister, Mrs Elizabeth Draper, descendants of George Green Moth's first marriage, for permission to reproduce the Green-Bromhead correspondence, the silhouette portrait of Edward Bromhead and the photographs relating to the Green family. Copies of these documents have been deposited in the Department of Manuscripts and Special Collections, Hallward Library, University of Nottingham. I owe much to the University Librarian, Mr Peter Hoare, and his colleagues, in particular Dr Dorothy Johnston, Mr Neville Green and Mr Michael Brook, for their unfailing help and resource. Mrs Joan Taylor and Mrs jane Corbett, her successor as Librarian of the Nottingham Subscription Library at Bromley House, provided ready access to the Library's minutes and records. I am likewise grateful to Mr Adrian Henstock, County Archivist, and his Deputy, Mr Chris Weir, at the Nottinghamshire County Record Office; and to Mr Stephen Best, until recently at the Nottingham County Library, especially for his detailed knowledge of Sneinton.

Some of the most rewarding hours working on this biography have been spent in Cambridge. Naturally, Green's college, Gonville and Caius, provided much essential information, and I must record my gratitude to those who welcomed me there and offered me their knowledge and friendship ... From Caius, the Green trail took me to Queens' College, where the Curator of the Old library, Mr Iain Wright, and Mrs Clare Sergent, shared with me the excitement of investigating Isaac Milner's inventories, and Dr John Twigg, College historian, provided valuable information on John Toplis. Miss Anne Stow, Secretary of the Cambridge Philosophical Society, produced minute books and records which allowed me to trace Green's connections with the Society, and in particular to investigate the intriguing discovery of the Jacobi papers. Mr Nicholas Smith, Librarian in the Rare Books Reading Room at the University Library, and Mr Michael Petty, at Cambridge County Library, each provided most useful material on Cambridge booksellers.

The project of writing this memoir would not have materialised without the loyal support of friends who are interested in making the name of George Green more widely known. From the beginning, Professor Lawrie Challis has been constant in his encouragement and practical help. It has proved both a privilege and a pleasure to support him and his colleagues in their project of establishing wider recognition in the scientific community and in the public mind at large for the genius of George Green. In particular I am most grateful to Professor Challis for reading the script and writing the Foreword.

Full appreciation of the scope and depth of Green's work is arguably possible only for the mathematician and physicist working in reasonably advanced areas of their discipline. It was felt, however, that some indication of its character should be provided. This has been done with clarity and conciseness by Mr Michael Thornley who, despite other claims on his time, produced Appendix I, which contains an analysis of Green's Essay of 1828 and an interpretation of some of its more archaic features for the benefit of modern scientific readers. I am most grateful to him for an indispensable contribution to this biography. Dr John Roche, of Linacre College Oxford, gave long-term support and encouragement; his suggestions and much-needed critical appraisal of the script are gratefully acknowledged. A collaborator of long standing is Mr Laurence Tate, who, with his daughters Helena and Barbara, typed and processed numerous drafts of the text with limitless patience and understanding. The production of this book would not have been possible without their expertise and sustained interest. Neither would it have been possible without the detailed help and advice I received from the Chairman of The Athlone Press, Mr Brian Southam, and his colleagues, Mrs Gillian Beaumont and Ms Helen Drake, who guided a first-time author through the unfamiliar paths of professional publication. Mr David Williams most kindly gave his time to read through the proof sheets of the text. I would like to acknowledge the co-operation of Chas, Goater and Son in providing copies of two illustrations from my previous publication. Most generous support in the publication of this biography has been given by the Physics Department of Nottingham University, the George Green Memorial Fund and the Barbara Dalton Trust of the Sneinton Environmental Society. Lastly, I would like to thank my family and my many friends and correspondents who, over a number of years, never failed in their interest and encouragement, particularly when it was most needed!

It will be evident, both from these acknowledgements, and from the Notes to the text, that the writer of this narrative has functioned more as editor than as prime researcher. In bringing together from many different sources the various pieces of information which constitute the life of George Green. I may perhaps, in common with others, claim with Montaigne: 'I have gathered a posy of other men's flowers and nothing but the thread that binds them is my own.'

**Review of the First Edition by: Rafe Mazzeo.**

*Mathematical Reviews*MR1287845**(95j:01029)**.

George Green, best known for his eponymous formula and for his discovery of "Green's function'' for the Laplace operator, had a much different background than other "gentleman-scholar-mathematicians'' in England in the early nineteenth century. Born the son of a miller near Nottingham, he had very little formal schooling, and worked until the age of 40 as a miller himself. His first mathematical work, an essay on electricity (in which he introduced the two concepts mentioned above), was written seemingly independently and with essentially no prior contact with other mathematicians. This essay, which contains his most important contributions, never received recognition during his lifetime, but was rediscovered not too long after his death by Lord Kelvin and published in Crelle's journal only in 1850. His talents recognised by Sir Edward Bromhead (1789-1855), he became an undergraduate at Caius College, Cambridge, at the age of 40, and later a Fellow there. Sadly, he held this position only for two terms, and died, possibly of influenza, at the age of 47. During his life he wrote only ten papers; his death occurred at a time when he finally could work comfortably amongst his peers.

It is remarkable how little is known about the facts of his life. There is not even a picture of him in this book! Cannell has done her research well, though, and has tracked down what few documents remain. Cannell discusses Green's family background and social milieu at some length, but must speculate about many particulars. Amongst the most interesting of these is how Green came to learn analysis as it was done on the continent at that time, rather than in the mode prevalent in England then, using Newton's fluxion notations. There are many other points about his personal and scientific life about which we may never know the answer.

This biography is written well, albeit in a rather formal style. It gives one a good sense of many facets of life in Green's time, and examines many of the social forces which hindered Green's mathematical development. A more technical treatment of his mathematics is relegated to an appendix, and is discussed clearly there. This book is certainly to be recommended.

**Review of the First Edition by: I Grattan-Guinness.**

*Isis***85**(4) (1994), 707.

... for more than a century Green's work has been standard fare - and not only known but even read and reprinted. The bicentenary of his birth was marked in July 1993 by the exceptional event of the unveiling of a plaque in Westminster Abbey in London, around others for Kelvin, Michael Faraday, and James Clerk Maxwell. Among celebratory events of the week was a day meeting at the Royal Society, where D M Cannell and I spoke on Green's life and work, respectively.

That meeting followed soon after the publication of this biography of Green. The author sets his career in the context of contemporary British mathematics, and also of French work that was to influence him profoundly; the story is not completely accurate in historical or mathematical detail but presents a fair and balanced portrait. Cannell also records the limited encouragement that Green received from contemporaries and Thomson's posthumous publicity for his achievements. She continues past Green's death to offer an account of the lives and deaths of his seven illegitimate children; their descendants, reunited shortly before the ceremony described above, laid wreaths on the plaque. Some technical details of Green's mathematics (although not their full historical setting) are furnished in a useful twenty-two-page appendix, by the mathematician M C Thorley. The plates include pictures of the mill, which was restored in full working order in 1985 and now functions also as a local science centre.

An educationist by career, the author has delved very well into archives and other sources in and around Nottingham to reveal the story of Green's life there and the interlude at Cambridge. Her diligence deserves much praise, for virtually no primary sources survive - no manuscripts, very few letters, not even a portrait. Overall, the volume is an excellent attempt to present an exceptionally fugitive figure and deserves regular use by students of Green and his times.

**Review of the First Edition by: Eric H Mansfield.**

*Notes and Records of the Royal Society of London***48**(2) (1994), 321-322.

Most mathematicians will have used, or at least know of, Green's Theorem and Green's functions, but they are probably unaware of the unusual background of their eponymous creator. Green also made pioneering contributions in electricity (where he introduced the term 'potential'), magnetism, hydrodynamics, elasticity, sound and light. Indeed, the intellectual profundity of his work, albeit encompassed in a mere ten publications, was recognised on the 200th anniversary of his birth, by the dedication of a plaque in Westminster Abbey where his name will be found amongst the greatest British men of science - Isaac Newton, John Frederick Herschel, Michael Faraday, James Clerk Maxwell, Lord Kelvin, George Gabriel Stokes, Lord Rayleigh, Lord Rutherford and J J Thomson. All of these had their work recognised during their own lifetime; in marked contrast, George Green, on his death, earned only a modest paragraph in a local newspaper as his sole obituary, and a grave neglected and forgotten for nearly 100 years. There are no portraits or photographs of him, no diaries or working papers, and little in the way of correspondence. Mary Cannell's book, which is written to interest the lay reader as much as the scientific specialist, provides the background to Green's unusual life and work.

George Green was the only son of a Nottingham baker, George Green Senior, who had prospered sufficiently to build a windmill at Sneinton, a village just outside the town boundary, to grind his own corn. As a young child George had shown an aptitude for mathematics, so much so that he was sent at the age of eight to the town's leading academy. After only four terms he had learnt all the mathematics and science that his masters could teach him, so he was set to work in his father's bakery and mill. Little is known of him during this period until, aged 30, he joined the Nottingham Subscription Library, where he had access to books, journals and periodicals that must have been of great help to anyone who was self-taught, as he had been since his four terms of formal education. His first and greatest work 'An Essay on the Application of Mathematical Analysis to Theories of Electricity and Magnetism' was published in 1828 by private subscription but, largely because of its limited circulation, it attracted scant attention. Despondently, Green returned to full-time milling until in 1830 he met local landowner and mathematics graduate, Sir Edward Bromhead, who recognised the originality of Green's work and encouraged him to resume his mathematical studies. This he was now able to do because, following his father's death in 1829, he found himself sufficiently affluent to be able to dispose of the family business and devote himself wholly to mathematics. Three further papers followed until, at the age of 40, he enrolled as an undergraduate at Cambridge University, taking the Mathematics Tripos in 1837 and being elected into a Caius College Fellowship in 1839. During this period he published a further six papers, but ill health compelled him to leave Cambridge some two terms after his election and he returned to Nottingham, where he died in May 1841, aged 47.

The above were the bare bones of George Green's life. To flesh it out, the author, Mary Cannell, spent several years as a researcher-cum-detective following up all known leads, many of which led to her interviewing people throughout the country and even as far afield as Melbourne, Australia. The resulting book must be regarded as the most complete account possible of Green's life. From a historical viewpoint, it also sheds much light on the social mores of the time. ...

**Review of the First Edition by: Crosbie Smith.**

*The British Journal for the History of Science***27**(4) (1994), 477-479.

On the one hand, we have the legacy of path-breaking mathematical texts, most notably 'An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism' (1828), and of mathematical techniques integral to the practice of modern theoretical physics. On the other hand, we have some fragmentary knowledge of Green as an apparently self-taught Nottingham miller whose privately printed 'Essay' appeared several years before its author's entry into Cambridge University. Such is the dichotomy that many a historian of science might be tempted to accept the irrecoverable nature of the author's life and to focus instead on analysis of the texts and their subsequent reworking in the hands of Thomson and later generations of mathematical physicists.

In her eminently readable biographical study, Mary Cannell accepts no such limitations. Instead, she 'sets out to investigate the circumstances in which Green found himself, to place the known facts in their context, and to trace the different stages of his life in which he produced his various investigations'. She has succeeded exceptionally well in recovering a great deal of highly revealing material which she uses very effectively to place Green in the key contexts of Nottingham and Cambridge. The result is a study which goes far to dispel historical myths of an archetypal British scientific genius as an isolated and heroic individual. The picture which emerges in Cannell's account is very different. Freed by his father from the constraints of rural life through economic prosperity in a period of industrial growth, Green initially identified with the new leisured and gentrified classes of his locality, centred around the Nottingham Subscription Library. Transcending such local groups, however, Green subsequently engaged with a Cambridge social network which eventually brought him as a forty-year-old undergraduate to the hallowed portals of Caius College.

Cannell's researches reveal a number of crucial bridges across the apparent gulf between Green's Nottingham circle and his Cambridge mathematical associates. Central to this story was the patronage of the well-connected Sir Edward Ffrench (sic) Bromhead, graduate of Caius College, Cambridge, High Steward of Lincoln, and Fellow of the Royal Societies of London and Edinburgh. Recognising the limitations of publication by private subscription which were besetting the reception of Green's 'Essay', Bromhead told the author that he would 'feel happy in communicating any Memoir which you may hereafter compose' to the Royal Societies of London or Edinburgh. ...

...

We have Mary Cannell to thank for a thought-provoking and informative study which challenges our received images of this fascinating nineteenth-century mathematician.

**Review of the First Edition by: Jeremey Gray.**

*New Scientist*(17 July 1993).

George Green was not much appreciated in his lifetime. No portrait of him survives (if one was ever made), and we know little about his life. Indeed, until the indefatigable Mary Cannell began work, and despite the best efforts of other, active, friends of Green such as Lawrie Challis, Green was nearly an invisible man. This attractive and well-illustrated book commemorates the life and work of Green, one of the most important British mathematicians of the 19th century, whose bicentenary falls this year ... . It is a significant addition to our knowledge of him.

Although we can still only conjecture who fostered Green's talent for mathematics and guided his early reading - Cannell makes some highly plausible suggestions - we can now see clearly for the first time the milieu in which Green worked. He earned a prosperous living as a miller in Nottingham, and had access to the best new French mathematics. He wrote his remarkable Essay in 1828, in which Green's theorem and Green's functions first appeared. This work brought him to the attention of Sir Edward ffrench Bromhead, a local dignitary and Cambridge graduate, and eventually to the University of Cambridge where Green became a fellow for a brief time. During this period, he wrote his few other papers, which deal with magnetism, electricity and hydrodynamics.

Green's work was saved for posterity by William Thomson, later Lord Kelvin, who tracked down the original Essay and saw that it was republished in an influential German journal. From then on, as this book shows so well, Green's theorem and Green's functions have steadily enjoyed the attentions of mathematicians and physicists. Not only particle physics, but fields as diverse as soil science and pure mathematics, continue to benefit from these ideas. A useful account of the Essay is given here in an Appendix by M C Thornley.

Cannell also describes Green's family. His steadfast common law wife, Jane Smith, bore him seven children, all illegitimate, but if she survived what surely was a local stigma, some of the children seem to have found it harder to bear. Their lives, and the precarious path of knowledge about Green down to the present day, make fascinating reading. Indeed, the book is eloquent testimony to the difficulties and pleasures of the historian's task. It provides a lucid insight into the times, and as much as is known of the life, of one of Britain's most creative mathematicians.

**Review of the First Edition by: Philip J Davis.**

*SIAM News***29**(1996).

The*American Mathematical Monthly*frequently runs a "picture puzzle", in which the reader is asked to identify a picture of a famous mathematician. There are no known likenesses of the person I have in mind, so I will post my puzzle verbally: What mathematician, on the defeat of a piece of legislation in 1831, took up a musket to defend his property against a rioting mob?

Very few professionals - indeed, very few people of any sort - know much about this person, although every undergraduate who has taken a course in multivariable calculus is familiar with one of his major contributions: Green's theorem (Ostrogradsky's theorem in Russia). Those who have studied differential equations may remember the Green's function of a linear differential equation. Some may even have studies Green's tensors. Other than his work, though, he left behind few traces.

The scientific life of George Green was very unusual even for the day. He was born in 1793 in Nottingham, England. His father, George Green senior, was a hard-working baker who, although only semiliterate, had a good head for business. Green senior build a windmill in Sneinton, a nearby village, to grind grain for his bakery; the business prospered.

At the age of eight, young George was enrolled in a local academy run by a certain Robert Goodacre, a mathematics enthusiast. As the child already had a passion for the subject, this was a fortunate conjunction, or perhaps it was the result of a deliberate decision on the part of George senior. Young Green stayed there only for four terms, having learned all that the masters could teach him.

At the age of nine, he was taken into his father's bakery and milling business, where he worked for 27 years. Although a reluctant miller, he carried on with it until 1823, when his father died. Green later leased the mill and sold the business, and with the addition of the rents from his father's Nottingham property, found himself sufficiently wealthy to support himself as a mathematician.

The riot alluded to earlier occurred as follows:In 1831 ... angered by the defeat of the Reform Bill, a mob of angry townspeople saw the mill as an immediate target ... The mathematician vigorously defended his property by firing on the crowd, and his young daughter Jane helped him to reload his musket.

We don't know too much about Green's personal life. A dozen or so letters and a few statements by contemporaries have been uncovered. When he was in his early twenties, he formed a relationship with Jane Smith, the daughter of his father's mill manager. He never married her, and she bore him seven illegitimate children. Why didn't he marry Jane, although he provided for her and their children very nicely? The reason is unknown, but conjecture has it that his father considered Jane too lower class.

In 1828, in his mid-thirties, Green published*An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism*. Published privately and by subscription, this was his magnum opus. About a hundred copies were printed; 51 subscribers had the privilege of buying the monograph at seven shillings sixpence. From a scientific-book collector's point of view, the monograph is very rare. (The rare book library at Brown University has only a copy of a facsimile edition produced in 1889.)

In 1833, having written four major papers (three of which were published in the Transactions of the Cambridge Philosophical Society and the other in the Transactions of the Royal Society of Edinburgh) Green enrolled at the age of 40 as an undergraduate in Gonville and Caius College, Cambridge University! In 1837, at the age of 44, he took the Mathematical Tripos and ended up as Fourth Wrangler (first-class honours, nonetheless; James Joseph Sylvester, aged 23, who came in second, was the only one of the top three who went on to achieve mathematical fame.) Two years later, Green was elected to a college fellowship at Caius (pronounced "Keys"). During those two years he produced six more papers, all published in the Transactions of the Cambridge Philosophical Society.

In the course of her book, Doris Cannell asks the critical question: "If even Cambridge did not teach continental analysis and use the works of Laplace, Lacroix, Poisson, and the rest, how did a provincial miller and untutored mathematician in Nottingham come across them and use them to such advantage?"

How did he learn what he learned? How did he study and plug himself into the latest in French mathematics? By working in some remote corner of his busy, noisy, dusty mill? Why not? Don't graduate students today do their work to canned music at full blast? How did he go beyond the existing knowledge to create what he created and thus bring to a close what Sir Edmund Whittaker called the darkest century in the history of science at Cambridge University? This is the mystery alluded to in the title of this review, and it is a mystery that remains unsolved - so little is known that biographers can only conjecture. Far more is known about another mathematical autodidact who comes to mind: Srinivasa Ramanujan, who was at Cambridge almost a century later.

In 1823, at the age of 30, Green was admitted to the Nottingham Subscription Library. Located in Bromley House, it was a centre for a variety of cultural activities, including scientific and philosophical speculation and debate. The library of Bromley House (for which records are available) did not have Green's major reference: the works, in French, of Biot, Lacroix, Poisson, and Coulomb.

Green was probably familiar with the Reverend John Toplis, a headmaster of the Nottingham Free School and an enthusiast of French mathematics, whose translation of Laplace's*Mécanique céleste*was published in 1814. Perhaps Toplis, who lived not far from Green's bakery, had been Green's mentor. Perhaps Green picked up references to the French works from Toplis or his translation.

There is information on individuals (among them Sir Edward Ffrench Bromhead) who supported Green psychologically and provided entrée into the intellectual world for "the son of a miller who has had only a common education in the town." And we do not know much more than this.

Green's major work was ignored for years. Mathematical England was not ready for it. By 1845, when it was recognised by William Thomson (Lord Kelvin), English mathematical science, which had been rigidly locked into Newtonian notations and formulations, had rejoined the Continent.

Green died in 1841. The cause of death was given as influenza, although it has been suggested that he had "miller's disease", a condition something like silicosis, caused by the flour and the dust-laden atmosphere of a mill. Felix Klein, writing in Germany 50 years after the fact, asserted that Green had died of alcoholism.

He died a wealthy "gentleman", a technical term in 19th-century England. His direct descendants are numerous. There is now a considerable George Green Memorial Fund, which, among other things, has restored the windmill to grinding condition and has established an adjacent museum of science of considerable popularity. There is a plaque to him in Westminster Abbey. In 1993, the bicentenary of Green's birth was celebrated in Nottingham, and at Gonville and Caius. The restored mill was on display, along with a number of Nobelists who, in their work in quantum mechanics, have made use of Green's function. A few numerical analysis, especially those who have promoted the finite element method, might also have been invited, for their work also carries the mark of Green.

This is the first substantial biography of Green, a man who was remarkable in his own day. Unique? Perhaps not. Boole, Faraday, and Whewell came from humbler circumstances. The author, in the absence of the vast quantities of material that allow the 700-page biographies so common today, has put together all that is now known. She has amplified it with an informative picture of science at Cambridge in the early 1800s - about which much is known. She has also included a nice mathematical appendix explaining the work of George Green; the author of the appendix, Michael C Cramley writes in conclusion: "He was a self-taught genius who provided one of the bridges between the earlier generations of Laplace and Lagrange, and the later generations of Thomson and Maxwell." There are many references to today's literature, on quantum theory, for example, where Green's ideas are employed.

Even with enough material for a 700-page biography, the final creative leap from the study of the masters to that which goes beyond, whether in the case of Green or any other mathematician, has been described only unsatisfactorily. The psychology of mathematical invention, despite the work of Jacques Hadamard and later writers, remains an enigma. The George Greens of the world cannot be programmed.

**Review of the First Edition by: David Sarpe.**

Mathematical Spectrum 26 (2) (1993/4), 61-62.

Why has the same picture of a windmill appeared in two issues of*Mathematical Spectrum*(Volume 20, Number 2, 1987/88 and Volume 25, Number 3, 1992/93)? This is the windmill in Sneinton, Nottingham, where George Green (1793-1841) was miller. Most of his life was spent in obscurity in Sneinton; no picture of Green could be unearthed for this biography. What education he had until he went as an undergraduate to Gonville and Caius College, Cambridge, at the mature age of 40, can only be surmised, but he was largely self-taught. Yet, at the age of 35, while still in Sneinton, he wrote 'An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism' containing startlingly new ideas with applications not only to electricity and magnetism but also in our own century to semiconductors, superconductors, atomic and nuclear forces and quantum mechanics. As Einstein remarked, Green anticipated the work of other mathematicians, especially Gauss. His essay went almost completely unnoticed, as did his later mathematical works. His struggle against the prejudices of his day, the discovery after his death of his work by Lord Kelvin, and the efforts in our own day to obtain due recognition for one of the finest and most original mathematicians that Britain has ever produced are movingly told in the present volume. Unfortunately, its high price will prevent most readers from obtaining their own copy, a poignant reminder perhaps of the battle over the years to make the name of George Green known,

Happily, however, the battle has finally been won. Generations of students of mathematics and physics know his name as they grapple with Green's theorem and Green's functions. But do they know who Green was? What would George Green have thought if he could go now to Westminster Abbey and see a plaque inscribed with his name alongside such greats as Isaac Newton and Michael Faraday; and then go to Sneinton to see his windmill in action and coffee mugs decorated with his mathematics being sold in the visitors' centre? It's a funny world! Read this book if you can get hold of a copy. If not, read the article in*Mathematical Spectrum*by Professor Lawrie Challis to whom the book is dedicated and who has done more than anyone in our own day to obtain public recognition for George Green. Then go to Westminster Abbey and honour a great mathematician. Finally, go to Sneinton. You can even buy a mug!

**Table of Contents of Second Edition.**

Foreword

Introduction

In Memoriam: Mary Cannell

1. Family Background

2. George Green's Education

3. Cambridge Interlude

4. Bromley House Library and the Essay of 1828

5. Sir Edward Bromhead

6. The Publication of George Green's Further Investigations

7. An Undergraduate at Cambridge

8. A Fellowship at Caius College

9. George Green's Family

10. William Thomson and the Rediscovery of the Essay of 1828

11. 'Honour in His Own Country'

Appendix I. The Mathematics of George Green by M C Thornley, formerly of the Mathematics Department, Nottingham Polytechnic

Appendix II. Mathematical Papers of George Green

Appendix IIIa. Account by William Tomlin, Esq.: 'Memoir of George Green, Esq.'

Appendix IIIb. Account by Sir E Ffrench Bromhead

Appendix IVa. Green Family Tree

Appendix IVb. Butler Family Tree

Appendix IVc. Smith Family Tree

Appendix IVd. Tomlin Family Tree

Appendix Va. Time Chart of British Mathematicians and Men of Science

Appendix Vb. Time Chart of Other Mathematicians and Men of Science

Appendix VIa. The Greening of Quantum Field Theory: George and I by Professor Julian Schwinger

Appendix VIb. Homage to George Green: How Physics Looked in the Nineteen-Forties by Professor Freeman Dyson

Notes

References I. Biographical

References II. Scientific

Index.

**From the Publisher of the Second Edition.**

Mathematicians and lay people alike will enjoy this fascinating book that details the life of George Green, a pioneer in the application of mathematics to physical problems. Green was a mathematical physicist who spent most of the first 40 years of his life working not as a physicist but as a miller in his father's grain mill. Green received only four terms of formal schooling, and at the age of nine he had surpassed his teachers. Green studied mathematics in his spare time and in 1828 published his most famous work,*An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism*. It was in this essay that the famous Green's Theorem and Green's functions first appeared. Although this work was largely ignored during his lifetime, it is now considered of major importance in modern physics.

**From the back of the book.**

Green was a mathematical physicist who spent most of the first 40 years of his life working not as a physicist but as a miller in his father's grain mill. Green received only four terms of formal schooling, and at the age of nine he had surpassed his teachers. Green studied mathematics in his spare time and in 1828 published his most famous work,*An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism*. It was in this essay that the famous Green's Theorem and Green's functions first appeared. Although this work was largely ignored during his lifetime, it is now considered of major importance in modern physics.

This is the first major biography of Green, and the most complete picture of Green's life and education, available today. Green is presented as a person rather than as merely the inventor of a mathematical function. The updated second edition includes a new section of scientific references along with the lectures given by Julian Schwinger and Freeman Dyson at the bicentenary celebration of George Green's birth held at the University of Nottingham in 1993.

**From the Preface to the Second Edition.**

There had always been the hope that the biography of George Green, originally published in 1993, would at some time be reprinted, since this would make the story of Green more readily available to a younger generation of scientists. There are few who do not come across Green's functions and his Theorem in the course of their studies and some will continue to use them throughout their careers.

Recently, it has become evident that there is increasing interest in the history of mathematics and in science as a whole. In addition to research in the development of ideas and concepts, there is a parallel curiosity about the men who produced them. As in the case of Green, some were the victim of circumstances; their work and their lives were shaped by various factors in the period in which they lived, their social status, the people they met and the degree of understanding with which their findings were received. Each individual case adds to the general picture; recent research has brought George Green more clearly into focus.

My thanks are due to SIAM, and in particular to Professor Robert E O'Malley Jr., for making the present reprint possible. One deficiency in the original publication was the sparse information concerning contemporary awareness of the nature of Green's wider contribution to modern physics and technology. To some extent this has been remedied by the addition of a new appendix and an expanded list of scientific references. The last chapter of the Green narrative now includes an account of the Bicentenary Celebrations of his birth in 1993, only in the planning stage at the time of the original publication. These included two major events: national recognition of George Green through the dedication of a plaque in his honour in Westminster Abbey in London, and international recognition through public lectures given in the University of Nottingham. These were delivered by two of the leading scientists in quantum electrodynamics of this century, Julian Schwinger, Nobel Laureate, and Freeman Dyson, F.R.S., of the Institute of Advanced Study, Princeton University, Princeton, New Jersey. Schwinger would seem to have been the pioneer in giving Green's functions a fresh and vigorous life in quantum physics. His lecture, along with Freeman Dyson's account of his earlier work in quantum field theory, throws light on a recent period of research of interest to younger mathematicians and scientists. Discussions of Green's importance in modern physics and technology are to be found in notes of lectures given during the Bicentennial Commemoration at the Royal Society in London ... .

Major acknowledgements are recorded with gratitude to Mrs Clarice Schwinger, who generously agreed to the inclusion of her late husband's paper on Green, and to Professor Freeman Dyson, who equally generously agreed to my including his paper. My debt to those who earlier gave permission for the inclusion of material in the original publication still stands high. Indeed a retrospective view of its reception would indicate a strong interest in the circumstances of Green's life. This confirms the importance of the two main sources which supplied the essential information. The first is the original research by H Gwynedd Green into the life of the mathematician and his family in Nottingham, and I would like to reiterate my thanks to his daughter, Mrs Hazel Bacon, for the use of this essential material. The unique glimpse (in the absence of other material) into George Green's mind and character is found in his letters to his patron, Sir Edward Bromhead, and I am grateful to his descendant, Mrs Anne German, for continuing to provide access to the family papers. For a non-mathematician, the help of a former collaborator, N J Lord, has proved invaluable, particularly in providing the notes on lectures given at the Royal Society Commemoration. Since 1993, the considerable importance of Appendix I by M C Thornley has become apparent. It takes readers to the coal-face, as it were, by introducing and elucidating the actual text of Green's famous and seminal Essay of 1828. I would like again to express my gratitude to him for providing such a significant contribution to our presentation of Green.

Professor Lawrie Challis, as in the past, has continued to give his stalwart support to this further development in the fortunes of George Green. Despite manifold scientific and professional pressures, he has always been ready, with his customary tact and wisdom, to offer help, share problems, and give advice when requested. I would also like to thank Mrs Jennifer Challis who, of similar mind and spirit, was most helpful at a particularly crucial time.

As an adopted member of the Nottingham University Physics Department, (now the School of Physics and Astronomy), I wish to express appreciation of much friendliness, interest and valued help; to Professor Colin Bates, Head of the Department and his colleagues; to Mrs Linda Wightman, for her efficiency, patience and good humour in acting as an unofficial secretary over the Green years; and to Mr Terry Davies, Department photographer, who provided additional photographs, including the highly prized one, taken in less than ideal circumstances, of Professors Schwinger, Dyson and Challis in conversation in the Physics Department after the public lectures. The equally prized lectures in the present volume are reprinted from the Nottingham University*Gazette*by kind permission of the University. I would also like to express my grateful thanks to Ms Deborah Poulson, Developmental Editor at SIAM, for her guidance in preparing the reprint for publication; her patience and quick response to queries have been much appreciated. Finally I must record deep gratitude to a recent collaborator, Mr John Clayton, whom I had the good fortune to meet a few years ago. With his professional experience and expertise, he has combined the services of word-processor operator and copy editor; without his generous help, this reprint would not have been possible.

**Review of the Second Edition by David Graves.**

*Mathematical Association of America*, Review.

https://www.maa.org/press/maa-reviews/george-green-mathematician-and-physicist-1793-1841-the-background-to-his-life-and-work

We all know about Green's theorem, and applied mathematicians probably know about Green's functions, but details of Green's life may have eluded many of us. A perusal of thirteen calculus or advanced calculus books on my shelves found nine stating Green's theorem without any mention of the person behind it, while the other four gave his first name and dates (but no other information). History of mathematics books in most cases do not go much further: Burton and Eves have just one page reference in the index for Green, and Boyer and Katz are only slightly more generous. If we rely on such sources, we are left to imagine perhaps a conventional British gentleman making his way through the usual educational steps, then embarking on a career of teaching and research.

In fact, George Green was the son of a prosperous miller (George Green Senior) at Sneinton, at the time a village about one mile from Nottingham. A notable near contemporary of Green's was (General) William Booth of Salvation Army fame, born in Nottingham in 1829. As a youth Green had only four terms of formal education (not uncommon for the time), and at the age of nine went to work at the bakery that was part of his father's milling operation. Green continued mathematical and scientific study on his own, possibly with the aid of a tutor. He became acquainted with Jane Smith, daughter of the mill manager, and fathered seven illegitimate children by her from 1824 to 1840. In 1828 Green published privately, through the Nottingham Subscription Library, his first and most important paper: "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism." Fifty-one individuals "subscribed" to this publication, but few of them could have understood any of it. One of these, however, Sir Edward Ffrench Bromhead, had contributed an article on calculus to the*Encyclopaedia Brittanica*, and recognised the worth of the Essay. Green had enough money on the occasion of his father's death in 1829 to sell the business and pursue mathematics, shortly producing another paper, this one on fluid equilibrium. Bromhead and Green were in communication, and eventually met, and Bromhead helped Green have the second and a subsequent paper published by the Cambridge Philosophical Society. In 1833, we find Green, at the age of forty, arriving at Cambridge to begin undergraduate studies at Gonville and Caius College. He completed his B.A. by 1838, and became a Fellow of the College, but ill health forced him to retreat to Nottingham, where he died in 1841. The cause of his death was listed as influenza, but biographer Mary Cannell suspects "miller's disease," a condition caused by the flour and dust present in a mill, and analogous to lung disease afflicting coal miners. Other accounts wonder if excessive alcohol consumption might have contributed to his demise. Green's total output consisted of ten papers on mathematical analysis of electricity and magnetism, and of wave motion of fluids, sound, and light. The all-important Essay of 1828 was little known until rediscovered in 1845 by William Thomson (later Lord Kelvin), who arranged to have it republished in three parts in Crelle's*Journal*(1850, 1852, and 1854).

The book under review is the second edition of a work published by Althone Press in 1993, Green's bicentenary year. Features new to this edition are: inclusion in the final chapter of an account of the Green bicentenary celebration that was held in Nottingham, Cambridge, and London; an expanded list of scientific references; and a new appendix containing the bicentenary talks given at Nottingham University by Julian Schwinger and Freeman Dyson. After Cannell's prefaces to each edition, there is a brief Foreword by Lawrie Challis (Nottingham physics professor) that includes Edmund Whittaker's claim that Green should be described as the real founder of the "Cambridge school" of natural philosophers (e.g., Kelvin, Stokes, Rayleigh, and Maxwell), and the observation that not only were Green's theorem and functions important tools in classical mechanics, but were revived with Schwinger's 1948 work on quantum electrodynamics that led to his 1965 Nobel prize (shared with Feyman and Tomonaga - later in the book Sylvan Schwebe is quoted as suggesting Dyson should also have had a share of the prize). Green's functions later also proved useful in analysing superconductivity, and Dyson ends his talk saying he would not be surprised if Green's functions were eventually to be reincarnated in superstring theory. An Introduction by Challis outlines what is known of Green's life, and is followed by "Mary Cannell: In Memoriam" - she died in April of 2000 before the second edition had been published.

The bulk of the book is Cannell's 179-page biography of Green. It is meticulously researched, as 44 pages of Notes attest, but it also includes a certain amount of speculation, since our record about Green's life is far from complete: there are no portraits of Green, and much correspondence is missing. Among several possible scenarios that the author constructs from scanty evidence is that after Green's brief elementary education at Goodacre's Academy, his father employed as mathematics tutor for his son one John Toplis, headmaster of the local grammar school. Toplis was a Cambridge graduate who had translated the first book of Laplace's*Mécanique Céleste*, and who in 1819 returned to Cambridge as a Fellow and Dean of Queens' College. He was instrumental in introducing continental - especially French - mathematics to a tradition-bound Cambridge (and Royal Society), so that fluxion notation was finally superseded by that of Leibniz, and the works of Laplace, Lagrange, Legendre, Poisson and others sparked a revival of learning. Further speculation is that Green was aware of these French analysts through the efforts of Toplis, and was therefore mathematically up to speed when he arrived at Cambridge in 1833, by which time (page 41) "... continental analysis was the accepted form of mathematics."

Mention of Toplis and French mathematics leads Cannell to report extensively on the educational and scientific situation in France, and there are similar detours throughout the narrative. Some of them are fascinating, such as the vivid description of windmill workings and conditions (pages 6-7), but the excursions into the founding and facilities of the Nottingham Subscription Library, various branches of Green's family (or of his common-law wife's family), the restoration of Green's mill, etc., may try the patience of some readers. Mary Cannell's background was in French language and literature and in school administration, and she understandably keeps the mathematical details at arm's length. She certainly acquired, though, a solid knowledge of who the important mathematicians and scientists of the time were: in addition to the names already mentioned, there is material on Babbage, Cayley, Coulomb, Gregory, Hamilton, Jacobi, Stokes, and many others. She reminds us that Boole and Faraday, like Green, were self-taught, points out that Sylvester left Cambridge in 1837 because "... as a Jew he was denied a degree on religious grounds" and that De Morgan "... left Cambridge for London, since as a Unitarian he was debarred from a Fellowship." [In fairness, she also tells us that both Cambridge and Oxford removed all such religious restrictions in 1883.] There is a wealth of detail in the biography, and those mainly interested in the mathematician and the mathematics may need to employ some skimming or speed-reading techniques.

Following the biography, there are several appendices. Appendix I ("The Mathematics of George Green" by M C Thornley) is an analysis of the 1828 Essay, quoting and commenting on several passages. A second appendix simply lists Green's ten published papers, and Appendix III contains two very brief accounts of Green's life by two contemporaries, William Tomlin (a brother-in-law) and Bromhead. The next two appendices give the Green, Butler, Smith, and Tomlin family trees, and time charts of mathematicians and scientists mentioned in the text. The two-part Appendix VI (new to the second edition) is an outstanding addition to the volume. It consists of Julian Schwinger's wittily titled "The Greening of Quantum Field Theory: George and I" and "Homage to George Green: How Physics Looked in the Nineteen-Forties" by Freeman Dyson. It is here that we learn how the nineteenth-century Green's functions took on new life and meaning in the second half of the twentieth century. The book concludes with the Notes on chapters of the biography (and one page of Notes on Thornley's contribution), four pages of biographical references on Green, five pages of scientific references, and a list of four websites (one discussing the Moon's George Green crater).

This is an interesting, if somewhat uneven, package of a book that is an obvious choice to be ordered for any college or university library, and will be a welcome addition to the personal libraries of those interested in the recent history of mathematical physics.

**Review of the Second Edition by: I Grattan-Guinness.**

*SIAM Review***44**(1) (2002), 144-145.

Sadly, the author died in 2000 before the edition was published; it seems to have been seen through the press by Lawrie Challis of the University of Nottingham, who contributes a short appreciation. Her main text is left unchanged, so that a few gaffes still remain: for example, that Green introduced the principle of conservation of energy in his book or that his old college published the edition of his works in 1871.

The new material is very welcome, but the book still suffers a considerable lacuna. The place of Green's contribution in modern physics is conveyed, especially in the new lectures; but then its important place in classical physics is restricted to brief summaries of Green's later papers in the last pages of Thornley's appendix and a few general remarks in the text about the popularisation of the book by William Thomson (Lord Kelvin) during the 1850s. A vast tale is still missing, especially for the second half of the 19th century: the great rise of potential (Green's word) theory in the development of mathematical physics, the discovery of further volume/surface and area/contour theorems, the controversial deployment of Dirichlet's principle (which Green had found independently), the ever-widening range of applications, profound "pure" questions such as conditions for uniqueness of potentials and distributions and the existence of the attendant integrals, and so on. Some interesting historiographical questions arise: in particular, both Schwinger and Dyson stress the importance of Green's functions in the modern contexts, whereas in the classical period Green's theorem seems to have gained rather more attention. A third edition would be welcome, with a substantial new chapter reviewing this story, which led to Green becoming a scientific household name by the late 19th century.

Last Updated December 2021