乔治·格林George Green

乔治·格林的父亲也叫格林，是诺丁汉的一名面包师。在诺丁汉当完面包师学徒后，格林老先生于1791年与萨拉·巴特勒（数学家的母亲）结婚，萨拉的父亲曾帮助格林老先生在诺丁汉的惠特谢夫院买下了自己的面包房。格林和萨拉育有一子一女。儿子就是数学家格林，虽然他的出生日期不详，但他于1793年7月14日受洗。他的妹妹安两年后出生，由于面包房生意兴隆，家境还算富裕。

1800年9月，英国因食品价格高涨、人们吃不饱而发生骚乱。粮食商人和面包师被指责囤积食物以待价格进一步上涨，成群的人闯入面包店试图偷取食物。格林的面包店遭到袭击，于是他给市长写了一封信请求保护（拼写和大写字母遵循格林的信件）：-

1800年9月1日 致尊敬的市长及诸位同仁：昨夜我所有的窗户都被打破，今晚又受到更多破坏的严重威胁，例如有人闯入我的房子，因此先生们，我极其谦卑地恳求您的保护，持此信者可以向您说明一切。您谦卑的仆人格林。

格林于1801年，即骚乱后的那一年，进入Robert Goodacre的学校。他开始上学时年仅八岁，1802年仲夏离开学校时年仅九岁。因此，他仅有的学校教育只有四个学期，但尽管在那里时间短暂，由于Robert Goodacre的学校是诺丁汉最好且最昂贵的学校，格林在这四个学期中学到了很多。格林的姐姐Ann后来嫁给了William Tomlin，而格林去世后，他将撰写格林的生平。关于他在Robert Goodacre学校的时间，Tomlin写道：-

……他始终如一地坚持不懈，如同成年后一样，对数学投入了极大的专注。……他在数学方面的深厚知识很快超过了Robert Goodacre。

很难确切看出格林为何在这个年龄对数学产生兴趣，或者就此而言，他是否能接触到任何类型的数学著作。然而，在1802年，格林九岁时离开学校，到父亲的烘焙生意中工作。他可能在学校学了一点拉丁语、希腊语和法语，但很难看出即使是一个在好学校里的聪明八岁男孩，也只能学到这些科目最简短的入门知识。

格林 Senior经营着一家成功的烘焙生意，他能够在诺丁汉购买几处房产。1807年，他在诺丁汉郊外的Sneinton购买了一块土地。这笔交易于1807年2月26日通过拍卖进行，在拍卖广告中，这块地被描述为：-

一块永久产权地产，免什一税，土地税已赎回，位于诺丁汉附近的Snenton；包括优质的牧场，并提供王国最佳的建筑位置之一，可俯瞰特伦特河、特伦特谷、克利夫顿森林、科尔威克、贝尔沃城堡以及一片富饶且高度耕种的土地，点缀着无数其他如画的景物……

买下这块地后，他在上面建了一座砖砌的风车玉米磨坊，这对面包师来说显然是一件有用的东西。磨坊高16米，是诺丁汉郡最早的兩座砖砌磨坊之一。格林的父亲雇了一名经理来经营磨坊，而格林本人也在那里工作。1817年，老格林在磨坊旁边建了一座家庭住宅，格林与他的母亲和父亲一起搬到了那里居住。[磨坊已经修复，我们强烈建议任何访问诺丁汉的人去参观一下。]格林的妹妹Ann没有搬到Sneinton，因为她在1816年嫁给了William Tomlin，他们住在诺丁汉的一个时尚地区。

格林在父亲磨坊工作的那些年里一定一直在研究数学。然而，我们完全不知道他如何能接触到当时最先进的数学，而事实上他确实做到了。在[3]中，Cannell讨论了诺丁汉是否有数学家能让格林接触到先进的法国数学思想。她只找到一位可能的候选人，即弗瑞兹·约翰·托普利斯，他是剑桥大学皇后学院的数学毕业生。

托普利斯对剑桥所教授的数学感到不满，并试图影响他人去学习更多在法国发展起来的数学。他将皮埃尔·西蒙·拉普拉斯的Mécanique céleste第一卷翻译成英文，并于1814年在诺丁汉出版。此时他是诺丁汉免费文法学校的校长，他一直留在那里直到1819年回到剑桥担任王后学院院长。当然，格林可能认识托普利斯，因为在1817年搬到磨坊的新家之前，格林住在诺丁汉的鹅门，与托普利斯当时居住的免费文法学校仅隔一条街。正如Cannell所写[3]：-

没有证据表明约翰 Toplis是格林的导师，但间接证据强烈表明，他在新的数学方面指导他，并帮助他学习法语，他无疑是为了阅读其他法国数学家的作品而掌握了法语，如西尔维斯特·佛朗索瓦·拉克鲁瓦、西莫恩·德尼·泊松和让-巴蒂斯特·毕奥。

格林磨坊的经理是威廉·史密斯，他有一个女儿简·史密斯。格林从未与简·史密斯结婚，但他们共同育有七个孩子。他与她的关系一定始于1823年或更早，因为他们的第一个孩子出生于1824年。当然，在1823年，格林加入了位于布罗姆利大厦的诺丁汉订阅图书馆。这对格林的科学发展是一个重要事件，因为这使他能够接触到一些科学著作，但也许最重要的是，这使他能够接触到Transactions of the Royal Society of London。在这份出版物中，格林可以读到一些最新的数学工作，它还报道了在其他国家发表的著作。

格林在磨坊的顶层完全独自学习数学。1823年至1828年间对格林来说并不容易，当然也不是最有利于学习的时期。除了在磨坊有一份全职工作外，还有两个女儿出生，一个是上面提到的1824年，另一个是1827年。在这两件事之间，他的母亲于1825年去世，他的父亲将于1829年去世。然而，尽管环境困难，尽管他的数学基础薄弱，格林在1828年发表了有史以来最重要的数学著作之一。

1827年12月14日，他在《诺丁汉评论》上刊登了一则广告：-

正在印刷中，不久将通过订阅出版，《论数学分析在电学和磁学理论中的应用》。作者格林。经许可，献给纽卡斯尔公爵阁下，K.G. 订阅者价格，7先令6便士。订阅者姓名将在书店和布罗姆利大厦图书馆接收。

Essay于1828年3月出版，有51位订户，其中大多数是诺丁汉订阅图书馆的成员，他们为一部几乎一个字也看不懂的著作支付了7先令6便士。在[1]中给出了格林序言的细节：-

在序言中，格林表示他“有限的信息来源”使他无法对电的数学理论给出恰当的历史概述，事实上，他引用的来源很少。其中包括卡文迪什1771年关于电的单流体理论研究、西莫恩·德尼·泊松1812年关于表面电的两篇论文和关于磁的三篇论文（1821-1823），以及弗朗索瓦·阿拉戈、皮埃尔·西蒙·拉普拉斯、约瑟夫·傅里叶、奥古斯丁·路易·柯西和T Young的贡献。序言最后请求读者鉴于作者所受教育的局限，宽容地阅读这部著作。

同样在[1]中，给出了这部重要出版物内容的一些细节：-

这篇论文以引言性观察开始，强调potential function的核心作用。格林创造了“势”这个术语，用来表示将一个系统所有粒子的质量分别除以它们到给定点的距离后相加所得的结果。势函数的一般性质随后得到发展，并应用于电和磁。连接面积分与体积分的公式，即现在所称的格林定理，在这部著作中被引入，“格林函数”也是如此，这一概念现在广泛用于求解偏微分方程。

这篇论文可能非常重要，但在出版时没有人意识到这一点。没有任何具备足够数学技能来领会其重要性的人看过这部著作。格林继续经营他的磨坊，并在1829年父亲去世后，独自负责家族生意。他的第三个孩子，也是第一个儿子，生于1829年。然而，当他与Edward Bromhead爵士取得联系后，情况发生了变化。

Edward Bromhead爵士是Essay的订阅者之一，他立即写信给格林，提出将任何进一步的论文寄给伦敦皇家学会、Royal Society of Edinburgh或剑桥哲学学会。Bromhead曾在剑桥学习数学，并曾是分析学会的成员。事实上，该学会的最后一次会议可能于1817年12月20日在Thurlby Hall举行，由Bromhead主持。尽管Bromhead无法欣赏格林论文的高度重要性，但他确实意识到格林是一位非常优秀的数学家。格林将Bromhead的提议视为仅仅是礼貌，直到1830年1月，一位朋友说服他跟进Bromhead的信，他才作出回应。

三年来，格林和Bromhead在Thurlby Hall会面，在此期间格林又写了三篇论文。两篇关于电的论文由Bromhead寄给剑桥哲学学会，分别于1833年和1834年发表。第三篇关于流体动力学，这篇著作由爱丁堡皇家学会（Bromhead是其会士）于1836年发表。Bromhead是格林结交的好人选，因为他与剑桥的数学家有着良好的联系。Bromhead在那里的密友包括查尔斯·巴贝奇、约翰·赫歇尔和乔治·皮科克，他在1833年4月向格林建议，他应该考虑在剑桥学习数学。1833年6月，Bromhead前往剑桥参加聚会，并邀请格林同行。然而格林肯定没有意识到自己工作的重要性。他写信给Bromhead：-

你善意地提到6月24日去剑桥看望你的朋友约翰·赫歇尔、查尔斯·巴贝奇以及其他构成英国科学骑士团的人。由于我还只是个初学者，我认为我没有权利去那里，必须推迟这份乐趣，直到我成为一个还算体面的科学人，如果那一天到来。

格林采纳了Bromhead的建议，离开了他的磨坊，于1833年10月成为剑桥的本科生，时年40岁。他被录取到Bromhead曾学习过的Caius学院。他在1834年5月写信给Bromhead：-

我在这里很快乐，我担心自己对剑桥过于满意。这在某种程度上使我偏离了那些本应是我正业的追求，但我希望在回来时放下我的新鲜感，成为一个正规的第二年学生。

数学考试对格林来说并不难，但其他科目如拉丁语和希腊语对只受过四个学期学校教育的人来说要难得多。他于1837年以第四名数学荣誉学位考试一等及格者（Wrangler）毕业，那一年的第二名Wrangler是詹姆斯·约瑟夫·西尔维斯特。以下引文出现在[16]中：-

格林和詹姆斯·约瑟夫·西尔维斯特是那一年的第一批人，但格林对普通男孩数学的不熟悉使他在时间竞赛中无法名列前茅。

毕业后，他留在剑桥并研究自己的数学。在1838年和1839年，他有两篇关于流体动力学（特别是运河中的波运动）的论文，两篇关于光的反射和折射的论文，以及两篇关于声音的反射和折射的论文，由剑桥哲学学会发表。

在格林毕业后的这些年里，哈维·古德温主教是剑桥大学的本科生。他这样写到格林[3]：-

他在大学内外所有同代人中鹤立鸡群。

古德温的话也被引用于[16]中：-

我曾两次接受格林的考试。在我的三次学院考试中，有两次的试题纸是他出的……据我所知，他从不参与讲课。这可能是由于他的生活习惯。他在考场上的举止温和而令人愉快。

格林于1839年10月31日当选为珀斯奖学金获得者。这当然是有可能的，因为他确实满足了未婚的条件，而当时已有六个孩子并不相关。当选奖学金后，他在剑桥的时间确实非常短。到1840年5月，他因健康不佳已回到诺丁汉。几周后，他的第七个孩子出生了。格林显然觉得他的病情非常严重，并于1840年7月立下遗嘱，其中陈述他的健康状况不佳，但没有给出疾病的具体细节。然而，他似乎仍希望回到剑桥，因为他这样描述自己：-

……原住诺丁汉郡斯内顿，现居剑桥大学凯厄斯学院，为该学院研究员。

他的遗嘱将他在诺丁汉的所有财产留给了简，而斯奈顿的财产则留给了他的七个孩子。

我们确实知道格林死在Jane Smith和他的七个孩子居住的房子里。Jane报告了他的死亡，并在格林去世时陪伴在他身边。相当值得注意的是，这是格林与Jane Smith及其孩子住在同一房子里的唯一记录。

《诺丁汉评论》于6月11日刊登了一则简短的讣告，表明他们对他的生平知之甚少，对其工作的重要性了解得更少：-

……我们相信他是一位磨坊主的儿子，居住在诺丁汉附近，但由于对学问的爱好，他将天赋的心智应用于数学科学，并取得了迅速的进步。在从男爵爱德华·弗伦奇·布罗姆黑德爵士那里，他找到了一位热忱的朋友，在剑桥求学期间，他受益于其影响良多。倘若他的生命得以延长，他或许会作为一位数学家而享有极高的地位。

当然，格林从未知道他的数学的重要性。这一点只有在他去世后才被认识到[1]：-

就在格林去世前几周，开尔文刚被剑桥大学圣彼得学院录取。在Robert Murphy发表于《剑桥哲学学会汇刊》的一篇论文中，汤姆森注意到了一处对格林的《论》的引用，尽管Murphy没有提及他在该期刊上发表的任何其他著作。开尔文一直未能找到《论》的副本，直到1845年1月他刚获得学位后，他的辅导教师威廉·霍普金斯给了他三本。六十年后，开尔文回忆起他自己以及约瑟夫·刘维尔和雅克·夏尔·弗朗索瓦·施图姆的兴奋之情，1845年夏天他在巴黎向他们展示了这部著作。回到剑桥后，开尔文负责重新出版这部著作，并附有一篇导论（1850-54）。通过开尔文、詹姆斯·克拉克·麦克斯韦等人，一位默默无闻、自学成才的磨坊主之子所发展出的一般位势数学理论，将导向支撑二十世纪工业的电学数学理论。

George Green's father, also called George Green, was a baker in Nottingham. After serving his apprenticeship to a baker in Nottingham George Green Senior had married Sarah Butler (the mathematician's mother) in 1791 and Sarah's father had helped George Green Senior to buy his own bakery in Wheatsheaf Yard in Nottingham. George and Sarah had one son and one daughter. The son was George Green, the mathematician and, although the date of his birth is unknown, he was baptised on 14 July 1793. His sister Ann was born two years later and the family were reasonably prosperous with the bakery business being successful.

In September 1800 there were riots in England when food prices were high and people did not have enough to eat. The corn dealers and bakers were blamed for keeping back food until the prices rose even higher and crowds of people broke into bakers and tried to steal food. George Green's bakery was attacked and the he wrote a letter to the mayor asking for protection (the spelling and capital letters follow Green's letter):-

Sept 1th 1800 To the Right Worshipfull the Mayor and his Bretheren haveing all my Windows Broke Last night and being much thretend tonight with more mischief being done to me such as entering my House therefore Gentlemen I most Humbly crave your protection such as the Berer of this can explain to you from your Humble servant George Green.

Young George Green went to Robert Goodacre's school in 1801, the year after the riots. He was only eight years old when he began his schooling and only nine when he left the school in midsummer 1802. His only schooling, therefore, consisted of four terms but, despite the short time he spent there, since Robert Goodacre's was the best and most expensive school in Nottingham, George was taught much in the four terms. George's sister Ann went on to marry William Tomlin and he was to write on George Green's life after George died. Of his time at Robert Goodacre's school, Tomlin writes:-

... he pursued with undeviating constancy the same as in his mature years an intense application to mathematics. ... his profound knowledge in mathematics soon exceeded that of Robert Goodacre.

It is hard to see quite why Green became interested in mathematics at this age or, for that matter, whether he had access to mathematical works of any type. However, in 1802, Green left school as a nine year old boy to work in his father's bakery business. He probably learnt a little of Latin, Greek and French at school but it is hard to see how even a bright eight year old boy in a good school could learn more than the briefest of introductions to these subjects.

George Green Senior ran a successful bakery business and he was able to buy several houses in Nottingham. In 1807 he bought a plot of land at Sneinton, just outside Nottingham. The sale was made by auction at 26 February 1807 and in the advertisement for the sale the plot is described as:-

A freehold estate, tythe-free, and the Land Tax redeemed, situate at Snenton, near Nottingham; consisting of excellent pasture land, and affording for Building upon one of the first Situations in the Kingdom, commanding most extensive Views of the River Trent, Trent Vale, Clifton Woods, Colwick, Belvoir Castle, and a rich and highly cultivated Country, diversified by numberless other picturesque objects...

Having bought the land, he built on it a brick wind corn-mill, clearly a useful thing for a baker to own. The mill stood 16 metres high and was one of the first two brick mills in the county of Nottinghamshire. Green's father employed a manager to run the mill, and Green himself worked there. In 1817 Green Senior built a family house beside the mill and Green together with his mother and father went to live there. [The mill has been restored and we strongly recommend anyone who is visiting Nottingam to pay a visit.] Green's sister Ann did not move to Sneinton as she had married William Tomlin in 1816 and they were living in a fashionable part of Nottingham.

Green must have continued working on mathematics through the years that he worked at his father's mill. However, we have no knowledge whatsoever of how he could have become acquainted with the most advanced mathematics of his day, which indeed is what happened. In [3] Cannell discusses whether there were any mathematicians living in Nottingham who could have given Green access to advanced French mathematical ideas. She comes up with only one possible candidate, John Toplis who was a mathematics graduate of Queens' College Cambridge.

Toplis had become unhappy with the mathematics being taught at Cambridge and had tried to influence others to learn more of the mathematics being developed in France. He translated the first volume of Laplace's Mécanique céleste into English and he published this in Nottingham in 1814. At this time he was the headmaster of the Free Grammar School in Nottingham, and he remained there until 1819 when he returned to Cambridge as Dean of Queens' College. Certainly Green could have known Toplis since, before he moved to the new family home at the mill in 1817, Green was living in Goosegate in Nottingham just one street away from the Free Grammar School where Toplis lived at that time. As Cannell writes [3]:-

There is no proof that John Toplis was George Green's mentor but circumstantial evidence suggests strongly that he was guiding him in the new mathematics and helping him with the French he undoubtedly acquired in order to read the works of other French mathematicians, such as Lacroix, Poisson and Biot.

The manager of Green's mill was William Smith and he had a daughter Jane Smith. George Green never married Jane Smith but together they had seven children. His relationship with her must have started in 1823 or earlier as their first child was born in 1824. Certainly in 1823 Green joined the Nottingham Subscription Library which was situated in Bromley House. This was an important event in Green's scientific development as it gave him access to a few scientific works, but perhaps most importantly of all, it gave him access to the Transactions of the Royal Society of London. In this publication Green could read some of the latest mathematical work and it also reported on works published in other countries.

Green studied mathematics on the top floor of the mill, entirely on his own. The years between 1823 and 1828 were not easy for Green, and certainly not the most conducive to study. As well as having a full time job in the mill, two daughters were born, the one in 1824 mentioned above, and a second in 1827. Between these two events his mother had died in 1825 and his father was to die in 1829. Yet despite the difficult circumstances and despite his flimsy mathematical background, Green published one of the most important mathematical works of all time in 1828.

On 14 December 1827 he published an advertisement in the Nottingham review:-

In the Press, and shortly will be published, by subscription, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. By George Green. Dedicated (by permission), to his Grace the Duke of Newcastle, K.G. Price to Subscribers, 7s. 6d. The Names of Subscribers will be received at the Booksellers, and at the Library, Bromley House.

The Essay was published in March 1828 and there were 51 subscribers, most of whom were members of the Nottingham Subscription Library and paid 7s. 6d. for a work of which they could hardly have understood a word. In [1] details are given of Green's preface:-

In the preface Green indicated that his "limited sources of information" prevented his giving a proper historical sketch of the mathematical theory of electricity, and indeed, he cites few sources. Among them are Cavendish's single-fluid theoretical study of electricity of 1771, two memoirs by Poisson of 1812 on surface electricity and three on magnetism (1821-1823), and contributions by Arago, Laplace, Fourier, Cauchy, and T Young. The preface concludes with a request that the work be read with indulgence, in view of the limitations of the author's education.

Also in [1] some details are given of the contents this important publication:-

The Essay begins with introductory observations emphasising the central role of the potential function. Green coined the term 'potential' to denote the results obtained by adding the masses of all the particles of a system, each divided by its distance from a given point. The general properties of the potential function are subsequently developed and applied to electricity and magnetism. The formula connecting surface and volume integrals, now known as Green's theorem, was introduced in the work, as was "Green's function" the concept now extensively used in the solution of partial differential equations.

The Essay may have been of great importance but this was not realised by anyone at the time of its publication. Nobody with sufficient mathematical skills to appreciate its importance had seen the work. Green carried on working his mill and, in 1829 on the death of his father, he became solely responsible for the family business. His third child, and first son, was born in 1829. Things changed however, when he made contact with Sir Edward Bromhead.

Sir Edward Bromhead was one of the subscribers to the Essay and he had written immediately to Green offering to send any further papers to the Royal Society of London, the Royal Society of Edinburgh or the Cambridge Philosophical Society. Bromhead had studied mathematics at Cambridge and had been a member of the Analytic Society. In fact what may have been the last meeting of that Society had been held at Thurlby Hall on 20 December 1817 with Bromhead in the chair. Although Bromhead was not able to appreciate the high importance of Green's essay, he did realise that Green was a very good mathematician. Green took Bromhead's offer as mere politeness and did not respond until January 1830 when a friend persuaded him to follow up Bromhead's letter.

For three years Green and Bromhead met at Thurlby Hall and during this time Green wrote three further papers. Two on electricity were sent by Bromhead to the Cambridge Philosophical Society where they were published, one in 1833 and the other in 1834. The third was on hydrodynamics and this work was published by the Royal Society of Edinburgh (of which Bromhead was a Fellow) in 1836. Bromhead was a good person for Green to become friendly with since he had good contacts with mathematicians at Cambridge. Bromhead's close friends there included Charles Babbage, John Herschel and George Peacock and he suggested to Green in April 1833 that he should consider studying mathematics at Cambridge. In June 1833 Bromhead went to Cambridge for a reunion and asked Green to go with him. However Green certainly did not realise the importance of his work. He wrote to Bromhead:-

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 the pleasure until I shall have become tolerably respectable as a man of science should that day ever arrive.

However Green took Bromhead's advice, left his mill and became an undergraduate at Cambridge in October 1833 at the age of 40. He was admitted to Caius College where Bromhead had studied. He wrote to Bromhead in May 1834:-

I am very happy here and am I fear too much pleased with Cambridge. This takes me in some measure from those pursuits which ought to be my proper business, but I hope on my return to lay aside my freshnesses and become a regular Second Year Man.

The mathematics examinations did not prove hard for Green, but the other topics such as Latin and Greek proved much harder for someone with only four terms of school education. He graduated as fourth Wrangler in 1837, the second Wrangler that year being Sylvester. The following quote appears in [16]:-

Green and Sylvester were the first men of the year, but Green's want of familiarity with ordinary boy's mathematics prevented him from coming to the top in a time race.

After graduating he remained at Cambridge and worked on his own mathematics. In 1838 and 1839 he had two papers on hydrodynamics (in particular wave motion in canals), two papers on reflection and refraction of light and two papers on reflection and refraction of sound published by Cambridge Philosophical Society.

Bishop Harvey Goodwin was an undergraduate at Cambridge during these years following Green's graduation. He wrote of Green [3]:-

He stood head and shoulders above all his contemporaries inside and outside the University.

Goodwin is also quoted in [16]:-

I was twice examined by Green. He set the problem paper in two out of the three of my college examinations... He never assisted as far as I know in lectures. This might be owing to his habits of life. His manner in the examination room was gentle and pleasant.

Green was elected to a Perse fellowship on 31 October 1839. This of course was possible since he did satisfy the condition of not being married, and having six children, which he had at this time, was not relevant. His time at Cambridge after being elected to the fellowship was very short indeed. By May 1840 he had returned to Nottingham suffering from ill health. A few weeks later his seventh child was born. Green clearly felt that his illness was very serious and in July 1840 he wrote a will in which he states that his health was poor but no details of the illness are given. However it would appear that he still hoped to return to Cambridge since he describes himself as:-

... late of Sneinton in the County of Nottingham and now of Caius College Cambridge, Fellow of such College.

His will left all his property in Nottingham to Jane while the property at Sneinton was left to his seven children.

We do know that Green died in the house where Jane Smith and his seven children lived. Jane reported his death and was with Green when he died. Rather remarkably, this is the only record of Green living in the same house as Jane Smith and his children.

The Nottingham Review published a short obituary on 11 June which showed they knew little of his life and less of the importance of his work:-

... we believe he was the son of a miller, residing near Nottingham, but having a taste for study, he applied his gifted mind to the science of mathematics, in which he made a 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.

Of course, Green never knew the importance of his mathematics. That was only realised after his death [1]:-

Only a few weeks before Green's death, William Thomson had been admitted to St Peter's College, Cambridge. In a paper by Robert Murphy published in the Transactions of the Cambridge Philosophical Society, Thomson noticed a reference to Green's Essay, although Murphy did not mention any of his other works published in that journal. Thomson was unable to find a copy of the Essay until, just after receiving his degree in January 1845, his coach, William Hopkins, gave him three copies. Sixty years later Thomson recalled his excitement and that of Liouville and Sturm, to whom he showed the work in Paris in the summer of 1845. After returning to Cambridge, Thomson was responsible for republishing the work, with an introduction (1850-54). Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son would lead to the mathematical theories of electricity underlying twentieth-century industry.