威廉·琼斯William Jones

威廉·琼斯的父亲是Siôn Siôr。一个明显的问题是：为什么他的父亲不叫‘琼斯’？答案很简单，他叫琼斯，因为这是威尔士语Siôn的英语版本。琼斯的母亲是Elizabeth Rowland，她来自安格尔西岛上的Llanddeusant。琼斯出生在安格尔西的一个农场，全家搬到安格尔西的Llanbabo，然后在琼斯的父亲去世后再次搬家。家里很穷，琼斯在距离安格尔西北海岸约3公里的Llanfechell的一所慈善学校上学。在那里，他的数学才能被当地地主发现，地主安排他在伦敦一家商人的账房工作。

这份工作让琼斯在海上航行至西印度群岛服役，1695年至1702年间他在船上教授数学和航海术。他服役于一艘海军舰艇，该舰艇属于乔治·鲁克爵士和奥蒙德公爵詹姆斯·巴特勒指挥的英荷联合舰队，1702年在西班牙西北部的维戈湾摧毁了一支法西联合舰队。航海是琼斯极为感兴趣的课题，他最早出版的著作是1702年出版的A New Compendium of the Whole Art of Navigation。在这部著作中，他将数学应用于航海，研究计算海上位置的方法。

维戈海战之后，琼斯离开海军，成为伦敦咖啡馆中的数学教师。这看起来可能很奇怪，但实际上当时咖啡馆有时被称为便士大学，因为它们提供廉价的教育。它们收取一便士的入场费，然后顾客在喝咖啡时可以听讲座。不同的咖啡馆迎合特定的兴趣，如艺术、商业、法律和数学。琼斯能够在圣保罗教堂墓地的柴尔德咖啡馆等咖啡馆讲课谋生。

很快他受雇辅导菲利普·约克，后者后来成为哈德威克的哈德威克男爵。这对琼斯来说是一个重要的职位，因为约克在从事法律职业后进入议会，先后成为副检察长（1720年）、总检察长（1724年）、王座法庭首席法官（1733年）和大法官（1737年）。琼斯辅导约克大约三年。他于1706年出版了Synopsis palmariorum mathesiosⓉ（初等数学概要），这是一本基于他的教学笔记、面向初学者的书。它包括微分、无穷级数，并且因其中π符号以其现代含义使用而闻名。1709年，他申请基督医院数学学校校长的职位，并提供了由艾萨克·牛顿和爱德蒙·哈雷写的推荐信。他未能获得该职位，因此继续在伦敦的咖啡馆讲课。

尽管作为研究数学家不太重要，琼斯在数学史家中却很有名，因为他与许多17世纪数学家通信，包括艾萨克·牛顿。然而，他于1711年当选为皇家学会会士。琼斯随后在1712年成立的皇家学会委员会任职，该委员会旨在裁定谁发明了无穷小微积分，艾萨克·牛顿还是哥特弗里德·威廉·莱布尼茨。我们现在应该描述琼斯如何被视为这场争论中重要的艾萨克·牛顿支持者。（Royal Society确保只有坚定的艾萨克·牛顿支持者才能在其委员会任职！）

通过在咖啡馆讲课，琼斯接触到了当时的主要科学家，如布鲁克·泰勒和罗杰·柯特斯。约翰·柯林斯因与众多科学家通信而闻名，他于1683年去世，1708年琼斯获得了他的数学论文。这些论文包括艾萨克·牛顿手稿的抄本、信件以及用无穷级数方法获得的结果，这些结果是艾萨克·牛顿大约在1664年发现的。艾萨克·牛顿将这些结果写入了De analysiⓉ（论分析），但它们未曾出版。在艾萨克·牛顿本人的协助下，琼斯于1711年出版了Analysis per quantitatum series, fluxiones, ac differentiaⓉ（论定量级数、流数和微分），尽管应当注意，1711年的第一版既没有记录艾萨克·牛顿的名字，也没有记录琼斯的名字。作为这部著作的附录，琼斯添加了艾萨克·牛顿的Tractatus de quadratura curvarumⓉ（论曲线求积），这是艾萨克·牛顿在1691年所写的分析微积分著作的删节版。Analysis per quantitatumⓉ（量的分析）的第二版于1723年出版，其中确实包含琼斯写的序言。琼斯对出版艾萨克·牛顿著作的另一贡献与Methods fluxionumⓉ（流数方法）有关，该书由艾萨克·牛顿于1671年写成。艾萨克·牛顿曾试图在五年内将其付印，但最终在1676年剑桥大学出版社拒绝后放弃。琼斯制作了拉丁文原稿的副本，将其命名为Artis analyticae specimina sive geometria analyticⓉ（模型的分析艺术或解析几何），最终出版的就是这个版本。1731年，琼斯出版了Discourses of the Natural Philosophy of the Elements。

我们在描述琼斯生活中的事件时，停在他未能获得基督医院数学学校校长职位之后。在此之前，他已娶了他在商人账房雇主的遗孀。除了在咖啡馆的角色外，他还担任乔治·帕克的导师，乔治是未来的麦克尔斯菲尔德伯爵的儿子，他获得这个职位是因为他以前的学生菲利普·约克是乔治·帕克父亲的朋友。琼斯长期与帕克家族有联系，并在他们位于希尔本的城堡中长期居住。菲利普·约克和乔治·帕克的友谊对他帮助很大，尤其是在他投资资金的银行倒闭使他失去所有钱财之后。他的两个以前的学生此时已是有巨大影响力的人物，能够为琼斯获得各种职位，为他提供收入而无需实际工作。

琼斯的第一任妻子去世后，他于1731年4月17日与Mary Nix再婚。结婚时她25岁，而琼斯已56岁。他们育有三个孩子，其中两个活到成年：Mary生于1736年，琼斯则生于10年之后。琼斯去世时留下了大量手稿和通信，看来他曾打算将其作为一部重要著作出版。其中有许多笔记和他所能接触到的原始手稿的抄写部分。约翰·沃利斯在[2]中写道：-

他约15,000册的藏书被认为是英格兰最有价值的数学图书馆，并遗赠给了第二代麦克尔斯菲尔德伯爵George Parker。他的论文不在遗赠之列；尽管如此，许多论文仍保存在Shirburn，直到1995年仍在那里，且查阅受到极严格限制。几乎唯一获准出版的是收录在两卷本Rigaud Correspondence中的那些论文。在琼斯的手稿中，还有另一部拟议中的数学著作，他的儿子Sir 琼斯曾打算出版，但未能成功。

William Jones' father was Siôn Siôr. An obvious question would be: why was his father not named 'Jones'? The answer is simple, he was named Jones since this is the English version of the Welsh Siôn. William's mother was Elizabeth Rowland who was from Llanddeusant in the island of Anglesey. William was born on a farm in Anglesey and the family moved to Llanbabo on Anglesey, then moved again after the death of William's father. The family were poor and William attended a charity school at Llanfechell about 3 km from the north coast of Anglesey. There his mathematical talents were spotted by the local landowner who arranged for him to be given a job in London working in a merchant's counting-house.

This job saw Jones serving at sea on a voyage to the West Indies, and he taught mathematics and navigation on board ships between 1695 and 1702. He was serving on a navy vessel which was part of the British-Dutch fleet under Sir George Rooke and James Butler, Duke of Ormonde, which destroyed a Franco-Spanish fleet in Vigo bay off northwestern Spain in 1702. Navigation was a topic which greatly interested Jones and his first published work was A New Compendium of the Whole Art of Navigation published in 1702. In this work he applied mathematics to navigation, studying methods to calculate position at sea.

After the battle of Vigo, Jones left the navy and became a teacher of mathematics in the coffee houses of London. This may seems strange but in fact at this time coffee houses were sometimes called the Penny Universities because of the cheap education they provided. They would charge an entrance fee of one penny and then while customers drank coffee they could listen to lectures. Different coffee houses catered to specific interests such as art, business, law and mathematics. Jones was able to make a living lecturing in coffee houses such as Child's Coffee House in St Paul's Churchyard.

Soon he was employed to tutor Philip Yorke, who was later to become Baron Hardwicke of Hardwicke. This was an important position for Jones since Yorke, after a legal career, entered parliament becoming solicitor general (1720), attorney general (1724), lord chief justice (1733), and lord chancellor (1737). Jones tutored Yorke for about three years. He published Synopsis palmariorum mathesios Ⓣ in 1706, a book based on his teaching notes intended for beginners. It included the differential calculus, infinite series, and is also famed since the symbol π is used in it with its modern meaning. In 1709 he applied for the position of master of Christ's Hospital Mathematical School and supplied references written by Newton and Halley. He failed to obtain the position so continued lecturing in the coffee houses of London.

Although of little importance as a research mathematician, William Jones is well known to historians of mathematics since he corresponded with many 17th century mathematicians, including Newton. He was, however, elected a Fellow of the Royal Society in 1711. Jones then served on the Royal Society committee set up in 1712 to decide who had invented the infinitesimal calculus, Newton or Leibniz. We should now describe how Jones came to be considered an important Newton supporter in the dispute. (The Royal Society made sure that only strong Newton supporters served on their committee!)

Through lecturing in the coffee houses, Jones came in contact with leading scientists of the day such as Brook Taylor and Roger Cotes. John Collins, famed for his correspondence with a wide range of scientists, had died in 1683 and in 1708 Jones acquired his mathematical papers. These included transcripts of Newton's manuscripts, letters and results obtained with the method of infinite series which Newton had discovered in about 1664. Newton had written up these results in De analysi Ⓣ but they had not been published. With assistance from Newton himself, Jones produced Analysis per quantitatum series, fluxiones, ac differentia Ⓣ in 1711 although it should be noted that this first edition of 1711 did not record either Newton's name nor that of Jones. As an appendix to this work Jones added Newton's Tractatus de quadratura curvarum Ⓣ which was a shortened version of the work on analytical calculus which Newton had written in 1691. The second edition of Analysis per quantitatum Ⓣ published in 1723 did contain a preface written by Jones. Another contribution made by Jones towards publishing Newton's work relates to the Methods fluxionum Ⓣ, written by Newton in 1671. Newton had tried to get it printed over a period of five years but finally gave up in 1676 when Cambridge University Press rejected it. Jones made a copy of the original Latin, giving it the title Artis analyticae specimina sive geometria analytic Ⓣ and it was this version which was eventually published. In 1731 Jones published Discourses of the Natural Philosophy of the Elements.

We left our description of the events in Jones' life after he was unsuccessful in obtaining the mastership of Christ's Hospital Mathematical School. He had, before this, married the widow of his employer in the merchant's counting-house. In addition to his coffee house role he also acted as a tutor to George Parker, son of the future earl of Macclesfield, a position he obtained since his former pupil Philip Yorke was a friend of George Parker's father. Jones was long associated with the Parker family and lived for long spells at their castle at Shirburn. He was greatly helped by his friendship of Philip Yorke and George Parker, particularly after he lost all his money when the bank in which his money was invested collapsed. His two former pupils were by this time men of great influence and were able to obtain various positions for Jones which provided him with an income without requiring any real work.

Jones' first wife died and he remarried several years later to Mary Nix on 17 April 1731. She was 25 years old and Jones was 56 at the time of their marriage. They had three children, two of whom survived to adulthood: Mary born in 1736 and William born 10 years later. On his death Jones left a large collection of manuscripts and correspondence which it appears he had intended to publish as a major piece of work. There are many notes and copied parts of original manuscripts to which he had access. Wallis writes in [2]:-

His collection of some 15,000 books was considered to be the most valuable mathematical library in England and was bequeathed to George Parker, the second earl of Macclesfield. His papers were not in the bequest; nevertheless many are at Shirburn, where they have remained (1995) with access extremely restricted. Almost the only permitted publication has been those papers contained in the two-volume Rigaud Correspondence. Among Jones's manuscripts was another projected mathematical book, which his son, Sir William, had intended, but failed, to publish.