约翰·佩尔John Pell

约翰·佩尔的父亲也叫佩尔，他的母亲是玛丽·霍兰德。玛丽来自肯特郡的哈尔登，她的丈夫来自南威克，他们的儿子弗瑞兹·约翰，即本传记的主题，就出生在那里。他是父母两个儿子中的第二个，但到他六岁时，他成了孤儿，父亲于1616年去世，母亲在第二年去世。老佩尔有一个很好的图书馆，这对小约翰的成长很有价值。在苏塞克斯的斯泰宁学校（一所免费学校）就读后，他于1624年进入剑桥大学三一学院。他于1628年获得学士学位，1630年获得硕士学位。此时他已经是拉丁语和希腊语的专家，尽管我们对他的数学训练知之甚少，但我们确实知道，在他获得学士学位的那一年，他与亨利·布里格斯就对数进行了通信。

离开剑桥后，佩尔成为了一名校长。他先在霍舍姆的科利尔学校担任助理教师，然后在苏塞克斯的奇切斯特学院工作。他于1632年7月3日与Ithumaria Reginolles结婚；他们育有四子四女。从1638年起，佩尔在伦敦教授数学五年。随后他出国，从1643年起在阿姆斯特丹的文理中学 Illustre担任数学教授，直到1646年在布雷达大学担任类似职位。1651年，英国颁布了《航海法案》，旨在阻止荷兰参与英国的海上贸易。英荷之间的紧张关系急剧上升，1652年5月发生了一起事件，荷兰军队被击败。佩尔意识到战争迫在眉睫，一旦战争爆发，他在布雷达将处于极其困难的境地。他返回英国，第一次英荷战争确实于1652年7月8日爆发。回国后，佩尔被奥利弗·克伦威尔任命在伦敦教授数学。

佩尔在1654年至1658年间在苏黎世担任政府职务。他是被克伦威尔派往那里执行外交任务的。1648年结束三十年战争的《威斯特伐利亚和约》使罗马天主教（此时与法国统治认同）重新获得了一些先前属于路德宗新教的领土。克伦威尔希望将瑞士的新教州分裂出来，加入一个以英国为首的新教联盟。然而，佩尔的谈判旷日持久，他回到英国向克伦威尔汇报，但仅在克伦威尔去世前不久。他无法汇报，因为他徒劳地等待与克伦威尔的会面，而会面无法安排。回到英国后，佩尔被任命为执事，然后在1661年成为牧师。他成为埃塞克斯郡Fobbing的牧师，并在1663年也成为埃塞克斯郡Laindon和Basildon的牧师。他在生命的最后二十年担任这两个教会职位。他的妻子Ithumaria于1661年去世，在1669年之前的某个时候他再婚了。

Malcolm在[7]中写道：-

数学家佩尔是17世纪英格兰思想史上的重要人物——然而，其重要性更多在于他的活动、交往和通信，而非其已发表著作。尽管如此，他为数不多的出版物仍是了解其思想传记的宝贵信息来源。

佩尔研究代数和数论。他在1668年给出了所有不超过100000的整数的因子表。佩尔方程$y^{2} = ax^{2} + 1$，其中$a$是非平方整数，最早由婆罗摩笈多和婆什迦罗第二研究。它的完整理论由约瑟夫·拉格朗日完成，而非佩尔。人们常说莱昂哈德·欧拉错误地将威廉·布朗克关于此方程的工作归功于佩尔。然而该方程出现在约翰·海因里希·雷恩的一本书中，这本书肯定是在佩尔的帮助下写成的：有人说完全由佩尔所写。也许莱昂哈德·欧拉在命名该方程时知道自己在做什么。

佩尔发表了许多著作，例如Idea of Mathematics（1638年）和两页的A Refutation of Longomontanus's Pretended Quadrature of the Circle（1644年）（以拉丁文重印为Controversiae de vera circuli mensura（1647年））。M J Klein写到Idea of Mathematics:-

佩尔列出了一系列任务，如果执行将促进英格兰数学的进步。他的计划包括编目所有过去的著作，描述数学的范围，选择过去最好的，描述已经取得的进展，描绘将证明有帮助的方法论，并指出无法解决的问题。

Refutation的写作是因为佩尔卷入了一场关于π值的争论。Longomontanus（Christian Severin）在1644年发表了他的化圆为方。事实上，Longomontanus于1647年去世，但争议并未随他的去世而结束，因为其他人加入了进来。在[9]中，van Maanen详细描述了佩尔和Charles Cavendish之间的通信，其中佩尔试图为他的论点一方争取支持者。佩尔还翻译了菲利普·范·兰斯贝尔热的表格，这些表格于1632年出版，并从事天文学工作。

佩尔于1663年5月20日当选为皇家学会。他在考虑机械和光学发明的委员会任职，并于1675年当选为副主席。

在2中，他被描述如下：-

佩尔是一个引人注目的人物，非常英俊，姿态挺拔、出色，深色头发和眼睛，声音好听。他的气质是 sanguine 和 melancholic。

在伦敦时，佩尔曾与约翰·柯林斯同住一段时间。然而在1664年秋天，瘟疫在城市贫穷的郊区开始流行。疫情在冬季后平息，但在1665年5月再次蔓延。国王和宫廷于6月逃离伦敦，那年夏天佩尔也离开了伦敦，应邀前往柴郡的布勒顿庄园，作为威廉·布勒顿的客人，他在荷兰期间曾担任其家庭教师。奥布里写道[3]：-

主人与学生之间从未有过比佩尔博士与其学生之间更深的爱，后者于1680年3月17日去世，使这位可敬的博士失去了一位聪慧的伴侣和一位有用的朋友。

此后，佩尔住在[3]：-

……在杰明街一个不起眼的住所，三层楼高，紧邻船形标志，不仅缺少书籍，还缺少他自己的手稿。

他现在负债并被投入监狱。获释后，他住在许多不同的地方，如医学院、他一个孙辈的房子，以及威斯敏斯特的一个住所，并在那里去世。

John Pell's father was also named John Pell and his mother was Mary Holland. Mary was from Halden in Kent and her husband was from Southwick where their son John, the subject of this biography, was born. He was the second of his parents two sons but by the time he was six years old he was an orphan, his father dying in 1616 and his mother in the following year. John Pell senior had a fine library and this proved valuable to John junior as he grew up. After attending Steyning School in Sussex, which was a free school, he entered Trinity College, Cambridge in 1624. He received his B.A. in 1628 and his M.A. in 1630. He was by this time an expert in Latin and Greek and, although we know little of his training in mathematics, we do know that he corresponded with Briggs about logarithms in the year in which he graduated with his B.A.

After leaving Cambridge, Pell became a schoolmaster. He worked first in Horsham, as an assistant master at Collyer's School, then in Chichester Academy in Sussex. He married Ithumaria Reginolles on 3 July 1632; they had four sons and four daughters. Pell spent five years from 1638 teaching mathematics in London. He then went abroad becoming Professor of Mathematics at the Gymnasium Illustre in Amsterdam from 1643 until he took up a similar post at the University of Breda in 1646. In 1651 the English brought in the Navigation Act which aimed to prevent the Dutch taking part in the English sea trade. Tensions between the English and the Dutch rose sharply and there was an incident in May 1652 when a Dutch force was defeated. Pell realised that war was imminent and that he would be in an extremely difficult position in Breda once war broke out. He returned to England and indeed the First Anglo-Dutch War did break out on 8 July 1652. After his return, Pell was appointed by Oliver Cromwell to a post teaching mathematics in London.

Pell spent the years 1654 to 1658 holding a government post in Zürich. He had been sent there by Cromwell on a diplomatic mission. The Peace of Westphalia of 1648 that ended the Thirty Years' War saw the Roman Catholicism (at this time identified with French rule) regain some territories which had previously been Lutheran Protestant. Cromwell wanted to split the Protestant cantons of Switzerland off to join a Protestant League, with England at its head. However Pell's negotiations were long drawn out and he returned to England to give his report to Cromwell only shortly before Cromwell's death. He was unable to report as he waited in vain for an audience with Cromwell which could not be arranged. After his return to England Pell was ordained a deacon, then a priest in 1661. He became vicar at Fobbing in Essex, and in 1663 he also became vicar of Laindon and Basildon in Essex. He held these two positions in the church for the last twenty years of his life. His wife Ithumaria died in 1661 and some time before 1669 he remarried.

Malcolm writes in [7]:-

The mathematician John Pell is a significant figure in the intellectual history of 17th century England - significant, however, more because of his activities, contacts and correspondence than because of his published work. His few publications are, nevertheless, valuable sources of information about his intellectual biography.

Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668. Pell's equation $y^{2} = ax^{2} + 1$, where $a$ is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation.

Pell published a number of works, for example Idea of Mathematics (1638) and the two page A Refutation of Longomontanus's Pretended Quadrature of the Circle (1644) (reprinted in Latin as Controversiae de vera circuli mensura (1647)). M J Klein writes of the Idea of Mathematics:-

Pell made a list of tasks that if executed would promote the progress of mathematics in England. His plans included cataloguing all past works, describing the extent of mathematics, selecting the best of the past, describing the advances already made, delineating the methodologies that would prove helpful, and noting the problems that cannot be solved.

The Refutation was written because of a dispute Pell was involved in over the value of π. Longomontanus (Christian Severin) had published his quadrature of the circle in 1644. In fact Longomontanus died in 1647 but the controversy did not end with his death since others joined in. In [9] van Maanen describes in detail the correspondence between Pell and Charles Cavendish in which Pell is trying to enlist supporters for his side of the argument. Pell also translated Lansberge's tables, which were published in 1632, and worked on astronomy.

Pell was elected to the Royal Society on 20 May 1663. He served on the committee considering mechanical and optical inventions and was elected vice-president in 1675.

He is described in [2] as follows:-

Pell was a striking figure, remarkably handsome, with strong, excellent posture, dark hair and eyes, and a good voice. His temperament was sanguine and melancholic.

When in London, Pell lived for a while with Collins. However in the autumn of 1664 an epidemic of the plague began in the poor outskirts of city. The epidemic died down after the winter but spread again in May 1665. The king and court fled from London in June and that summer Pell also left London being invited to Brereton Hall in Cheshire as the guest of William Brereton whom he had tutored while in the Netherlands. Aubrey writes [3]:-

Never was there greater love between master and scholar then between Dr Pell and this scholar of his, whose death on 17 March 1680 hath deprived this worthy doctor of an ingenious companion and a useful friend.

After this Pell lived [3]:-

... in an obscure lodging, three stories high, in Jermyn Street, next to the sign of the Ship, wanting not only books but his proper manuscripts.

He was now in debt and put in prison. After his release he lived in a number of different places such as the College of Physicians, the house of one of his grandchildren, and a lodgings in Westminster where he died.