弗朗西斯·伊西德罗·埃奇沃思Francis Ysidro Edgeworth

弗朗西斯·伊西德罗·埃奇沃思的父母是西班牙人Rosa Florentina Eroles和来自一个有着浓厚文学渊源的爱尔兰家庭的埃奇沃思 Beaufort 埃奇沃思。他的祖父是Richard Lovell 埃奇沃思，一位作家、发明家和教育家，结过四次婚，有22个孩子。在这22个孩子中，有埃奇沃思的父亲，还有Maria Edgeworth，后者以儿童故事作家以及描写爱尔兰生活的小说而闻名。Richard Lovell 埃奇沃思在都柏林西北的Edgeworthstown有一处庄园，埃奇沃思就出生在这处庄园。

埃奇沃思原名埃奇沃思 埃奇沃思，但他调换了自己的名。他是父母五个儿子中最小的，年仅两岁时父亲就去世了。两年后，也住在这处庄园的Maria也去世了。他没有上学，而是在自己家中由私人教师教育，直到达到上大学的年龄。

在人生的这个阶段，埃奇沃思对数学没有特别的兴趣。他是在大学教育结束后才开始学习统计学的；他在大学时的兴趣是古代语言和现代语言。他17岁进入都柏林圣三一学院，学习法语、德语、西班牙语和意大利语。毕业后，他获得奖学金前往牛津学习，并于1867年1月进入埃克塞特学院。在牛津，他先后在莫德林学院和贝利奥尔学院度过了一段时间，1869年毕业。

埃奇沃思离开牛津后那些年究竟做了什么并不清楚，但可以肯定的是，他住在伦敦，经济支持很少。这一时期的一个重要影响来自威廉·斯坦利·杰文斯，他是埃奇沃思的朋友，也是近邻。他一定曾在某个时候学过法律，因为他在1877年获得了律师资格。然而三年后，他在伦敦国王学院讲授逻辑学。1888年，他被任命为伦敦国王学院政治经济学教授，两年后，他被任命为Tooke经济科学讲席。

令人惊讶的是，在这段多变的职业生涯中，埃奇沃思在某处学习过数学。我们不得不假设他在数学上是自学成才的，这或许可以解释为什么他似乎认为高等数学是所有人都能理解的。例如，他第一部严肃的出版物New and old methods of 伦理学（1877年）在[7]中被莫里斯·肯得尔描述如下：-

在他一生中的任何时候，他的著作都不是那种本身令人愉悦的散文或有序的思想呈现，而在这部特别的著作中，他实际上写下了变分积分，这必定使当时大多数对伦理问题感兴趣的人无法理解。

1881年，他出版了Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences。这部作品实际上是关于经济学的，探讨了经济微积分和功利微积分。事实上，他的大部分工作可以说是数学心理学的应用，埃奇沃思将其视为类似于数学物理学。它们被应用于效用的度量、伦理价值的度量、证据的度量、概率的度量、经济价值的度量以及经济均衡的确定。他用数学公式表达了幸福的能力和工作的能力。他得出的结论——女性在享受和工作方面的能力低于男性——在今天不会受欢迎。

埃奇沃思于1885年出版了Methods of Statistics，其中阐述了用于均值比较的显著性检验的应用和解释。

1891年，埃奇沃思离开伦敦，前往牛津担任德拉蒙德政治经济学讲席。他在万灵学院获得了一份会士职位，并一直担任讲席和会士，直到1922年退休。1891年另一个重要事件是Economic Journal开始出版，埃奇沃思担任其第一任编辑。该期刊是皇家经济学会的出版物，该学会成立于1890年，埃奇沃思被任命为学会秘书。然而[2]：-

……他对各国经济学和经济学家的广泛了解，以及他的勤奋和浓厚兴趣，与对商业和行政事务的完全无知结合在一起。

他继续担任编辑直到1926年，约翰·梅纳德·凯恩斯接任编辑一职。

1892年，埃奇沃思在一系列论文中研究了相关性和估计相关系数的方法。这些论文中的第一篇是Correlated Averages。

埃奇沃思的工作影响了卡尔·皮尔逊，尽管两人之间产生了不快，后来卡尔·皮尔逊否认了埃奇沃思的影响。在1926年2月的弗朗西斯·高尔顿晚宴上，卡尔·皮尔逊谈到了几天前埃奇沃思的去世：-

……我们几乎可以称他为生物统计学家，因为他为Biometrika撰稿……就在去年十二月，他来了，像他一直以来那样发言……他的批评像以往一样失败了，因为他说的不是人民的语言。……如果他总是沿着我们犁沟的路线横穿而过，我倒愿意把他算作生物统计学家之一。此外，我们欠他一些东西，像一个优秀的德国人，他知道希腊字母k不是现代的c，如果你们中任何人曾经想知道Biometrika中的k从何而来，我坦率地承认我从埃奇沃思那里偷来的。每当你们看到那个k，就想起亲爱的老埃奇沃思。

在[2]中，对他的性格和兴趣有极好的描述：-

埃奇沃思未婚。他是一个不知疲倦的读者，但他对散步、登山、高尔夫和划船的热爱，加上他严格而有规律的习惯，使他直到最后都保持着惊人的活力。每年夏天，即使到了80岁，他也会在早餐前在Parson's Pleasure游泳，人们经常看到他在牛津周围的乡间骑自行车，或在Cowley的球场上打球。但作为步行者，他也许是最不知疲倦的；他是那些周日远足的活力和灵魂，这些远足多年来一直是他学院的习俗。他有一种也许来自他西班牙母亲的宫廷优雅，又加上了爱尔兰人的幽默、想象力和慷慨。一位终身朋友从未见过他发脾气或说别人的坏话。他的甜蜜和光明很好地结合在一起。他是最快乐的人，似乎拥有身心永葆青春的秘诀。

Francis Edgeworth's parents were Rosa Florentina Eroles, who was Spanish, and Francis Beaufort Edgeworth, who came from an Irish family with strong literary connections. His grandfather was Richard Lovell Edgeworth, an author, inventor and educationalist who was married four times and had 22 children. Among these 22 children were Edgeworth's father and also Maria Edgeworth who was well known as a writer of children's stories and also for novels about life in Ireland. Richard Lovell Edgeworth had an estate at Edgeworthstown, northwest of Dublin, and it was on this estate that Edgeworth was born.

Francis Ysidro Edgeworth was originally named Ysidro Francis Edgeworth but transposed his forenames. He was the youngest of his parents five sons and when he was only two years old his father died. Two years later Maria, who also lived on the estate, also died. He did not attend school, but was educated by private tutors in his own home until he reached the age to enter university.

At this stage in his life Edgeworth had no particular interest in mathematics. He came to study statistics after only after his university education had finished; his interests at university were in ancient and modern languages. He entered Trinity College, Dublin at the age of 17 and studied French, German, Spanish and Italian. After graduating, he was awarded a scholarship to study at Oxford and he entered Exeter College in January 1867. At Oxford he spent some time at Magdalen and at Balliol, graduating in 1869.

Exactly what Edgeworth did in the years after leaving Oxford is unclear but certainly he lived in London with little financial support. One important influence from this period was Jevons who was a friend and near-neighbour of Edgeworth. He must have studied law at some time since he was called to the Bar in 1877. Three years later, however, he was lecturing on logic at King's College, London. In 1888 he was appointed Professor of Political Economics at King's College, London and, two years later, he was appointed to the Tooke chair of Economic Science.

The surprising part is that somewhere in this varied career Edgeworth studied mathematics. We have to assume that he was self-taught in mathematics and this might explain why he seemed to believe that advanced mathematics was understood by all. For example his first serious publication New and old methods of ethics (1877) is described by Kendall in [7] as follows:-

None of his writings, at any time in his life, consisted of the kind of prose, or orderly presentation of ideas, which give pleasure for their own sake, and in this particular work he actually writes down variational integrals, which must have put it beyond the understanding of most of those who were interested in ethical problems at that time.

In 1881 he published Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. This work, really on economics, looks at the Economical Calculus and the Utilitarian Calculus. In fact most of his work could be said to be applications of mathematical psychics which Edgeworth saw as analogous to mathematical physics. They were applied to the measure of utility, the measure of ethical value, the measure of evidence, the measure of probability, the measure of economic value, and the determination of economic equilibria. He formulated mathematically a capacity for happiness and a capacity for work. His conclusions that women have less capacity for pleasure and for work than do men would not be popular today.

Edgeworth published Methods of Statistics in 1885 which presented an exposition of the application and interpretation of significance tests for the comparison of means.

In 1891 Edgeworth left London to take up the Drummond Chair of Political Economy at Oxford. He obtained a fellowship at All Souls College and he held both the chair and the fellowship until he retired in 1922. Another event of significance in 1891 was that the Economic Journal began publication with Edgeworth as its first editor. This journal was the publication of the Royal Economic Society which had been set up in 1890 with Edgeworth appointed as secretary to the Society. However [2]:-

... his extensive knowledge of economics and economists in all countries, and his great industry and keen interest, were coupled with a complete innocence of business and administrative affairs.

He continued to be editor until 1926 when Keynes took over the editorship.

In 1892 Edgeworth examined correlation and methods of estimating correlation coefficients in a series of papers. The first of these papers was Correlated Averages.

Edgeworth's work was to influence Pearson although bad feeling developed between the two and later Pearson was to deny Edgeworth's influence. At the Galton dinner in February 1926 Pearson spoke of Edgeworth's death a few days earlier:-

... him we can almost call a biometrician for he contributed to Biometrika ... Only last December he came and spoke as he had always spoken ... and his criticism failed as it had always failed, because he spoke not the language of the people. ... I should like to reckon him among the biometricians if he ploughed always right across the line of our furrows. Besides we owe him something, like a good German he knew that the Greek k is not a modern c, and, if any of you at any time wonder where the k in Biometrika comes from, I will frankly confess that I stole it from Edgeworth. Whenever you see that k call to mind dear old Edgeworth.

In [2] there is an excellent description of his character and interests:-

Edgeworth was unmarried. He was an insatiable reader, but his love of walking, mountaineering, golf, and boating, with his strict and regular habits, maintained to the last his wonderful vitality. Every summer, even at the age of 80, he used to bathe at Parson's Pleasure before breakfast, and he would often be seen riding his bicycle in the country round Oxford or playing on the course at Cowley. But as a walker he was perhaps most indefatigable; and he was the life and soul of those Sunday tramps which have for years been a custom of his College. To a courtly grace, derived perhaps from his Spanish mother, he added the Irish characteristics of humour, imagination and generosity. A lifelong friend has never known him to be out of temper or speak ill words of others. In his sweetness and light were well combined. He was the merriest of men, and seemed to possess the secret of perpetual youth, both of mind and of body.