数学家传记
乔治·比德尔·艾里是剑桥大学的卢卡斯教授和皇家天文学家。他对数学和天文学做出了许多重大贡献。
乔治·比德尔·艾里的父亲是William Airy,母亲是Ann 艾里。William Airy来自林肯郡,Ann是萨福克郡一位农民的女儿。最初William也是农民,但他自学成才,升到了税务稽查员的职位。艾里出生时,他的父母住在诺森伯兰,William在那里担任消费税征收员,但第二年William被调往赫里福德,全家便搬到了那里。
艾里在科尔切斯特就读于拜厄特·沃克学校,十岁时在小学阶段结束时取得第一名。他在学校学到了一些有用的技能,如算术、复式记账以及如何使用计算尺。然而,他很可能从研读父亲的书籍中学到了更多。他在自传中写道(见[4]):——
……他在同学中并不受欢迎。
埃根写道[1]:——
作为一个内向但并不害羞的孩子,艾里即便在当时、尤其是就其处境而言,也是个年轻的势利眼。尽管如此,他凭借制作豌豆射手和其他类似装置的出色技巧和创造力,克服了同学们对他的部分厌恶。
艾里离开拜厄特·沃克学校后,他父亲再次搬迁,这一次搬到了埃塞克斯。从1812年起,艾里每年夏天都与他的叔叔阿瑟艾里一起度过,后者在伊普斯威奇附近有一个农场。显然,艾里在家里不太开心,因为他问叔叔能否和他一起生活,而不是和自己的家人住在一起。自1813年父亲失去税务员工作后,家里的情况变得更糟,从那时起全家生活贫困。由于经济状况,家人似乎相当乐意让艾里的叔叔几乎接替了父亲的角色。
在接下来的五年里,艾里大约有一半时间与叔叔一起度过,这对他很重要。Arthur 艾里是个有学问的人,拥有一座精美的图书馆,藏有化学、光学和力学方面的书籍,艾里如饥似渴地研读这些书,此外他还有许多顶尖科学家朋友。他们对年轻的艾里产生了显著影响,是他寻求学术生涯的主要因素。
在这五年间,即1814年至1819年,艾里就读于科尔切斯特文法学校,在那里他[8]:
……以记忆力著称,在一次考试中背诵了2394行拉丁文诗句。
艾里于1819年进入剑桥大学三一学院,身份是减费生(Sizar),这意味着他支付减免的学费,但基本上要作为仆役来弥补学费的减免。然而,只是因为他叔叔提供了经济支持,他才得以接受大学教育。为了补充收入,艾里招收私人学生,这当然减少了他自己学习的时间。尽管如此,他的表现非常出色,于1823年以高级牧马人(一等荣誉生第一名)毕业,并获得史密斯奖。罗伯特·伍德豪斯于1822年离开卢卡斯讲席成为普卢米安天文学教授,是艾里的史密斯奖考官之一,另一位是接替罗伯特·伍德豪斯担任卢卡斯讲席的托马斯·特顿。次年,艾里获得三一学院的研究员职位,开始了他的学术生涯。
我们应该评论一下为什么艾里在荣誉学位考试中表现如此出色,远远领先于第二名的学生。当时的荣誉学位考试与其说是测试数学能力,不如说是测试考生学习大量材料和方法的能力。在这方面,艾里证明异常出色,部分是因为他出色的记忆力,但也因为他非凡的组织能力。作为本科生,他身边总是放着纸,记录下每一个想法。后来,一切都转移到他所保存的书籍和日记中。他一生都保持这种习惯,这份几乎记录了他每一个想法的记录仍然存在,为那个时期提供了非凡的证据[4]:
他性格的主要特征是秩序。从进入剑桥到生命结束,他的秩序体系一直严格维持。
艾格尼兹·玛丽·克勒克在[8]中写道:-
他从不销毁任何文件,而是设计了一个巧妙的方案,便于查阅他大量的论文。
1824年,艾里在徒步度假时遇到了Richarda Smith。他们初次见面两天后他就求婚了,但她的父亲Richard Smith——查茨沃斯附近一座教堂的牧师——拒绝允许这桩婚事,理由是艾里在经济上无法养活他的女儿。这使艾里下定决心要获得一个职位,其经济地位能让他结婚。
从剑桥毕业仅三年后,他就被任命为剑桥的卢卡斯数学讲席教授。相当令人惊讶的是,卢卡斯讲席教授每年只收到99英镑,而艾里作为助理导师已经收到150英镑。艾里在1826年被告知Turton即将离任时,不知道自己是否有能力竞争这个讲席,但乔治·皮科克说服他,地位比金钱更重要。他成为三位候选人之一,另外两位是French和查尔斯·巴贝奇。当查尔斯·巴贝奇表示他打算就选举一事启动法律程序时,French退出了。艾里获胜,与查尔斯·巴贝奇之间持续多年的竞争由此开始。
除了卢卡斯讲席之外,艾里还被任命为经度委员会成员,只要他出席四次会议,每年就能再获得100英镑。他解释了自己的行为(见[4]):-
如果我能等待的话,我在法律或其他行业的前景可能不错,但那样婚姻就无从谈起了,而我更愿意在不太长的时间内获得一份中等收入。我现在已在某种程度上把科学作为我的方向(但并非不可更改),我认为最好至少在一段时间内把它做好,然后等待机会。
当然,这些话并非出自一个被对学科的热爱所驱使的人之口。他肯定仍然没有足以让他娶Richarda的经济地位,所以他尝试谋求其他职位。他争取爱尔兰皇家天文学家空缺职位的努力在1827年失败了。
艾里是Smith奖的考官,并在担任卢卡斯讲席期间授课。他讲授光学,在这些讲座中他解释了散光问题。这是一种艾里自己也患有的眼睛缺陷,他是第一个设计眼镜来矫正它的人。他早些时候就此问题发表了一篇论文On a peculiar Defect in the Eye,他是第一个提供实际解决方案的人。
1828年,乔治·皮科克告知艾里,天文学Plumian教授罗伯特·伍德豪斯已时日无多,并建议他谋求这个讲席。他写道[4]:-
我让人知道我是候选人,没有人认为值得反对我。……我告诉所有人,薪水(约300英镑)不够,并起草了一份给大学的请愿书要求加薪。……大学以前从未以这种方式被突然袭击,对此有一些骚动。我相信很少有人会采取这一步。……我毫不怀疑会成功。
艾里被任命为剑桥大学普卢米安天文学讲席教授和剑桥天文台台长。大学满足了他增加薪水的要求,他每年获得的500英镑足以让他与Richarda Smith结婚,他于1830年3月24日这样做了。
他于1835年成为皇家天文学家,当时从剑桥搬到格林尼治。在那里,他对皇家天文台进行了重组,这在许多方面是积极的,但也有一些不幸的副作用。由于他不能容忍他的员工自行思考,在他担任皇家天文学家期间,天文台没有培养出任何年轻科学家。然而,他相当出色的工程能力在翻新天文台的仪器方面得到了很好的利用。他担任皇家天文学家一职直到1881年辞职,余生与他的两个未婚女儿住在格林尼治公园附近的White House。
艾里写了On the Algebraic and Numerical Theory of Errors of Observations and the Combinations of Observations一书。尽管当时有人说它:-
……除了那些已经彻底熟悉该主题的人之外,无法阅读,
这本书在剑桥被使用,并影响了卡尔·皮尔逊。这本书是艾里出版的十一本书之一,其他一些包括Trigonometry(1825年)、Gravitation(1834年)和Partial differential equations(1866年)。他非凡的出版记录包括500多篇论文和报告。这源于他极其努力的工作以及高度组织化、高效的工作方式,这使他能够完成比几乎所有其他科学家都多得多的工作。
他对数学的态度非常像一位应用数学家,认为研究这门学科本身没有意义。他的儿子在[4]中写道:-
他的天性极为务实,相应地,他对纯理论问题和研究十分厌恶。在这个问题上,他不断与一些剑桥数学家发生争执。年复一年,他严厉批评参议院楼试卷和史密斯奖试卷,并就同一主题与阿瑟·凯莱进行有趣而尖刻的私人通信。
艾里在1845年迟迟未按约翰·柯西·亚当斯建议的位置搜寻海王星,使约翰·柯西·亚当斯未能获得其工作的全部荣誉,尽管在许多方面他因这一事件受到了不公正的批评。然而,艾里确实对数学和天文学作出了许多重大贡献。他改进了金星和月球的轨道理论,研究了光学中的干涉条纹,对彩虹进行了数学研究,并通过在深矿井顶部和底部摆动摆锤计算了地球的密度。我们应当注意,他得到的值偏大了相当多。
艾里 于1834年被任命为建立标准度量衡委员会的主任。他于1835年当选为 爱丁堡皇家学会 的会士,并于1836年当选为 伦敦皇家学会 的会士,此前于1831年获得了该学会的科普利奖章。他于1840年向该学会做了题为 On the theoretical explanation of an apparent new polarity of light 的贝克讲座。他于1845年因一篇关于爱尔兰潮汐的论文获得了该学会的皇家奖章。
Royal Astronomical Society 于1845年选举 艾里 为主席。然后,在1851年,艾里 当选为 英国协会 的主席,并于1871年当选为 伦敦皇家学会 的主席,担任该职位两年。法兰西学院选举他为成员,以填补1872年 约翰·赫歇尔 去世后空缺的职位,同年他接受了爵士头衔,此前曾三次拒绝,理由是他负担不起费用。此后不久,在1874年,他组织了一次探险,观察金星的 中天。
除了专业科学兴趣之外,艾里 是一个兴趣广泛的人。他喜欢诗歌、历史、神学、古物、建筑、工程和地质学。他甚至发表了一些关于其他兴趣的论文,包括一篇试图确定尤利乌斯·凯撒在英国的登陆地点和离开地点的论文。此外,他还发表了许多关于宗教问题的论文。
他的性格中确实有一些方面使他不受周围人的欢迎。我们已经提到他在学校时是个势利眼。在后来的生活中,他讽刺挖苦,并对皇家天文台的工作人员实行严格的纪律。为他辩护,我们必须注意到,他对自己也实行了如此严格的纪律,以至于他期望别人也这样做对他来说一定显得很自然。
艾里的性格可以从他与查尔斯·巴贝奇长期不断的争执中看出来。1832年他们因一架望远镜的质量发生争执,十年后他说查尔斯·巴贝奇的计算引擎“毫无价值”,并实际上终止了政府对这一项目的资助,1854年他又支持铁路的窄轨,而查尔斯·巴贝奇支持宽轨。在所有这些争执中艾里都是赢家,但他在这些争论中是否站在“正确”的一边,远非清楚。
我们应当以几句话来结束关于艾里作为科学家的重要性的讨论。他自己的话确实表明他对自己有现实的认识(例如见[1]):-
……在天文学中那些……[只需要]方法和判断、所雇用人员科学素养很低的领域,我们做了很多;而在那些完全依赖个人努力的领域,我们做得很少……我们的主要进展是在天文学较低分支中取得的,而对于科学较高分支,我们没有增添任何东西。
Eggen在[1]中写道:-
艾里不是一位伟大的科学家,但他使伟大的科学成为可能。
然而,其他人对艾里的成就评价更高。西德尼·查普曼 [7] 认为:-
艾里被不公平地排挤到了科学边缘……
他的儿子这样总结艾里的一生 [4]:-
艾里的一生基本上是一个勤奋商人的一生,与其他勤奋的人的不同之处仅在于他工作的质量和多样性。这不是激动人心的一生,但充满了趣味……
George Airy's father was William Airy while his mother was Ann Biddell. William Airy was from Lincolnshire and Ann was the daughter of a farmer from Suffolk. Originally William had been a farmer too, but he had educated himself and risen to the position of tax inspector. When George was born his parents were living in Northumberland where William was a collector of excise, but in the following year the family moved to Hereford when William was transferred there.
George attended Byatt Walker's school in Colchester and at the age of ten he took first place at the end of his primary school career. He had learnt some useful skills at the school such as arithmetic, double-entry book keeping and how to use a slide rule. He had probably learned more, however, from studying his father's books. He wrote in his autobiography that (see [4]):-
... he was not a favourite with his school mates.
Eggen writes [1]:-
An introverted but not shy child, Airy was, even for the time and especially for his circumstances, a young snob. Nevertheless, he overcame some of the dislike of his schoolmates by his great skill and inventiveness in the construction of peashooters and other such devices.
Before Airy left Byatt Walker's school his father had transferred again, this time to Essex. From 1812 Airy spent his summers with his uncle, Arthur Biddell, who had a farm near Ipswich. Clearly Airy was not too happy at home because he asked his uncle if he could live with him rather than with his own family. Things had taken a turn for the worse at home since his father lost his tax collectors job in 1813 and the family were, from that time, living in poverty. Because of the financial circumstances the family seem to have been quite glad that Airy's uncle had almost taken over the role of his father.
The fact that Airy spent about half his time with his uncle over the next five years was important for him. Arthur Biddell was a man of learning who had a fine library containing books on chemistry, optics and mechanics which Airy avidly studied, and in addition he had many leading scientists as his friends. Their influence on the young Airy was marked and was a major factor in his seeking an academic career.
During these five years, 1814 to 1819, Airy attended Colchester Grammar School where he was [8]:-
... noted for his memory, repeating in one examination 2394 lines of Latin verse.
Airy entered Trinity College, Cambridge in 1819 as a sizar, meaning that he paid a reduced fee but essentially worked as a servant to make good the fee reduction. However it was only because his uncle provided financial support that he was able to undertake university studies at all. To supplement his income Airy took private pupils and this, of course, gave him less time for his own studies. Despite this his performance was outstanding and he graduated as Senior Wrangler (the top First Class student) in 1823 and was a Smith's prizeman. Woodhouse, who had left the Lucasian chair in 1822 to become Plumian Professor of Astronomy, was one of Airy's examiners for the Smith's prize, the other being Thomas Turton who had succeeded Woodhouse to the Lucasian chair. In the following year Airy was awarded a fellowship at Trinity College and began his academic career.
We should comment on why Airy did so well in the Tripos examinations, being far ahead of the next best student. The Tripos examinations at that time were less a test of mathematical ability and more a test of the candidates ability to learn vast amounts of material and methods. At this Airy proved exceptionally good, partly because of his excellent memory, but also because of his remarkable organisational abilities. As an undergraduate he kept paper beside him to record every thought he had. Later everything was transferred to the books and diaries which he kept. He maintained this routine throughout his life and this record, almost of his every thought, still exists to provide remarkable evidence of the period [4]:-
The ruling feature of his character was order. From the time he went up to Cambridge to the end of his life his system of order was strictly maintained.
Clerke writes in [8]:-
He never destroyed a document, but devised an ingenious plan of easy reference to the huge bulk of his papers.
In 1824 Airy met Richarda Smith while on a walking holiday. He proposed two days after they first met but her father, Richard Smith, the vicar of a church near Chatsworth, refused to allow the marriage on the grounds that Airy could not support his daughter financially. This made Airy determined to obtain a position with the financial status which would allow him to marry.
Only three years after graduating from Cambridge, he was appointed Lucasian Professor of Mathematics at Cambridge. It is rather surprising that the Lucasian Professor only received £99 per year while Airy was already receiving £150 as an assistant tutor. Airy wondered whether he could afford to compete for the chair when he was advised in 1826 that Turton was leaving, but Peacock persuaded him that the status was more important than the money. He became one of three candidates, French and Babbage being the other two. When Babbage stated that he was about to start legal proceedings over the election, French withdrew. Airy triumphed and a rivalry with Babbage which was to last for many years began.
In addition to the Lucasian Chair, Airy was appointed a member of the Board of Longitude which gave him another £100 per year provided he attended four meetings. He explained his actions (see [4]):-
My prospects in the law or other profession might have been good if I could have waited but marriage would have been out of the question and I much preferred a moderate income in no long time. I had now in some measure taken science as my line (but not irrevocably) and I thought it best to work it well for a time at least and wait for accidents.
These, of course, are not the words of a man driven by a love of his subject. He certainly still did not have the financial position to allow him to marry Richarda so he tried for other posts. His attempt to secure the vacant post of Astronomer Royal for Ireland failed in 1827.
Airy was an examiner for the Smith's Prize and gave lectures while holding the Lucasian Chair. He lectured on light and in these lectures he explained the problem of astigmatism. It was an eye defect which Airy suffered from himself and he had been the first to design glasses to correct it. He had earlier published a paper On a peculiar Defect in the Eye on this problem for which he was the first to provide a practical solution.
In 1828 Peacock informed Airy that Woodhouse, the Plumian Professor of Astronomy, had not long to live and advised him to seek this chair. He wrote [4]:-
I made it known that I was a candidate and nobody thought it worthwhile to oppose me. ... I told everyone that the salary (about £300) was not sufficient and drafted a manifesto to the University for an increase. ... the University had never before been taken by storm in such a manner and there was some commotion about it. I believe that very few people would have taken that step. ... I had no doubt of success.
Airy was appointed Plumian Professor of Astronomy at Cambridge and Director of the Cambridge Observatory. The University had complied with his request for the salary to be increased and the £500 per year he received was sufficient to allow him to marry Richarda Smith , which he did on 24 March 1830.
He became Astronomer Royal in 1835 moving at that time from Cambridge to Greenwich. There he undertook a reorganisation of the Royal Observatory which was positive in many ways but also had some unfortunate side effects. Since he could not tolerate his staff thinking for themselves no young scientists were trained at the Observatory during his period as Astronomer Royal. However, his considerable engineering ability was put to good use in renovating the instruments at the observatory. He held this post of Astronomer Royal until 1881 when he resigned and lived the rest of his life with his two unmarried daughters in the White House close to Greenwich Park.
Airy wrote the text On the Algebraic and Numerical Theory of Errors of Observations and the Combinations of Observations. Although said at the time to be:-
... unreadable except by those already thoroughly acquainted with the subject,
the book was used at Cambridge and influenced Pearson. This text was one of eleven books which Airy published, some of the others being Trigonometry (1825), Gravitation (1834), and Partial differential equations (1866). His remarkable publication record included over 500 papers and reports. This resulted from his extremely hard work and also his highly organised, efficient way of working which enabled him to get through far more work than almost every other scientist.
His attitude to mathematics was very much as an applied mathematician who saw no point in the study of the subject in its own right. His son writes in [4]:-
His nature was eminently practical, and his dislike of mere theoretical problems and investigations was proportionally great. He was continually at war with some of the Cambridge mathematicians on this subject. Year after year he criticised the Senate House papers and the Smith's Prize papers very severely, and conducted an interesting and acrimonious private correspondence with Professor Cayley on the same subject.
Airy's delay, in 1845, of searching for Neptune at the location suggested by Adams prevented Adams obtaining full credit for his work although in many ways he has been unfairly criticised over this episode. Airy did, however, make many major contributions to mathematics and astronomy. He improved the orbital theory of Venus and the Moon, studied interference fringes in optics, made a mathematical study of the rainbow and computed the density of the Earth by swinging a pendulum at the top and bottom of a deep mine. We should note that the value he obtained was too large by a fair amount.
Airy was made chairman of the Commission set up to construct Standard Weights and Measures in 1834. He was elected a Fellow of the Royal Society of Edinburgh in 1835, and a Fellow of the Royal Society of London in 1836, having received the Society's Copley Medal in 1831. He gave the Bakerian lecture to the Society entitled On the theoretical explanation of an apparent new polarity of light in 1840. He received the Society's Royal Medal in 1845 for a paper on the Irish tides.
The Royal Astronomical Society elected Airy to be their President in 1845. Then, in 1851, Airy was elected President of the British Association, and in 1871 he was elected President of the Royal Society of London holding the post for two years. The Institut de France elected him to membership to fill the position which became vacant on the death of John Herschel in 1872 and in the same year he accepted a knighthood having declined it on three previous occasions on the grounds that he could not afford the fees. Soon after this, in 1874, he organised an expedition to observe the transit of Venus.
Outside his professional scientific interests, Airy was a man of broad tastes. He liked poetry, history, theology, antiquities, architecture, engineering, and geology. He even published papers on his other interests including one which tried to identify the exact place where Julius Caesar landed in Britain and the exact place from which he left. In addition he published a number of papers on religious matters.
There were certainly sides to his character which made him unpopular with those around him. We have already mentioned how he was a snob at school. In later life he was sarcastic and enforced a rigid discipline on his staff at the Royal Observatory. In his defence we would have to note that he enforced such a rigid discipline on himself that it must have seemed natural to him to expect the same from others.
An illustration of Airy's personality is shown from his long running disagreements with Babbage. They had a dispute over the quality of a telescope in 1832, he stated that Babbage's calculating engine was "worthless" ten years later and effectively stopped government funding of the project, and in 1854 he took the side of the narrow gauge for railways while Babbage supported the wide gauge. In all these disputes Airy came out the winner, but it is far from clear that he took the "right" side in the arguments.
We should end with a few words on Airy's importance as a scientist. His own words certainly show that he had a realistic view of himself (see for example [1]):-
... in those parts of astronomy which ... [require] only method and judgement, with very little science in the persons employed, we have done much; while in those which depend exclusively on individual effort we have done little ... our principal progress has been made in the lower branches of astronomy while to the higher branches of science we have not added anything.
Eggen writes in [1]:-
Airy was not a great scientist, but he made great science possible.
However, others have a higher opinion of Airy's achievements. Chapman [7] believes that:-
Airy has been unfairly relegated to the scientific sidelines ...
His son summed up Airy's life as follows [4]:-
The life of Airy was essentially that of a hard-working business man, and differed from that of other hard-working people only in the quality and variety of his work. It was not an exciting life, but it was full of interest ...
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