数学家传记
查尔斯·道奇森是一位数学讲师和数学书籍作者，以笔名刘易斯·卡罗尔更为人所知。他尤其以《爱丽丝梦游仙境》闻名。
查尔斯·勒特威奇·道奇森以笔名“刘易斯·卡罗尔”更为人所知。尽管他是一位数学家，但他最为人所知的是Alice's adventures in wonderland（1865年）和Through the looking glass（1872年）的作者，这两本儿童读物是有史以来最受欢迎的书籍之一。它们以讽刺和文字机智而著称。道奇森以自己的名字撰写数学著作，但为他的儿童读物，他发明了笔名“刘易斯·卡罗尔”，将他的前两个名字“Charles Lutwidge”翻译成拉丁文“Carolus Lodovicus”，然后将其英语化并颠倒顺序。
查尔斯·勒特威奇·道奇森的父亲是查尔斯·道奇森牧师。老查尔斯·道奇森生于1800年，就读于牛津大学，在数学和古典学方面均获得一等学位。他被任命为牛津大学的数学讲师，并拥有一个研究员职位，但在1827年与表妹弗朗西斯·简·勒特威奇结婚后，他不得不放弃牛津的研究员职位。随后，他成为达斯伯里诸圣教堂的助理牧师，正是在这个镇上，查尔斯和弗朗西斯的十一个孩子中有十个出生。
查尔斯·勒特威奇是父母三个男孩中的长子，他有两个姐姐：范妮，生于1828年；伊丽莎白，生于1830年。查尔斯于1832年7月11日在他父亲的教堂受洗，在一个严格的基督教家庭中长大。他的早期教育，像他的兄弟姐妹一样，是由父母提供的。他小时候主要阅读宗教书籍，他进步迅速的一个迹象是，他在七岁时就已经读过Pilgrim's Progress。查尔斯敬仰他的父亲，希望像他一样。由于数学是他父亲最喜欢的科目，很容易看出查尔斯是如何早期就爱上数学的。查尔斯不仅以父亲为榜样，他的父亲也希望儿子追随他的脚步，在牛津学习数学，然后获得研究员职位，结婚并成为牧师。
在达斯伯里，道奇森一家经济上不得不挣扎，所以当查尔斯的父亲于1843年搬到约克郡的蒂斯河畔克罗夫特担任牧师时，这是一种解脱，他的收入大幅增加。在克罗夫特，一家人住在一个带美丽花园的大牧师住宅里，但选择过比他们本可以过的更简朴的生活。1844年8月1日，查尔斯进入里士满学校寄宿，住在校长家里。学校离他家只有十英里，所以他的父母在他到达后一周多就能来看他。他们发现他适应得很好，事实上在这所学校，他接受了极好的教育基础，在数学方面表现出色。
1846年1月27日，查尔斯十四岁生日那天，他进入了拉格比学校。这是一所著名的学校，但查尔斯在这里觉得极其艰难。他是一个害羞、敏感、口吃的男孩，受到年长男孩的欺凌，正如克拉克所写[7]：-
从各方面来看，拉格比的生活对年轻的道奇森来说都是一场个人灾难。
尽管深感不幸，道奇森在学业上仍达到了高标准，不断获得奖励。数学再次成为他最喜欢的科目，但他在神学方面也很出色。他在1848年患上的若干疾病产生了持久的影响。首先是他在春天染上的百日咳。他留下了持续不断的咳嗽，这一症状在他一生中多次复发。秋天他得了腮腺炎，这使他的右耳有些失聪，这一问题从未好转。他后来写到自己在拉格比的日子（例如见[9]）：-
在我逗留期间，我想我在各种学问上取得了一些进步，但没有一样是带着热爱去做的，而且我花了无法估量的时间抄写罚写作业——我认为这后一点是拉格比学校的主要缺点之一。我在那里交了一些朋友……但我不能说，我回顾自己在公学的生活时带着任何愉悦之感，也不能说任何世俗的考虑会促使我重新经历那三年。
他于1849年12月离开拉格比，次年5月前往牛津大学，为在那里开始学业做必要的安排。
正如他父亲的愿望，道奇森进入了牛津的基督堂学院，这也是他父亲曾就读的学院。然而，起初事情并不顺利，因为住宿紧张，他不得不回到位于克罗夫特的父母家中，等待住宿安排妥当后才能开始大学生活。1851年1月24日，道奇森返回牛津，与父亲的朋友雅各布·利牧师同住。两天后，他的母亲突然去世，年仅47岁，他不得不再次返回克罗夫特。回到牛津后，他下定决心努力学习，以便赢得奖学金并在经济上独立。他能够将社交和文化活动与数学上的刻苦学习相结合，1851年11月，他获得了每年价值20英镑的鲍尔特奖学金。1852年12月，他在古典学中获得二等荣誉，在数学中获得一等荣誉后，被授予每年25英镑的终身研究员职位。这伴随着居住在基督堂学院的权利，尽管没有要求他取得进一步的学术成就，但他被要求接受圣职并保持未婚。
道奇森的父亲对儿子的成功感到无比欣喜，而且他本人已于1852年被任命为里彭大教堂的教士，两年后又成为里士满的副主教。这一年，道奇森完成了学业，获得古典学三等学位，但在数学一等荣誉学位获得者名单中遥遥领先。接下来的挑战是高级奖学金竞争，他知道，若能在其中成功，几乎肯定会被任命为数学讲师。然而，此时一向勤勉的道奇森过于沉迷于休闲和文化活动，未能在数学上投入必要的功夫。他开始招收学生，尽管并非作为正式的大学导师，这想必也占去了他大量时间。1855年3月22日的两场奖学金考试以及次日上午的考试，他对自己的表现感到失望，于是放弃，没有出席3月23日下午的最后一场考试（只有两名学生参加了那场考试）。当然，他没有获得奖学金，并在日记中写道（例如见[9]）：——
想到这多么令人懊恼……我本可以多么轻易地得到它，只要我这学期好好用功，而我恐怕必须认为这学期是浪费了。不过，现在我还有一年时间，以这过去的一学期为教训……我打算到下次之前读完积分学、光学（以及光的理论）、天文学和高等动力学。我记下这个决心，以便让自己羞愧，万一1856年3月发现我仍未做好准备，因为我知道我一生中已经有过多少类似的失败。
他的日程仍然排得很满，辅导学生，而且自1855年2月起，他还正式受聘为基督堂的副图书馆员。在另一次奖学金考试中，他再次未能获奖，但随后为数学考官辅导了十四名学生。这项任务（例如见[9]）：——
……不会给我任何正式职位，因为这只是我们之间的私人安排：这对我日后获得讲师职位无疑有利，尽管它绝不能保证这一点。
1855年夏天，道奇森在他父亲位于克罗夫特的学校任教，到10月返回牛津时，他已是一名数学讲师，正是他所寻求的职位。这意味着他现在不必按原计划参加1856年3月的奖学金考试。道奇森留在牛津基督堂，讲授数学并为学生撰写论著和指南，直到1881年。尽管他于1861年接受了执事圣职，但道奇森从未被任命为牧师，部分原因是他患有口吃，使布道困难，部分原因也许是他发现了戏剧等其他兴趣。然而，随着时间的推移，他似乎越来越难以接受非基督徒应受谴责的观点，而作为一个极为诚实的人，他会因此觉得成为牧师所必须宣誓的誓言无法接受。
道奇森的爱好之一是摄影，他在这方面变得非常精通。他的兴趣始于1855年拜访叔叔时，当时他用叔叔的设备拍了一些照片。1856年3月，他购买了自己的相机和显影化学品，并开始尝试拍摄风景、建筑、雕塑，尤其是人物。他的家人、朋友和同事成为他摄影的对象，但他尤其擅长拍摄儿童，这是他最大的乐趣。爱丽丝·利德尔是基督堂学院院长亨利·乔治·利德尔的三个女儿之一，也是他摄影的对象之一，并且是虚构爱丽丝的原型。其他拍摄对象包括作家乔治·麦克唐纳的孩子们和诗人阿尔弗雷德·丁尼生勋爵的儿子们。道奇森不仅喜欢拍摄儿童，也喜欢他们的陪伴。1932年，爱丽丝·利德尔回忆她和姐妹们洛琳娜和伊迪丝如何：-
……常常坐在大沙发上的他两侧，他一边给我们讲故事，一边用铅笔或墨水画图说明……他似乎有无穷无尽的这些奇幻故事，他边讲边编，同时忙着在一大张纸上画画。这些故事并不总是全新的。有时它们是旧故事的新版本；有时它们从旧的基础上开始，但由于频繁的打断而发展成新的故事，这些打断开启了新的、意想不到的可能性。
正是在1862年，道奇森应爱丽丝的要求写下了这些故事。作家亨利·金斯利拜访了利德尔家，偶然拿起了道奇森的故事。他明确表示必须说服道奇森出版他的作品。三年后，在润色并添加了一些材料后，道奇森出版了他的第一本“爱丽丝书”，名为Alice's Adventures in Wonderland。
作为一名数学家，道奇森相当保守，但确实彻底而谨慎。他著有不少数学书籍，包括：A syllabus of plane algebraical geometry（1860年）、Two Books of Euclid（1860年）、The Formulae of Plane Trigonometry（1861年）、Condensation of Determinants（1866年）、Elementary Treatise on Determinants（1867年）、Examples in Arithmetic（1874年）、Euclid and his modern rivals（1879年）、Curiosa Mathematica, Part I: A New Theory of Parallels（1888年）和Curiosa Mathematica, Part II: Pillow Problems thought out during Sleepless Nights（1893年）。除了Euclid and his modern rivals（1879年）具有历史意义外，他的数学书籍都没有持久的的重要性。道奇森写这本书是为了捍卫使用欧几里得的Elements作为几何教学手段。这本书以戏剧形式写成，其中欧几里得的幽灵回来向现代几何学家捍卫他的书。欧几里得总结说：-
让我带着这样的希望：我已经使你们相信保留我的顺序和编号，以及我处理直线、角、直角，尤其是平行线的方法的重要性，如果不是必要性的话。把这些留给我不动，我将非常满意地看着其他变化发生……
这是一部严肃的作品，在几何教学方面各方都有充分论证的案例。它也包含了许多道奇森幽默的证据，例如在欧几里得的幽灵首次出现后，他离开时说：-
……我们现在的访谈就到此结束；所以等您逐一评述了我的《现代竞争者》之后，我们再见面。如果您手边有慢节奏的音乐，我会随着它消失：既然如此……[没有慢音乐就消失了]
尽管道奇森在此主张保留欧几里得处理平行线的方式，但在九年后出版的Curiosa Mathematica, Part I: A New Theory of Parallels中，他提出了自己关于处理平行公设的想法。
作为一名数学逻辑学家，他有兴趣通过将其视为一种游戏来增进理解。他于1887年出版了The Game of Logic，1896年出版了Symbolic Logic Part I。在后一部著作中，道奇森提出了一种用图表直观表示命题的方法，该图表类似于约翰·维恩于1881年开发的维恩图，但道奇森的图具有某些优势。然而，约翰·维恩图如今被广泛使用，而道奇森的游戏板方法已被遗忘。Symbolic Logic Part I中包含以下陈述：-
我手头有第二部和第三部的大量手稿，希望能够——如果生命、健康和机会允许我的话——将它们出版……
事实上，在1959年至1970年间，威廉·沃伦·巴特利找到了缺失部分的片段，并于1977年首次出版。在文章[23]中，巴特利声称，先前未出版的材料显示了可归功于道奇森的具体成就。这些是：-
其他近期研究再次使道奇森的数学贡献得到了比以往更为有利的评价。例如在[20]中，Abeles写道：-
本文讨论了C L 道奇森（刘易斯·卡罗尔）在1873年至1876年间撰写的关于选举与委员会的三本小册子。文章认为，道奇森关于循环的工作预示了Thompson和Remage在1964年提出的一个随机模型，并包含了极大似然估计的基本思想。
在[18]中，我们也看到对道奇森在选举理论方面众多贡献的非常积极的评价，其中或许最重要的当属均写于1884年的Parliamentary Elections和The Principles of Parliamentary Representation：-
道奇森的工作对当时正在讨论的选举改革问题提出了一种完整而统一的方法，但在此过程中，他发展并贡献了博弈论和分配方面的思想，这些思想远远超前于1880年代。
最后我们应该提到道奇森对智力游戏的热爱[9]：-
他擅长猜字谜，会唱歌，会讲故事。很快，笑话、智力游戏、游戏、问答、数字和文字戏法以及思维练习就成了他日常消遣的手段，也成了他的家人和朋友乐趣与消遣的来源。他也玩传统游戏——国际象棋、槌球、台球、纸牌——但他的头脑并不满足于这些，他扩展、延伸并试验各种形式和样式，把传统娱乐推向极限，并发明新的娱乐。19世纪70年代，他创造出了名副其实的谜题与智力挑战宝库，为魔术和游戏玩法增添了精彩内容……他如此富有创造力、如此多产，以至于他的游戏和消遣足以填满相当规模的选集。
这本书[14]包含“42个令人愉快消遣的思维难题”，这些是道奇森去世时正在研究的谜题。他的去世很突然。1898年1月初，他得了感冒，起初似乎很轻微，但后来发展成胸部问题，医生坚持让他卧床休息。他的呼吸变得越来越困难，于1月14日下午2点30分去世。
道奇森以刘易斯·卡罗尔为笔名写作，贡献了精彩的胡话诗范例，其中最著名的是出自Through the Looking-Glass的《Jabberwocky》。这首诗开头是：-
‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
The Hunting of the Snark由道奇森（以刘易斯·卡罗尔为笔名）于1876年出版，被称为：-
……英语语言中最长且最连贯的胡话诗。
他的胡话诗中的几个词已进入标准英语用法。例如，'chortle'一词，结合了'snort'和'chuckle'，出现在⟦N1⟧的⟦L1⟧中。
Charles Lutwidge Dodgson is better known by the pseudonym "Lewis Carroll". Although he was a mathematician, he is best known as the author of Alice's adventures in wonderland (1865) and Through the looking glass (1872), children's books that are among the most popular of all time. They are distinguished as satire and as examples of verbal wit. Dodgson wrote mathematical works under his own name but for his children's books he invented the pen name "Lewis Carroll" by translating his first two names "Charles Lutwidge" into Latin as "Carolus Lodovicus", then anglicising and reversing their order.
Charles Lutwidge Dodgson's father was the Reverend Charles Dodgson. Charles Dodgson senior was born in 1800 and studied at the University of Oxford where he gained a First Class degree in both mathematics and classics. He was appointed as a mathematics lecturer at Oxford where he held a Fellowship but, on marrying his cousin Frances Jane Lutwidge in 1827, he had to give up his Oxford Fellowship. He then became a curate at All Saints' Church in Daresbury and it was in that town that ten of Charles and Frances' eleven children were born.
Charles Lutwidge was the eldest of his parents three boys, having two elder sisters Fanny, born in 1828, and Elizabeth, born in 1830. Charles was baptised on 11 July 1832 in his father's church and grew up in a strict Christian household. His early education, like that of his brothers and sisters, was provided by his parents. He read mostly religious books as a child and an indication of his rapid progress is that he had read Pilgrim's Progress by the time he was seven. Charles looked up to his father and wished to be like him. Since mathematics was his father's favourite subject, it is easy to see how Charles gained an early love for it. Not only did Charles model himself on his father, but his father also wanted his son to follow in his footsteps by studying mathematics at Oxford, then obtaining a Fellowship, marrying and becoming a vicar.
At Daresbury the Dodgson family had to struggle financially, so it was a relief when Charles's father moved to become vicar at Croft-on-Tees in Yorkshire in 1843 where his income was substantially increased. At Croft the family lived in a large rectory with a wonderful garden but chose to live much more simply than they might have done. On 1 August 1844 Charles enter Richmond School as a boarder, living in the headmaster's house. The school was only ten miles from his home and so his parents were able to visit him just over a week after he arrived. They found that he was settling in well and indeed at this school he received an excellent foundation for his education, excelling in mathematics.
On 27 January 1846, Charles' fourteenth birthday, he enrolled at Rugby School. This was a famous school but one where Charles found things extremely difficult. A shy, sensitive boy with a stammer, he suffered bullying from the older boys and, as Clark writes [7]:-
From every point of view life at Rugby was a personal disaster for young Dodgson.
Despite being deeply unhappy, Dodgson achieved high standards in his school work, receiving a steady stream of prizes. Again mathematics was his favourite subject but he also excelled at divinity. A number of illnesses which he suffered from in 1848 had a lasting effect. The first was whooping cough which he caught in the spring. He was left with a persistent cough which returned at various times throughout his life. In the autumn he contracted mumps and this left him somewhat deaf in his right ear, a problem which never improved. He wrote afterwards of his time at Rugby (see for example [9]):-
During my stay I made I suppose some progress in learning of various kinds, but none of it was done with love, and I spent an incalculable time in writing out impositions - this last I consider one of the chief faults of Rugby School. I made some friends there ... but I cannot say that I look back upon my life at a Public School with any sensations of pleasure, or that any earthly considerations would induce me to go through my three years again.
He left Rugby in December 1849 and in the following May he travelled to the University of Oxford to make the necessary arrangements to begin his studies there.
As his father wished, Dodgson matriculated at Christ Church, Oxford, which had been his father's College. Things did not start very well for him, however, for there was a shortage of accommodation and he had to return to his parent's home in Croft and wait until accommodation could be arranged before starting his university studies. On 24 January 1851 Dodgson returned to Oxford to live with the Rev. Jacob Ley, a friend of his father. Two days later his mother died suddenly at the age of 47 and again he had to return to Croft. When he returned to Oxford he was filled with a determination to work hard so that he might win scholarships and become financially independent. He was able to mix social and cultural activities with hard work at mathematics and in November 1851 he was awarded a Boulter Scholarship worth 20 pounds a year. After receiving a Second Class in classics and a First Class in mathematics in December 1852 he was awarded a Fellowship of 25 pounds a year for life. This came with the right to live in Christ Church, but although there were no requirements to any further academic achievements, he was required to take Holy Orders and to remain unmarried.
Dodgson's father was absolutely delighted with his son's success and, moreover, he himself had been made Canon of Ripon Cathedral in 1852, going on to become Archdeacon of Richmond two years later. This was the year when Dodgson completed his studies receiving a Third Class Degree in Classics but topping the list of those receiving First Class honours in mathematics by a good margin. The challenges ahead were now the senior scholarship competition and he knew that success in that would almost certainly lead to his appointment as a lecturer in mathematics. At this point, however, the usually conscientious Dodgson became too taken up with leisure and cultural activities and failed to put in the necessary work at mathematics. He did begin to take pupils, although not as an official university tutor, and this too must have taken much of his time. Disappointed with his own performance in the two scholarship examination papers on 22 March 1855, and that on the morning of the following day, he gave up and did not turn up to sit the final paper on the afternoon of 23 March (only two students did sit it). Of course he did not receive the scholarship and wrote in his diary (see for example [9]):-
It is tantalizing to think how easily ... I might have got it, if I had only worked properly during this term, which I fear I must consider as wasted. However, I have now got a year before me, and with this past term as a lesson ... I mean to have read by next time, Integral Calculus, Optics (and theory of light), Astronomy, and higher Dynamics. I record this resolution to shame myself with, in case March 1856 finds me still unprepared, knowing how many similar failures there have been in my life already.
He still had a hectic schedule, coaching pupils, and he also had, since February 1855, an official appointment as sub-librarian at Christ Church. In another scholarship examination he again failed to win an award but then took on coaching fourteen pupils for the Mathematical Examiner. This task (see for example [9]):-
... will give me no official position as it is merely a private arrangement between ourselves: it is decidedly favourable to my getting the lectureship hereafter, though it by no means secures it.
During the summer of 1855 Dodgson taught at his father's school in Croft and by the time he returned to Oxford in October it was as a Mathematics Lecturer, the position that he had sought. It meant that he now did not need to take the scholarship examinations in March 1856 as he had planned. Dodgson remained at Christ Church, Oxford, lecturing on mathematics and writing treatises and guides for students until 1881. Although he took deacon's orders in 1861, Dodgson was never ordained a priest, partly because he was afflicted with a stammer that made preaching difficult and partly, perhaps, because he had discovered other interests such as the theatre. It seems likely, however, that as time went on he found it harder to accept the view that non-Christian were condemned and, as a man of great honesty, would therefore find the oaths he would be required to swear to become a priest unacceptable.
Among Dodgson's hobbies was photography, at which he became highly proficient. His interest began when visiting his uncle in 1855, and at that time he took some photographs with his uncle's equipment. He purchased his own camera and developing chemicals in March 1856 and began to experiment with pictures of landscapes, architecture, sculptures and, most of all, of people. His family, friends and colleagues became the subjects of his photographs but he excelled especially at photographing children, which was his greatest pleasure. Alice Liddell, one of the three daughters of Henry George Liddell, the dean of Christ Church, was one of his photographic subjects and the model for the fictional Alice. Other subjects were the children of the writer George Macdonald and the sons of the poet Alfred, Lord Tennyson. Not only did Dodgson enjoy photographing children, but he also enjoyed their company. In 1932 Alice Liddell recalled how she and her sisters Lorina and Edith:-
... used to sit on the big sofa on each side of him, while he told us stories, illustrating them by pencil or ink drawings as he went along ... He seemed to have an endless store of these fantastical tales, which he made up as he told them, drawing busily on a large sheet of paper all the time. They were not always entirely new. Sometimes they were new versions of old stories; sometimes they started on the old basis, but grew into new tales owing to the frequent interruptions which opened up fresh and undreamed-of possibilities.
It was in 1862 that Dodgson wrote down the stories at Alice's request. Henry Kingsley, the author, visited the Liddells and happened to pick up Dodgson's stories. He made it very clear that Dodgson had to be persuaded to publish his writings. Three years later, after polishing them and adding some more material, Dodgson published his first "Alice book" as Alice's Adventures in Wonderland.
As a mathematician, Dodgson was rather conservative but certainly thorough and careful. He was the author of a fair number of mathematics books including: A syllabus of plane algebraical geometry (1860), Two Books of Euclid (1860), The Formulae of Plane Trigonometry (1861), Condensation of Determinants (1866), Elementary Treatise on Determinants (1867), Examples in Arithmetic (1874), Euclid and his modern rivals (1879), Curiosa Mathematica, Part I: A New Theory of Parallels (1888), and Curiosa Mathematica, Part II: Pillow Problems thought out during Sleepless Nights (1893). None of his mathematics books have proved of enduring importance except for Euclid and his modern rivals (1879) which is of historical interest. Dodgson wrote it to defend using Euclid's Elements as a means of teaching geometry. The book is written in the form of a play in which the ghost of Euclid returns to defend his book to modern geometers. Euclid sums up saying:-
Let me carry with me the hope that I have convinced you of the importance, if not the necessity, of retaining my order and numbering, and my method of treating straight lines, angles, right angles, and (most especially) parallels. Leave me these untouched, and I shall look on with great contentment while other changes are made ...
It is a serious work with well argued cases on all sides regarding the teaching of geometry. It contains much evidence of Dodgson's humour too as for example after the ghost of Euclid makes his first appearance he leaves saying:-
... that concludes our present interview; so we will meet again when you have reviewed my Modern Rivals one by one. If you had any slow music handy, I would vanish to it: as it is ... [Vanishes without slow music]
Although Dodgson argued here for retaining Euclid's way of treating parallels, in Curiosa Mathematica, Part I: A New Theory of Parallels published nine years later, he presented his own ideas on dealing with the parallel axiom.
As a mathematical logician, he was interested in increasing understanding by treating it as a game. He published The Game of Logic in 1887 and Symbolic Logic Part I in 1896. In the latter work Dodgson presented a way of visually representing propositions in a diagram which is similar to Venn diagrams, developed by John Venn in 1881, but Dodgson's pictures have certain advantages. However, Venn diagrams are today much used and Dodgson's gameboard method is forgotten. Symbolic Logic Part I contains the statement that:-
I have a quantity of manuscript in hand for Parts II and III, and hope to be able - should life, and health, and opportunity, be granted to me - to publish them...
In fact between 1959 and 1970 portions of the missing parts were found by William Warren Bartley and published for the first time in 1977. In the article [23] Bartley claims that the previously unpublished material shows specific achievements which can be credited to Dodgson. These are:-
Other recent work has again put Dodgson's mathematical contributions in a much more favourable light than it was previously seen. For example in [20] Abeles writes:-
A discussion is given of three pamphlets on elections and committees by C L Dodgson (Lewis Carroll) written between 1873 and 1876. It is argued that Dodgson's work on cycles anticipates a stochastic model proposed by Thompson and Remage in 1964 and includes ideas that are basic to maximum likelihood estimation.
In [18] we also have a very positive view of Dodgson's numerous contributions to the theory of elections, perhaps his most significant being Parliamentary Elections and The Principles of Parliamentary Representation both written in 1884:-
Dodgson's work present a complete and unified approach to the electoral reform issues which were being discussed at the time, but in doing so he developed and contributed ideas to game theory and apportionment which are well in advance of the 1880s.
Finally we should mention Dodgson's love of puzzles [9]:-
He was good at charades, he sang, he told stories. Soon enough, jokes, puzzles, games, questions-and-answers, tricks with numbers and with words, and mental exercises became for him a means of everyday amusement and for his family and friends source of fun and diversion. He also played traditional games - chess, croquet, billiards, cards - but his mind was not content with these, and he expanded, extended, and experimented with all forms and fashions, pushing traditional entertainments to their outer limits and inventing new ones. in the 1870s he created a veritable cornucopia of conundrums and mental challenges, brilliant additions to the store of magic and game playing ... He was so creative and so productive that his games and diversions fill sizeable anthologies.
The book [14] contains "42 delightfully diverting mind-benders", puzzles which Dodgson was working on at the time he died. His death was sudden. He contracted a cold in early January 1898 which at first seemed very minor but it developed into a chest problem and his doctor insisted he go to bed. His breathing became more and more difficult and he died at 2.30 in the afternoon of 14 January.
Dodgson, writing as Lewis Carroll, contributed wonderful examples of nonsense verse the best known of which is 'Jabberwocky' from Through the Looking-Glass. This begins:-
'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
The Hunting of the Snark, published by Dodgson (as Lewis Carroll in 1876), has been called:-
... the longest and best sustained nonsense poem in the English language.
Several words from his nonsense poems have entered standard English language usage. For example, the word 'chortle', a word that combines 'snort' and 'chuckle', appears in 'Jabberwocky'.
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