**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 College 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 College, 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 March1856finds 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:-

*By*1896*Dodgson had developed a mechanical test of validity for a large part of the logic of terms, an achievement usually credited to Leopold Löwenheim*[*in*1915].*As early as 1894 Dodgson used truth tables for the solution of specific logic problems. The application of truth tables and matrices did not come into general use until 1920*.*By*1896*Dodgson had developed the method of trees for determining some validity, which bears a resemblance to the trees frequently employed by contemporary logicians*.

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 between1873and1876. It is argued that Dodgson's work on cycles anticipates a stochastic model proposed by Thompson and Remage in1964and 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 the1880s.

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 the1870s 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'.

**Article by:** *J J O'Connor* and *E F Robertson*