Symbolism in the text

Oxford Locations

Most of the book's adventures may have been based on and influenced by people, situations and buildings in Oxford and at Christ Church, e.g., the "Rabbit Hole," which symbolized the actual stairs in the back of the main hall in Christ Church. A carving of a griffon and rabbit, as seen in Ripon Cathedral, where Carroll's father was a canon, may have provided inspiration for the tale.

Mathematics

Since Carroll was a mathematician at Christ Church, it has been suggested that there are many references and mathematical concepts in both this story and also in Through the Looking-Glass; examples include:

• In chapter 1, "Down the Rabbit-Hole", in the midst of shrinking, Alice waxes philosophic concerning what final size she will end up as, perhaps "going out altogether, like a candle."; this pondering reflects the concept of a limit.
• In chapter 2, "The Pool of Tears", Alice tries to perform multiplication but produces some odd results: "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate!" This explores the representation of numbers using different bases and positional numeral systems: 4 x 5 = 12 in base 18 notation, 4 x 6 = 13 in base 21 notation, and 4 x 7 could be 14 in base 24 notation. Continuing this sequence, going up three bases each time, the result will continue to be less than 20 in the corresponding base notation. (After 19 the product would be 1A, then 1B, 1C, 1D, and so on.)
• In chapter 5, "Advice from a Caterpillar", the Pigeon asserts that little girls are some kind of serpent, for both little girls and serpents eat eggs. This general concept of abstraction occurs widely in many fields of science; an example in mathematics of employing this reasoning would be in the substitution of variables.
• In chapter 7, "A Mad Tea-Party", the March Hare, the Mad Hatter, and the Dormouse give several examples in which the semantic value of a sentence A is not the same value of the converseof A (for example, "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"); in logic and mathematics, this is discussing an inverse relationship.
• Also in chapter 7, Alice ponders what it means when the changing of seats around the circular table places them back at the beginning. This is an observation of addition on the ring of integersmodulo N.
• The Cheshire cat fades until it disappears entirely, leaving only its wide grin, suspended in the air, leading Alice to marvel and note that she has seen a cat without a grin, but never a grin without a cat. Deep abstraction of concepts (non-Euclidean geometry, abstract algebra, the beginnings of mathematical logic...) was taking over mathematics at the time Dodgson was writing. Dodgson's delineation of the relationship between cat and grin can be taken to represent the very concept of mathematics and number itself. For example, instead of considering two or three apples, one may easily consider the concept of 'apple', upon which the concepts of 'two' and 'three' may seem to depend. However, a far more sophisticated jump is to consider the concepts of 'two' and 'three' by themselves, just like a grin, originally seemingly dependent on the cat, separated conceptually from its physical object.

Mathematician Keith Devlin asserted in the journal of The Mathematical Association of America that Dodgson wrote Alice in Wonderland in its final form as a scathing satire on new modern mathematics that were emerging in the mid-1800s.

The French language

It has been suggested by several people, including Martin Gardner and Selwyn Goodacre,that Dodgson had an interest in the French language, choosing to make references and puns about it in the story. It is most likely that these are references to French lessons—a common feature of a Victorian middle-class girl's upbringing. For example, in the second chapter, Alice posits that the mouse may be French and chooses to speak the first sentence of her French lesson-book to it: "Où est ma chatte?" ("Where is my cat?"). In Henri Bué's French translation, Alice posits that the mouse may be Italian and speaks Italian to it.

Pat's "Digging for apples" could be a cross-language pun, as pomme de terre means potato and pomme means apple, which little English girls studying French would easily guess.

Classical languages

In the second chapter, Alice initially addresses the mouse as "O Mouse", based on her vague memory of the noun declensions in her brother's textbook: "A mouse (nominative)— of a mouse (genitive)— to a mouse (dative)— a mouse (accusative)— O mouse! (vocative)." This corresponds to the traditional order that was established by Byzantine grammarians (and is still in standard use, except in the United Kingdom and some countries in Western Europe) for the five cases of Classical Greek; because of the absence of the ablative case, which Greek does not have but is found in Latin, the reference is apparently not to the latter as some have supposed.

In Through the Looking-Glass and What Alice Found There, the White Queen offers to hire Alice as her lady's maid and to pay her "Twopence a week, and jam every other day." Alice says that she doesn't want any jam today, and the Queen tells her: "You couldn't have it if you did want it. The rule is, jam tomorrow and jam yesterday- but never jam to-day." This is a reference to the rule in Latin that the word iam or jam meaning now in the sense of already or at that time cannot be used to describe now in the present, which is nunc in Latin. Jam is therefore never available today.

Historical references

In the eighth chapter, three cards are painting the roses on a rose tree red, because they had accidentally planted a white-rose tree that the Queen of Hearts hates. Red roses symbolized the English House of Lancaster, while white roses were the symbol for their rival House of York. Therefore, this scene may contain a hidden allusion to the Wars of the Roses.