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.
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 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 × 5 = 12 in base 18 notation, 4 × 6 = 13 in base 21 notation, and 4 × 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 7, “A Mad Tea-Party”, the March Hare, the Hatter, and the Dormouse give several examples in which the semantic value of a sentence A is not the same value of the converse of 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 integers modulo 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, such as non-Euclidean geometry, abstract algebra, and 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. 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 Melanie Bayley asserted in the magazine of The New Scientist that Dodgson wrote Alice in Wonderland in its final form as a scathing satire on new modern mathematics that were emerging in the mid-19th century.
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. She therefore 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 (literally; “apple of the earth”) means potato and pomme means apple, which little English girls studying French would easily guess.
In the second chapter, Alice initially addresses the mouse as “O Mouse”, based on her memory of the noun declensions “in her brother’s Latin Grammar, ‘A mouse — of a mouse — to a mouse — a mouse — O mouse!'” These words correspond to the first five of Latin’s six cases, in a traditional order established by medieval grammarians: mus (nominative), muris (genitive), muri (dative), murem (accusative), (O) mus (vocative). The sixth case, mure (ablative) is absent from Alice’s recitation.
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. This scene is an allusion to the Wars of the Roses.
Symbols (objects, characters, figures, or colours used to represent abstract ideas or concepts.)
Objects in Alice in Wonderland can assume different values and meaning depending on the situations.
1. The Garden: may symbolize the Garden of Eden, an idyllic space of beauty and innocence; the experience of desire. The two symbolic meanings work together to underscore Alice’s desire to hold onto her feelings of childlike innocence that she must relinquish as she matures.
2. The Caterpillar’s Mushroom: may be seen as a sexual threat (phallic shape); or a psychedelic hallucinogen. Anyhow Alice must master the properties of the mushroom to gain control over her fluctuating size, which represents the bodily frustrations that accompany puberty.
3. Identities: Alice is puzzled because she can’t recognize herself during her journey and she admits she has lost her identity. Also the characters do not know who she is really and sometimes mistakes her for someone else
4. Knowledge: Alice repeats the lessons she’s learned in school both to test herself whether or not she is the same little girl that she used to be, and because someone asks her to explain what she knows. When Alice fails repeating what she has learnt or when the characters she meets contradict her or tell her that she is wrong, she fears that she has indeed become a different stupid child and becomes frustrated. To Alice, an important distinction between children and grown-ups is that children have a lot to learn and are always being subjected to some educational exercise while adults apparently don’t have to learn anything.
5. Meaning: Alice is surprised and disconcerted when she finds herself speaking nonsense, and most of the times she understands the meanings of each individual word, but is unable to find meaning in a statement as a whole.In the novels there are humorous nonsense verses, most of which are parodies of popular poems from Carroll’s time.
Examples: the Mad Hatter demonstrates an important distinction between statements with apparently identical meanings (“I say what I mean” and “I mean what I say”); the Duchess advises Alice that if the meanings are right, then the proper form will follow as a matter of course (English proverb “Take care of the pence and the pounds will take care of themselves.”); the Mock Turtle exclaims that there’s no point in Alice reciting her lessons if she can’t explain what she recites; the trial is rich with nonsensical words.
The Tragic and Inevitable Loss of Childhood Innocence – Alice feels discomfort while she goes through a variety of absurd physical changes and struggles to maintain a comfortable physical size. These constant fluctuations represent the way a child may feel as her body grows and changes during puberty.
Life as a Meaningless Puzzle – Alice encounters a series of puzzles – Caucus race, Mad Hatter’s riddle, the Queen’s ridiculous croquet game – that seem to have no clear solutions, no purpose or answer which imitates the ways that life frustrates expectations, even when problems seem familiar or solvable.
Death as a Constant and Underlying Menace – Alice continually finds herself in situations in which she risks death; this suggest that death lurks just behind the ridiculous events of Alice’s Adventures in Wonderland as a present and possible outcome. (ex.: Alice falls falling off her own house, the Queen who is always screaming “Off with its head!”)
Motifs (recurring structures, or literary devices that develop and inform the major themes).
1. Dream: Alice’s adventures take place in her dream, where the characters and phenomena of the real life mix with elements of Alice’s unconscious state. For this reason there are many nonsensical and disparate events in the story and the narrative follows the dreamer who tries to interpret her experiences in relationship to herself and her world.
2. Subversion: Alice quickly discovers one aspect certain in her travels; everything will frustrate her expectations and challenge her understanding of the natural order of the world and the relationship between cause and effect.
3. Language: Carroll makes use of puns and plays on multiple meanings of words, invents words and expressions and develops new meanings expanding the lexicon beyond expectation and convention. Anything is possible in Wonderland, and Carroll’s manipulation of language reflects this sense of unlimited possibility.