Martin Gardner and other scholars have shown the book to be filled with many parodies of Victorian popular culture, suggesting it belongs in spirit with Gilbert & Sullivan's Topsyturveydom.
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 symbolised 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 4 × 12 = 19 in Base 39, the product would be 4 × 13 = 1A in Base 42, 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 a converse relation.
- 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.
Literary scholar Melanie Bayley asserted in the magazine 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 symbolised 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.
While the book has remained in print and continually inspires new adaptations, the cultural material that it references has become largely specialized knowledge. Dr Leon Coward asserts the book 'suffers' from "readings which reflect today's fascination with postmodernism and psychology, rather than delving into an historically informed interpretation," and speculates that this has been partly driven by audiences encountering the narrative through a 'second-hand' source, explaining "our impressions of the original text are based on a multiplicity of reinterpretations. We don't necessarily realise we're missing anything in understanding the original product, because we're usually never dealing with the original product."
Eating and devouring
Carina Garland notes how the world is "expressed via representations of food and appetite", naming Alice's frequent desire for consumption (of both food and words), her 'Curious Appetites'. Often, the idea of eating coincides to make gruesome images. After the riddle "Why is a raven like a writing-desk?", the Hatter claims that Alice might as well say, "I see what I eat…I eat what I see" and so the riddle’s solution, put forward by Boe Birns, could be that "A raven eats worms; a writing desk is worm-eaten"; this idea of food encapsulates idea of life feeding on life, for the worm is being eaten and then becomes the eater – a horrific image of mortality.
Nina Auerbach discusses how the novel revolves around eating and drinking which "motivates much of her [Alice's] behaviour", for the story is essentially about things "entering and leaving her mouth" The animals of Wonderland are of particular interest, for Alice's relation to them shifts constantly because, as Lovell-Smith states, Alice's changes in size continually reposition her in the food chain, serving as a way to make her acutely aware of the ‘eat or be eaten’ attitude that permeates Wonderland.