A popular anecdote recounts that Queen Victoria loved Alice’s Adventure in Wonderland so much that she demanded to be presented with the author’s next book as soon as possible. She soon received a scholarly book on mathematics, An Elementary Treatise on Determinants. Although this anecdote is unfounded, it amusingly shows the tight relationship between mathematics and Alice in Wonderland, as well as the seemingly contradictory nature of a mathematician writing fiction.

Charles Dodgson (1832-1898) was a math lecturer at Oxford University, with his primary focus on geometry, linear algebra, and mathematical logic. Since a young age, though, Dodgson enjoyed writing poems and short stories, and had published several literary works under the pseudonym “Lewis Carroll,” among which the most famous are Alice’s Adventures in Wonderland in 1865 and its sequel Through the Looking-Glass, and What Alice Found There in 1871.

Considering the connection between math and Alice in Wonderland, the dominant opinion in literary criticism is that Charles Dodgson, who approached mathematics in a conservative fashion, incorporated many allusions to “new math” in his two Alice books. In particular, he supposedly mocked the development of axiomatic systems and non-Euclidean geometry, designating them nonsense. The most conspicuous example of this is the dichotomy between the ordinary world and the wonderland: the world Alice comes from can be thought of as the traditional arithmetic world, whereas the irrational wonderland symbolizes Boolean algebra.

Boolean algebra, introduced by George Boole in The Mathematical Analysis of Logic in 1847, is a six-tuple that consists a set $$\mathcal{B}, 0, 1 \in \mathcal{B}$$, two binary operations + and $$\cdot$$, and a unary operation $$-$$, such that for all elements $$a, b, c \in \mathcal{B}$$, the axioms of associativity, commutativity, distributivity, identity, complements, and absorption hold.

Boolean algebra describes logical operations the same way that elementary algebra describes numerical operations. In modern days, it became fundamental to the development of digital electronics and programming languages. But in the Victorian age, conservative mathematicians like Dodgson regarded such symbolic algebra as absurd.

In his book, Alice enters the wonderland where arithmetic does not work— she cannot remember the multiplication table correctly. She shrinks into 3 inches after eating cake, and the mushroom stretches her neck but contracts her torso. By Alice’s words to the Caterpillar, which represents Dodgson’s conventional arithmetic view, a physical object “being so many different sizes . . . is very confusing.”

Another “new math” concept Dodgson mocks in Alice in Wonderland is believed to be projective geometry[1]. Jean-Victor Poncelet’s principle states that “Let a figure be conceived to undergo a certain continuous variation, and let some general property concerning it be granted as true, so long as the variation is confined within certain limits; then the same property will belong to all the successive states of the figure.”

In Alice in Wonderland, Dodgson depicts that after the Duchess gives a baby to Alice, the baby gradually turns to a pig in the chapter of meeting Cheshire Cat. Playfully switching the meaning of “figure” from the geometric definition, Dodgson lets the baby undergo a continuous variation to satirize projective geometry.

In the one and a half century since Alice in Wonderland has been published, not only that characters such as the Queen of Hearts, Mad-hatter, and Cheshire cat have become iconic children literature figures across the world, but also, Charles Dodgson himself and the heroine Alice have been part of the mathematical culture in fictions. Several mathematically related characters have been named or referred to Alice and Charles Dodgson: Donald Knuth’s Surreal Numbers (1974), Paolo Giordano’s The Solitude of Prime Numbers (2009), Gaynor Arnold’s After Such Kindness (2012), and more[2].

Works Cited

Devlin, K. (2010). “The hidden math behind Alice in Wonderland.” [online] Maa.org. Available at: https://www.maa.org/external_archive/devlin/devlin_03_10.html

Mann, T. “Mathematics and mathematical cultures in fiction: the case of Catherine Shaw.” University of Greenwich. Available at: https://gala.gre.ac.uk/id/eprint/16760/3/16760%20MANN_Mathematics_and_Mathematical_Cultures_2016.pdf.