A lot of us must have heard about the story of how Alice mistakenly fell into a wonderland in pursuit of a rabbit that was wearing a waistcoat and muttering the words, “Oh dear! Oh dear! I shall be too late.” Despite its popularity and fame in literature, especially in the genre of children’s fiction, there is a lot of seriousness and a lot of meaning behind the characterisation, the plot, the dialogues and the nonsensical-looking questions posed in the masterpiece, “Alice’s Adventures in the Wonderland”.
Charles Lutwidge Dodgson aka Lewis Carroll was a mathematician who was also keenly interested in literature. He is known for his fictional pieces including “Alice’s Adventures in Wonderland” besides “Through the Looking Glass” and for his fantastic literary non-sense poems “The Hunting of the Snark” and “Jabberwocky”.
In the words of Johann Wolfgang von Goethe, “Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.” It appears that Carroll did precisely what Goethe said. Given the fact that Carroll was a traditionalist, in Alice’s Adventures in Wonderland, Carroll gave vent to his distress that was caused by the new theories which were sweeping away the realistic spirit that mathematics possessed. One could argue that Alice’s Adventures in Wonderland was, in fact, a mathematical satire and a masterful way of belittling the transition that was going on in the mathematical world at the time of Carroll.
Mentions of magical mushrooms, babies transforming into pigs, and questions that have no answers were made to show how pointless, wasteful and annoying these new theories were. A clothed white rabbit with a pocket watch, the hookah-smoking caterpillar, the mad tea party, and others seem to have been on-purpose and brought about to ridicule the mathematicians and the theories they presented which were, to Carroll, snatching the realistic touch and relevance that the old theories of algebra and geometry possessed.
Carroll liked the old-style mathematics and was somewhat non-receptive to the alternate theories that were being popularised in his time. For him, two and two made four and there was no other possibility. Regarding this, Alice says, “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!” Herein Carroll made an artful comment on the other-than-ten base arithmetic. This was nothing less than a satire on the use of switching over to base representations other than that of the decimal one.
However, Carroll does acknowledge that, on one hand, these new theories are bizarre and misleading, yet on the other hand, going through these new motions is the only way forward for if one gets stuck to tradition, one is akin to be left high and dry. Alice’s frustrations and her not being able to get on with the multiplication table points out that those who do not embrace the newfangled theories in mathematics are going to be left in a state of puzzlement and self-disbelief like that of Alice.
Regarding the incident of a child turning into a pig, it seems to be the case of what happened to Euclidean geometry with the advent of subjects like topology. Since in mathematical branch of topology, completely different geometrical objects could be considered the same, Carroll believed that the innocent baby-like geometry has turned into an abominable pig-like one; though a traditionalist would consider a baby and a pig different, yet for a topologist, there is no difference between the two. A topologist does not differentiate between a teacup and a torus. Taking the bull by the horns, Carroll craftily expresses his contempt for the work of mathematician, Jean-Victor Poncelet who propounded that geometric figures undergoing a continuous transformation, without any sharp changes or deletions, are likely to retain some of their original features. The transforming of a baby into a pig is a way Carroll shows how absurd and unwelcome such a notion is.
Apart from these, there is a lot more in the story that could be commented upon from a purely mathematical viewpoint. This includes commenting upon the infamous Cheshire cat, the dragon called The Jabberwocky, the Dormouse and the Hatter.
Take time and have a fresh reading of the story while imagining Carroll as a mathematician and not just as an author of children’s fiction.

—The writer is Assistant Professor at Government Degree College Sopore. [email protected]

Firdous Ahmad Mala