Alice’s Adventures in Wonderland is a childhood classic and one of my favorite books. Written by Charles Lutwidge Dodgson (under the pseudonym Lewis Carroll), it tells the story of Alice falling down the rabbit hole into a world of fantasy with strange and peculiar creatures. As many know, Dodgson was a mathematician, so the work contains many references to mathematics. Just for fun, I thought I’d use this post to enumerate on some of the mathematical references in Alice’s Adventures in Wonderland, especially those relevant to coursework in Math 152:

In chapter two, “The Pool of Tears,” Alice says, “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!” Seems like nonsense, but Alice could be multiplying in base notation (four times five is twelve in base 18, four times six is thirteen in base 21, four times seven can be fourteen in base 24…)

Alice then goes on to say, “However, the Multiplication Table doesn’t signify: let’s try Geography. London is the capital of Paris, and Paris is the capital of Rome, and Rome–no, that’s all wrong, I’m certain!” Sounds a lot like the cyclic notation of permutations…

In chapter seven, “A Mad Tea-Party,” there are many references to logic. The Mad Hatter, the March Hare, and the Dormouse discuss converses:

“Not the same thing one bit!” said the Hatter. “Why, you might as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see!'” “You might just as well say,” added the March Hare, that ‘I like what I get’ is the same thing as ‘I get what I like’!” “You might just as well say,” added the Dormouse, which seemed to be talking in his sleep, “that ‘I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!”

Also in chapter seven, Alice wonders about movement around a circular table, which is similar to the addition on a ring of integers modulo n. Here’s the quote:

“Then you keep moving around, I suppose?” said Alice. “Exactly so,” said the Hatter: “as the things get used up.” “But what happens when you come to the beginning again?” Alice ventured to ask.

And just for good measure, I’ll include my favorite quote (from chapter five in Through the Looking Glass):

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things.” “I daresay you haven’t had much practice,” said The Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes sometimes I’ve believed as many as six impossible things before breakfast.”

There are plenty more fun references to mathematics, including some to geometry, calculus, and arithmetic. I highly recommend reading The Annotated Alice–lots of cool stuff in there. Have a great weekend!