Alice’s Adventures in Wonderland: Is it really about math?

This comment is more of an essay, so read at your own peril.

One of the big ideas I keep seeing in this sub and others is that Alice's Adventures in Wonderland is secretly a story about advanced mathematics. Whenever someone mentions Alice, someone will inevitably show up to inform us that it's all about numbers, and people who disagree just don't get it. On the surface it makes sense, because Lewis Carroll was a mathematician; but I strongly suspect this idea has been exaggerated, and I want to try to explain why.

There is math in Alice. There's actually quite a bit of it. But why do people keep saying there's hidden math? It's tempting to read all sorts of interpretations into Alice, because it's such an absurd story; but if you pick up the book and read it, you'll find the jokes about math are usually just…well, jokes. They're simple witticisms. A great example is this lovely chunk of dialogue:

"Take some more tea," the March Hare said to Alice, very earnestly.
"I've had nothing yet," Alice replied in an offended tone: "so I can't take more."
"You mean you can't take less," said the Hatter: "it's very easy to take more than nothing."

I've seen comments claiming this particular section is an ingenious critique against Victorian mathematics who portrayed negative numbers as physically real concepts, even naming academic adversaries that Carroll is allegedly attacking here. But the actual dialogue as written by Carroll is quite simple: it's really just a cute word game. It feels almost heretical to simplify Alice in this way, but in this case it seems painfully clear that people are seeing complexity that just isn't there. But why are people so keen on doing this?

I believe this trend of looking for complex math in Alice got started with Martin Gardner's The Annotated Alice. Just to make it clear, this book is fantastic. Gardner is great at identifying satire and jokes about Victorian society in Alice. The issue is that he identifies hidden math in everything, and sometimes struggles quite hard to justify it; on several occasions, his only justification is that Carroll was a mathematician, so of course it's a hidden math problem. This leads to him severely overstating the role of mathematics in Alice. Here's an example of some of his least convincing reasoning:

The quote from Alice:

"All right," said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. "Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!"

Gardner's analysis:

The phrase "grin without a cat" is not a bad description of pure mathematics. Although mathematical theorems often can be usefully applied to the structure of the external world, the theorems themselves are abstractions that belong in another realm "remote from human passions," as Bertrand Russell once put it in a memorable passage, "remote even from the pitiful facts of Nature . . . an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world."

It's hard to tell someone that they're overanalyzing without feeling a little stupid; but in this case, it really does seem like Gardner is overanalyzing. He does this quite a bit, which I think is sad because his book has become the go-to source for understanding Alice. It's actually worth noting that he sometimes says himself that he's reaching; but somehow, people discussing the book don't seem to read that part. I could list more examples, but my point is that people who assert that Carroll is hiding fantastic mathematical formulations in Alice are doing so largely because of Gardner's book, and Gardner's book isn't all that good at identifying math.

I can't end the post without mentioning one article which I've seen circulating the subreddit. It's Alice's adventures in algebra: Wonderland solved, by Melanie Bayley. Her takes seem pretty popular. However, if you actually read the thing you'll notice that she never justifies her arguments with anything other than "Because Carroll was a mathematician." None of the math she discusses is in the text; she derives it from the text, in a way which frankly baffles me sometimes. You remember the part where the baby turns into a pig? Bayley claims this is a reference to projective geometry, the principle of continuity, and Bayley's personal distrust of modern mathematics. This is not a good analysis of the book.

Again, there is math in Alice, and yes, Carroll was a mathematician; but good God, the things people see in this book is far beyond what's actually written in it. I'm not saying we can't look for interesting things in Alice, but please be careful when you do! The only thing we know for sure is that it's a largely nonsensical (in the literary sense) book written for children. Carroll himself never discussed hidden motivations or secret mathematical references. This is why I believe the role of mathematics in Alice is overstated. That role is there, to some degree, largely in the form of wit and and logical puzzles that children can appreciate. But there's no reason to read Newton's gravitational constant into the flamingo croquet match.

I'd love to hear thoughts on this.

And for God's sake, stop referencing the Bayley article.