In Lewis Carroll's Alice's Adventures in Wonderland, there aren't mathematical symbols as such, but there arereferences to mathematical ideas and concepts.

Wikipedia gives some examples. (See Related Links below)

'Shun' means 'to avoid deliberately; keep away from.'

But it is not one of the words which Lewis Carroll invented for his poem Jabberwocky. So while that is what it means within the poem, it is also what it means everywhere else.

Alice certainly looks quite annoyed in John Tenniel's illustration of the Mad Tea Party. (see related link below) This is probably because it depicts the moment in the story when the Hatter tells Alice that she needs a haircut.

`Your hair wants cutting,' said the Hatter. He had been looking at Alice for some time with great curiosity, and this was his first speech.

`You should learn not to make personal remarks,' Alice said with some severity; `it's very rude.'

Lewis Carroll, whose real name was Charles Lutwidge Dodgson.

Charles Lutwidge Dodgson (1832-1898), was an Oxford mathematics professor and amateur photographer who wrote "Alice's Adventures in Wonderland" (1865) under the pen name 'Lewis Carroll'. He also wrote "Through the Looking-Glass and What Alice Found There" (1872), "The Hunting of the Snark", and "Sylvie and Bruno".

In Lewis Carroll's book, Alice's Adventures in Wonderland, the Hatter's famous riddle - "Why is a raven like a writing desk?" - has no answer.

"Have you guessed the riddle yet?" the Hatter said, turning to Alice again.

"No, I give it up," Alice replied. "What's the answer?"

"I haven't the slightest idea," said the Hatter.

"Nor I," said the March Hare.

Alice sighed wearily. "I think you might do something better with the time," she said, "than wasting it in asking riddles that have no answers."

When he wrote the book, Carroll had no answer for the riddle either, nor did he intend there to be one. However, over subsequent years, so many people asked him the answer that in the preface to the 1896 edition he wrote:

"Enquiries have been so often addressed to me, as to whether any answer to the Hatter's Riddle can be imagined, that I may as well put on record here what seems to me to be a fairly appropriate answer, viz: 'Because it can produce a few notes, though they are very flat; and it is nevar put with the wrong end in front!' This, however, is merely an afterthought; the riddle as originally invented, had no answer at all."

(Note that he spells "nevar" as "raven" written backwards - a joke which overenthusiastic copy editors "corrected" in later editions.)

Carroll is not the only person to offer an answer after the fact, other solutions have also been given, the best known being, "because Poe wrote on both." Other suggestions include, "because there is a 'b' in both and an 'n' in neither," "because they are both nouns," and "because they both have inky quills."

It has been claimed that Carroll is satirizing philosophical paradoxes and riddles. As a logician he may be poking fun at our need for an answer to every question. In reality it is not a riddle at all, but a pseudo-problem masquerading as a riddle. He believed that most riddles are fallacious because they lead the reader to believe that such events are possible or even answerable.

Ultimately, it could be true to say that the real answer to the question is that there is no answer.

The Dormouse

"...the last time she saw them, they were trying to put the Dormouse into the teapot."

In the original book, Alice's Adventures in Wonderland, the Caterpillar doesn't have a name, he is simply known as the Caterpillar.

In Tim Burton's 2010 movie, he has been named Absolem and is played by Alan Rickman.
He smokes hookah and gives Alice advice.

Lewis Carroll offered definitions for 'gyre' and 'gimble' on two separate occasions. While the definition of 'gimble' remains consistent, the meaning of 'gyre' changes entirely.

1855

GYRE: verb (derived from 'gyaour' or 'glaour', "a dog") "to scratch like a dog."

GYMBLE: (whence 'gimblet') to screw out holes in anything

1871

`To "gyre" is to go round and round like a gyroscope.

To "gimble" is to make holes like a gimblet.'

This demontrates that the meanings of the words in Jabberwocky are not absolute, but are open to interpretation.

The Queen of Hearts from Alice in Wonderland is the most famous person to say "off with his head."

In movie versions, her character is often combined with that of the Red Queen, although she was originally an entirely separate person who first appeared in Through the Looking Glass.

"Off with his head" was also said by Queen Margaret in Shakespeare's play Henry VI. It is possible that this may be the original inspiration for Lewis Carroll's tyrannical Queen of Hearts.

There is very little information available about the banning of Alice in Wonderland. It is difficult to find reliable evidence that it ever was banned, much less information on what saved it.

The sum total of information on Alice's brush with censorship available on the internet amounts to this:

Alice's Adventures in Wonderland
Lewis Carroll
1900
Suspended from classroom use, pending review, at the Woodsville High School in Haverhill, New Hampshire, because the novel contains expletives, references to masturbation and sexual fantasies, and derogatory characterizations of a teachers and of religious ceremonies.
1931
Banned by the Chinese Governor of Hunan Province on the ground that "Animals should not use human language, and that it was disastrous to put animals and human beings on the same level."

The claim about the Woodsville High School banning is unsourced, and the claim about the Hunan Province ban appears to trace back to a single book, Banned Books 387 B.C. to 1978 A.D., by Anne Lyon Haight, and Chandler B. Grannis, R.R. Bowker Co, 1978. No other evidence seems to be available online, and it is therefore difficult to know whether either of these claims is relaible.

Time, which is represented as though it were a real person, is angry with the Hatter and has fixed things so that it is always six o'clock and therefore always teatime.

Alice sighed wearily. `I think you might do something better with the time,' she said, `than waste it in asking riddles that have no answers.'

`If you knew Time as well as I do,' said the Hatter, `you wouldn't talk about wasting IT. It's HIM.'...

'Now, if you only kept on good terms with him, he'd do almost anything you liked with the clock. For instance, suppose it were nine o'clock in the morning, just time to begin lessons: you'd only have to whisper a hint to Time, and round goes the clock in a twinkling! Half-past one, time for dinner!'...

`We quarrelled last March--just before HE went mad, you know--' (pointing with his tea spoon at the March Hare,)...

`And ever since that,' the Hatter went on in a mournful tone, `he won't do a thing I ask! It's always six o'clock now.'

A bright idea came into Alice's head. `Is that the reason so many tea-things are put out here?' she asked.

`Yes, that's it,' said the Hatter with a sigh: `it's always tea-time, and we've no time to wash the things between whiles.'

Perhaps the Cheshire Cat in Alice in Wonderland grins because it's amused by the foolishness of people.

The origins of the phrase 'grinning like a Cheshire cat' are unknown, but there are several theories. According to Martin Gardner, in his Annotated Alice, the two leading theories are:

1. A sign painter in Cheshire (the county, by the way, where Carroll was born) painted grinning lions on the sign boards of inns in the area.
2. Cheshire cheeses were at one time molded in the shape of a grinning cat.

(This answer is based on the book.)

Alice sees a white Rabbit and follows it down a hole, which is very deep.

Alice grows very big and cries. She then shrinks and gets very wet in her pool of tears. She and other creatures try to get dry by having a caucus-race and by listening to the mouse's long tail.

Alice meets a caterpillar that is sitting on a mushroom smoking. The caterpillar tells Alice that by eating the mushroom she can get back to her normal size.

Alice meats the Duchess, Cook and Chessire cat. When she left the Duchess' house the Duchess' baby follows her but she doesn't return the baby because it turns out to be a pig.

Alice joins the March Hare, Mad Hatter and Doormouse for tea.

Alice plays a game of croquet with the Queen.

Alice meets the Duchess and the Duchess tells a Gryphon to take Alice to meet the Mock Turtle. The Mock Turtle and Alice exchange stories and the Mock Turtle shows Alice the lobster-quadrille.

Alice goes to the trial and is accused of stealing the Queen tarts. Alice tells the Queen and other card looking figures that they are just a deck of cards. They then turn into cards and fly at Alice.

Alice wakes up in her sister's lap.