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### Converse Statements - From *Alice in Wonderland*

### The Four Branches of Arithmetic - From *Alice in Wonderland *

### Performing Sums - From *Through the Looking Glass *

### Proving 2 + 1 - From *The Hunting of the Snark*

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Lewis Carroll, being a mathematician as well as a famous author of nonsense, sometimes combined his talents to write math-related nonsense. These are a few quotations from his work.

`Come, we shall have some fun now!' thought Alice. `I'm glad they've begun asking riddles.--I believe I can guess that,' she added aloud.

`Do you mean that you think you can find out the answer to it?' said the March Hare.

`Exactly so,' said Alice.

`Then you should say what you mean,' the March Hare went on.

`I do,' Alice hastily replied; `at least--at least I mean what I say--that's the same thing, you know.'

`Not the same thing a bit!' said the Hatter. `You might just 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, who seemed to be talking in his sleep, `that "I breathe when I sleep" is the same thing as "I sleep when I breathe"!'

`It IS the same thing with you,' said the Hatter, and here the conversation dropped, and the party sat silent for a minute, while Alice thought over all she could remember about ravens and writing-desks, which wasn't much.

`I couldn't afford to learn it.' said the Mock Turtle with a sigh. `I only took the regular course.'

`What was that?' inquired Alice.

`Reeling and Writhing, of course, to begin with,' the Mock Turtle replied; `and then the different branches of Arithmetic-- Ambition, Distraction, Uglification, and Derision.'

`I never heard of "Uglification,"' Alice ventured to say. `What is it?'

The Gryphon lifted up both its paws in surprise. `What! Never heard of uglifying!' it exclaimed. `You know what to beautify is, I suppose?'

`Yes,' said Alice doubtfully: `it means--to--make--anything-- prettier.'

`Well, then,' the Gryphon went on, `if you don't know what to uglify is, you ARE a simpleton.'

`And you do Addition?' the White Queen asked. `What's one and one and one and one and one and one and one and one and one and one?'

`I don't know,' said Alice. `I lost count.'

`She can't do Addition,' the Red Queen interrupted. `Can you do Subtraction? Take nine from eight.'

`Nine from eight I can't, you know,' Alice replied very readily: `but -- '

`She can't do Subtraction,' said the White Queen. `Can you do Division? Divide a loaf by a knife -- what's the answer to that?'

`I suppose -- ' Alice was beginning, but the Red Queen answered for her. `Bread-and-butter, of course. Try another Subtraction sum. Take a bone from a dog: what remains?'

Alice considered. `The bone wouldn't remain, of course, if I took it -- and the dog wouldn't remain; it would come to bite me -- and I'm sure I shouldn't remain!'

`Then you think nothing would remain?' said the Red Queen.

`I think that's the answer.'

`Wrong, as usual,' said the Red Queen: `the dog's temper would remain.'

`But I don't see how -- '

`Why, look here!' the Red Queen cried. `The dog would lose its temper, wouldn't it?'

`Perhaps it would,' Alice replied cautiously.

`Then if the dog went away, its temper would remain!' the Queen exclaimed triumphantly.

Alice said, as gravely as she could, `They might go different ways.' But she couldn't help thinking to herself, `What dreadful nonsense we are talking!'

`She can't do sums a bit!' the Queens said together, with great emphasis.

"Two added to one--if that could but be done,"

It said, "with one's fingers and thumbs!"

Recollecting with tears how, in earlier years,

It had taken no pains with its sums.

"The thing can be done," said the Butcher, "I think.

The thing must be done, I am sure.

The thing shall be done! Bring me paper and ink,

The best there is time to procure."

The Beaver brought paper, portfolio, pens,

And ink in unfailing supplies:

While strange creepy creatures came out of their dens,

And watched them with wondering eyes.

So engrossed was the Butcher, he heeded them not,

As he wrote with a pen in each hand,

And explained all the while in a popular style

Which the Beaver could well understand.

"Taking Three as the subject to reason about--

A convenient number to state--

We add Seven, and Ten, and then multiply out

By One Thousand diminished by Eight.

"The result we proceed to divide, as you see,

By Nine Hundred and Ninety Two:

Then subtract Seventeen, and the answer must be

Exactly and perfectly true.

"The method employed I would gladly explain,

While I have it so clear in my head,

If I had but the time and you had but the brain--

But much yet remains to be said.

"In one moment I've seen what has hitherto been

Enveloped in absolute mystery,

And without extra charge I will give you at large

A Lesson in Natural History."

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