Jack Sparrow said it best.

Will Turner: This is either madness… or brilliance.

Jack Sparrow: It’s remarkable how often those two traits coincide.

I define *original* to mean both *useful* and *least like other ideas*.
There’s plenty of unique but worthless ideas out there, and we’re going
to ignore them. Just string random words together and you get something
like “a book about a unicorn in a wheat field in Slovenia”.

So by those criteria, Georg Cantor’s ideas about the sizes of infinity are the most original ones that I know of.

They led, at least loosely, to the following ideas:

- The idea that “counting” a set \(X\) is just finding a bijection \(f: X \to \mathbb{N}\)
- A proper subset of a set \(X\) can have the same cardinality as the whole set
- Not all infinities are the same size
- Diagonalize attn arguments, which Godel’s theorem used
- Godel’s incompleteness theorems
- A proof that almost all functions are not computable
- Isomorphisms in category of sets
- influenced idea of isomorphism in general, a view picked up by category theory

To say “there are as many even numbers as even **and** odd numbers”
sounds insane. But it’s true in a way that corresponds to intuition
about counting and indicates that infinity is a strange thing.