Gödel's incompleteness theorems

Can a puzzle have missing pieces we can't see?

Imagine you're trying to finish a puzzle with a friend, but you realize there are pieces that you can't find, no matter how hard you search.

Gödel's incompleteness theorems show that in certain puzzles (formal systems), there are truths (pieces) that can't be found (proven) within the rules of the puzzle.

Example

You're searching for a piece that fits perfectly, but it's missing, even though you know it should be there.

Remember this

Some puzzles have missing pieces that we can't solve, no matter how well we understand the rules.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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