Gödel's incompleteness theorem

Imagine you have a big puzzle, and you are trying to put all the pieces together to complete it. Gödel's incompleteness theorem says that sometimes, a puzzle may not have all the pieces you need and you can't put them all together.

In a more technical way, Gödel's theorem is about mathematical theories, which are a set of rules and statements for solving math problems. A mathematical theory is considered "complete" if it can solve every math problem and prove every statement within the theory. However, Gödel showed that there are theories that are not complete and that cannot prove everything within them.

He did this by creating a math problem that could not be solved or proven within a specific theory. This means that there will always be some statements or problems that the theory cannot handle, and you need another theory to solve them.

So, just like you might need extra puzzle pieces to complete a puzzle, sometimes you need extra theories to solve math problems that can't be solved within a given theory.