Gödel's Loophole
Ok, so imagine you have a really smart person named Gödel. And he was thinking about math problems that nobody else could solve. He was so smart that he found a loophole in the rules of math.
The loophole was basically this: In math, there are some things that can be neither true nor false. They are kind of like when you ask a question to which there doesn't really exist a correct answer.
So Gödel realized that if he made up a really tricky math problem that was like this, then he could prove that it was impossible to solve it. And he could prove it in a way that made it impossible to prove that it was impossible to solve.
That might sound kind of confusing, but it's like when you play rock-paper-scissors and you can't beat someone who always picks paper. If you can't beat them, then they win every time.
So Gödel found a way to create a problem that he won every time, no matter what!
The loophole was basically this: In math, there are some things that can be neither true nor false. They are kind of like when you ask a question to which there doesn't really exist a correct answer.
So Gödel realized that if he made up a really tricky math problem that was like this, then he could prove that it was impossible to solve it. And he could prove it in a way that made it impossible to prove that it was impossible to solve.
That might sound kind of confusing, but it's like when you play rock-paper-scissors and you can't beat someone who always picks paper. If you can't beat them, then they win every time.
So Gödel found a way to create a problem that he won every time, no matter what!