How the mathematician goedel proved that not everything can be proven?

There once was a mathematician named Gödel who showed that some truths are hidden, and you can’t always find them just by working hard.

Imagine you have a big puzzle book with lots of puzzles inside, each one is a problem to solve. Now, suppose the book has a special rule: every single puzzle in it must be solved using only the rules in the book. That sounds fair, right?

But Gödel came up with a clever idea. He created a new puzzle that said: "This puzzle can't be solved using the rules in this book." If you try to solve it using the rules, you end up proving that it can’t be solved, and if you say it can’t be solved, then you’re actually solving it!

It's like having a toy box where every toy has a rule about how to play with it. But then someone makes a new toy that says: "You can't use the rules to figure out how I work." If you try to use the rules, they tell you the toy doesn’t follow them, but that’s exactly what you did!

That's how Gödel showed that not everything can be proven, some truths are tricky, and sometimes they play games with your rules!