Hadwiger's theorem

Ok kiddo, so imagine you have a bunch of shapes - like circles and squares - and you want to know if you can color them all in with just two colors, let's say red and blue. Hadwiger's theorem says that if you have a big enough shape, you can definitely color it in with just two colors.

But there's a catch - if the shapes have corners, it might be a little trickier. For example, a square might be easy to color with two colors, but a rectangle with more sides might be harder. That's because the more sides a shape has, the more corners it has, and the harder it is to color it in without using more than two colors.

Overall, Hadwiger's theorem helps mathematicians understand how to color different shapes. It's kind of like a puzzle, and the more sides a shape has, the harder the puzzle is to solve. But with this theorem, we know that there's always a solution if the shape is big enough. Cool, huh?