Yamabe problem

Okay kiddo, imagine that there's a special math problem called the Yamabe problem. It's kind of like a puzzle that math people try to solve.

The Yamabe problem is all about shapes called manifolds. A manifold is like a really bumpy hill, with lots of ups and downs. But instead of being made of dirt and grass, it's made of numbers and formulas.

Now, the Yamabe problem asks a really interesting question. It wants to know if you can take any old bumpy manifold and make it into a smooth one. That's like making the hill super flat, so it's easy to walk up and down.

But it's not just any kind of smoothing out that counts. There's a special formula called the Yamabe constant that has to be the same before and after the smoothing. So it's like saying you have to make the hill flat, but you can't change how steep it is overall.

This problem is really hard, and math people have been working on it for a long time. But it's important because it helps us understand more about the shapes and spaces around us.