ELI5: Explain Like I'm 5

Calabi conjecture

Okay kiddo, listen up! The Calabi Conjecture is a math problem that some really smart people came up with a long time ago. It's all about shapes called manifolds, which are kind of like the hills and valleys on a map. But instead of hills and valleys being made of dirt, manifolds are made of numbers and equations!

The Calabi Conjecture asks whether there's a special kind of equation that can be used to make a perfect, smooth manifold. That means it would have no bumps or rough spots like a dirt road. This equation is called the Calabi-Yau equation.

Now, even though lots of brilliant mathematicians have puzzled over this problem for years, nobody has been able to prove whether it's true or false. It's one of the biggest mysteries in math! Some people think the answer is yes, and some people think the answer is no. But nobody really knows for sure.

So, the Calabi Conjecture is kind of like a big puzzle that we haven't solved yet. And if we do solve it one day, it could help us understand more about these weird and wonderful shapes called manifolds. Pretty cool, huh?