Thom conjecture

The Thom Conjecture is a big idea about shapes that mathematicians have been thinking about for a long time. Imagine that you have a big round ball and you want to know how many different ways you can stretch and shape it without tearing it. Well, the Thom Conjecture says that no matter how you stretch and shape the ball, it will always be able to fit inside a certain shape called a "simple space." This is kind of like fitting a puzzle piece into a puzzle - no matter how you turn it, it will always fit into the same spot.

Now, some really smart people have been working to prove that the Thom Conjecture is true for many different types of shapes, but it's a really hard problem to solve. It's like trying to solve a really tricky puzzle, and even the smartest mathematicians have been working on it for a long time without finding a solution yet. But if someone does manage to solve it, they'll have made a really important contribution to our understanding of shapes and space.