Mountain pass theorem

Okay kiddo, let me tell you about the mountain pass theorem in a way that you will easily understand. Imagine you are walking up a hill or a mountain, and you want to find the highest point, which is called the summit.

The mountain pass theorem is like a strategy to find the summit of the mountain. It tells us that if we want to find the highest point of a mountain, we need to look for the lowest point or valley in between two peaks. We call this valley a "mountain pass".

Once we find the mountain pass, we need to take a path that starts from the bottom of the mountain on one side of the pass, and goes up to the summit on the other side of the pass.

This path is like a crescent shape, and it's called a critical point. The point at the top of the crescent is the summit, which is the highest point on the mountain.

So, to sum up, the mountain pass theorem tells us to look for the lowest valley between two peaks, and then find a special path that starts on one side of the valley and ends at the top of the crescent on the other side. This path helps us find the highest point on the mountain, which is the summit.