Hello! I came across Jordan Curve Theorem while reading something on Complex Analysis. I don't know much about topology and I apologize if my questions is silly, but from what I understand the theorem states that a closed curve in the complex plane separate the plane into an inner region and an outer region whose boundary is the curve. I read that the theorem has a rich history and it was even checked using computer programs, but to me it seems quite obvious. What exactly am I missing about it (why it is considered so important)? Thank you!