A theorem is a statement that has been proven to be true based on previously established statements, such as other theorems, axioms, and definitions. In mathematics, theorems are essential because they provide a foundation for further exploration and understanding of concepts. For example, the famous Pythagorean Theorem describes the relationship between the sides of a right triangle. To prove a theorem, mathematicians use logical reasoning and evidence. Once a theorem is proven, it can be used as a building block for proving other theorems. This interconnectedness is what makes mathematics a powerful and cohesive discipline, allowing for the development of complex ideas from simple truths.