What is a theorem? How are they used?

A theorem is a logical statement or proposition that can be proven using accepted mathematical principles. Theorems are used as a tool to provide insight into the relationships between different mathematical objects. Theorems often provide direction in the development of mathematics by uncovering useful information and helping to further our understanding of the world around us. They are used in a variety of fields, such as mathematics, science, philosophy, and computer science. Theorems help us make predictions and provide us with a way to explore new ideas and make logical progress.