A mathematical principle is a fundamental truth or proposition that serves as the foundation for mathematical reasoning and problem-solving. These principles often arise from logical deductions and can be applied across various fields of mathematics, such as algebra, geometry, and calculus. They help in understanding relationships between numbers, shapes, and patterns. Examples of mathematical principles include the Pythagorean theorem, which relates the sides of a right triangle, and the commutative property, which states that the order of addition or multiplication does not affect the result. These principles guide mathematicians and students in exploring more complex concepts and solving real-world problems.