In mathematics, a law refers to a universally accepted principle or rule that describes a particular mathematical relationship or property. These mathematical laws are typically proven truths, derived from axioms or basic assumptions, that hold under specific conditions.

For example, the Law of Sines is a fundamental relationship in trigonometry that relates the lengths of the sides of a triangle to the sines of its angles. Similarly, the Commutative Law states that the order in which you add or multiply numbers does not affect the result.

Here’s a representation of the Law of Sines:

And here’s the Commutative Law for addition:

In mathematics, understanding and applying these laws is essential for problem-solving and for proving other mathematical theorems or propositions.

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems. Theorems are central to mathematics because they establish truths that we can rely on for solving problems and understanding the structure of mathematical systems.

An axiom, in mathematics and logic, is a statement or proposition that is regarded as being self-evidently true, without the need for proof. Axioms serve as the starting points for developing a mathematical theory. Different sets of axioms can give rise to different, but consistent, mathematical systems.

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems. Theorems are central to mathematics because they establish truths that we can rely on for solving problems and understanding the structure of mathematical systems.