Can you explain the differences between scientific theories, hypotheses, laws, and axioms/postulates (in math)?

Scientific theories, hypotheses, laws, and axioms/postulates are all important concepts in science and mathematics. Each of these concepts represents a different level of certainty or degree of generality.

A scientific theory is a well-substantiated explanation of some aspect of the natural world that is based on empirical evidence. Theories are generally supported by a large body of evidence and are used to explain a wide range of phenomena. Theories can also be used to make predictions and guide further research.

A hypothesis is a testable prediction about a phenomenon or set of phenomena that is based on limited evidence. Hypotheses are used to guide research and can be modified or refined based on new evidence. If a hypothesis is supported by a large body of evidence, it may be considered a theory.

A scientific law is a descriptive generalization about how some aspect of the natural world behaves under certain conditions. Laws are typically expressed mathematically and are often based on empirical observations. They are generally more limited in scope than theories.

In mathematics, an axiom or postulate is a statement that is accepted as true without proof. Axioms are used as starting points for logical arguments and theorems, which are proven using deductive reasoning based on these axioms. Axioms are also sometimes called postulates.