Axioms are recognized, need not be proved, and are often unprovable. Just use them.

Theorems generally come from axioms and can be proved to be correct and conform to objective laws.

A formula is a way to express a theorem or something with a mathematical formula, which is a mathematical formula!

In fact, the concept and definition are somewhat similar. When you come into contact with a new mathematical knowledge, you will always define it, and this definition can also be said to be the concept of this mathematical knowledge!

There is no need to make mathematics so literal. Books are generally described in bold. If you understand the meaning and can do the problem, you will learn math well! thank you