What is Math? Axioms and Deductive Reasoning

Mathematics uses axioms to come to conclusions. (Axioms are a formal
statement or principle from which other statements can be obtained.)
Axioms are supposed to be self-evident
e.g.
b+a = a+b
Some examples of mathematical axioms of addition and multiplication.

These axioms can be substituted for each other as long as they are equivalent.
e.g. f = ma
and
a = km
r2
therefore we can arrive
at a new axiom: f = kMm (law of gravitation)
r2

Like letters and words, axioms can be recombined many ways, only a few of
which make sense to us (always trying to cancel out / substitute elements in an
effort to simplify an equation)

*NEW* knowledge can be created by substituting / cancelling in equations

The conclusions are arrived at by deductive reasoning, which guarantees the
correctness of the conclusion.

There is nothing more factual or (capital T) True than empirical mathematical
knowledge