  Modern mathematics is known for its rigorous proofs and tight analysis. Math
is the paradigm of objectivity for most. We identify the source of that
objectivity as our knowledge of the physical world given through our senses. We
show in detail, for the core of modern mathematics, how modern mathematical
formalism encapsulates deep realities about extension into a system of symbols
and axiomatic rules. In particular, we proceed from the foundations in our
senses to the natural numbers through integers, rational numbers, and real
numbers, including introducing the concept of a field. An appendix shows how
the formalism of complex numbers arises.
