What is math?

Math is the study of abstract patterns;
science is the study of concrete patterns.

Thus science is written in math
(it's not a coincidence)
and the study of the structure of science is math,
while the study of the structure of math is more math (metamath):
a different area of math, but still math.

Completeness
real numbers, representable functors, etc.
[First order logic doesn't work...]