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#+title: mathematics
#+author: Preston Pan
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* Mathematics is Logic
With a couple of set theory axioms. One might
describe it as an extrapolation framework
without grounding (i.e. a set of implications;
if p then q, but never specifying if p is a property
of a real system or not). Therefore, mathematics
is suitable for modeling other things if we believe
those other things have some rules and are logically
consistent.

There are many subfields in math, ranging from group theory
to complex analysis. However, much of the time we are able to find
morphisms between these different fields in mathematics, which we
model using category theory.

** Mathematical Models
*** [[id:ece8bf94-4e3c-4939-a77a-9949c1ec0dc6][Physics]]
Physics is the study of the natural world and its laws, usually resorting to a mathematical framework.

*** Economics
the study of human behavior; generally speaking, economists use mathematical models for models of the macroeconomy.