The reason to explore is captured in the title of R.P. Feynman’s
Book: The pleasure of finding things out.

The
things to explore are things that capture our thoughts and surprise
us. Be that as it may, humans have evolved a reward system so that
when objects strike us as pretty, perhaps a better way of saying
that, is symmetric.

When in
the gamut of human experience does the ability to describe things
happen?

To
answer this question we perhaps need first to have looked for a
language to describe the world around us.

Formal
description that is nouns, dogs, cats, trees, numbers, patterns all
needed for the purposes of description to have a way of codify them
to an acceptable level of depth.

On
patterns and numbers we have abstracted relationships of things to or
perhaps better said between each other.

In
order to facility this exploration we have defined the knowledge of
philosophy to this subject to be named mathematics.

To
capture these things we humans have divided up some portions of the
universe for the purpose of discussion called domains at least in the
English language.

Insider
the domain of mathematics there are many discrete headings;

arithmetic,

geometry,

trigonometry,

graphy
theory,

proof
theory,

statistics,

game
theory,

manifolds,

calculus,

algebra,

topology,

logic,

set
theory,

real
analysis,

it also
includes the study of ideas which as the infinite, the infinitesimal
and many other topics, all of which fall within the domain.

Now to
address the question I began with, but didn’t state as yet.

I’m
asked now and again what is it I study in Mathematics, I wanted to
answer this but then I decided that the word study is wrong, perhaps
I don’t study, I explore small regions of some of these things and
eventually perhaps I am at best a very curious onlooker.

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