Pure
Mathematics

You know,

as someone whose enjoyment of mathematics

is now more to do with mathematics as an aesthetic,

observing in awe and wonder what other people can do with it,

with the actual numbers on the blackboard

mostly incomprehensible.

But even if doing little more maths than the occasional sudoku,

we can still hopefully come to some sort of understanding

of what mathematicians are trying to say

with those numbers that we can't understand.

At least we can try to understand what it is

that defines different branches of mathematics,

and we can try to understand

what makes their associated problems

so hard to solve,

and why they are important enough to warrant

so much time and effort to solve them.

But that is the beauty of Pure Mathematics

in that the fact that a problem is hard to solve

is reason enough to warrant the time and effort.

And sometimes when problems are solved

magic happens.

So how do we categorise

the different approaches

to mathematical problems?

Beginning with the original numbers

it is a journey that will pass through strange types of numbers

and different types of number systems.

Then there's the maths of geometry,

trigonometry,

and fractal and differential geometries,

and different algebras,

and number theory,

and combinatorics and topology,

all with their own approach to problems,

as well as problems specific to themselves.

Then there's the maths of motion,

mapping changes through calculus,

and vector calculus,

exploring dynamical systems,

and trying to come to terms with unpredictability with chaos theory,

and using complex analysis with complex functions.

Any of which should be enough to keep an interested mathematician happy,

or equally so for an inquisitive mathematical voyeur.

Take your pick,

there's something for everyone.