Number
&
Exploration

You know,

it is of the nature of increase in knowledge

that it fosters increase in specialisation

The creation is too vast for any one person to absorb

even a microscopic fraction of

the whole of human knowledge acquired so far.

And like Homer Simpson bemoaning the fact

that when one bit of information goes in

it pushes another bit out,

one brain does not have the space to take it in.

And our lives are not long enough to read all the books,

let alone see all the sights

and hear all the sounds,

and feel all the emotions

that will form our personal and communal knowledge and understanding.

So it is with the world of mathematics,

it is a world of spacio-numerical understanding

that is too vast for one person to encompass,

and would seem to have no limit

in any direction you wish to explore.

If you come to a dead end there is always another road

heading outward close by.

But sooner or later

most non-professional mathematicians reach a point

where they don't have time or energy or interest enough

to do the work to get any further.

They are specialising in other things.

And so it is up to those who have

the time, the talent and passion for mathematics

to take the story on from here,

because specialisations lead to further specialisations,

and the obscurity of the outer reaches

may seem quite unintelligible

even to mathematicians following a different path,

so what chance have lesser mortals?

But even they can see that all these mathematical languages

spring from the same origin,

and thus have a commonality of understanding at their source.

And to define the directions taken from that central shared space,

we can think of mathematics as following certain general groupings or directions

by which mathematicians define their work

when they publish papers.

Inevitably, general groupings in the hands of mathematicians

quickly develop even more specialised categories

beyond most people's grasp,

but we can all get some of the way.

To keep it simple

we surely need to begin at the beginning,

where we started long ago.

We needed practical mathematics,

to count sheep and construct buildings,

useful maths,

Applied Maths

developed with the specific aim and purpose

of affecting or interacting with the world.

But humans love their abstraction,

so inevitably maths was explored

for no immediately practical reasons

mathematics for no more than intellectual curiosity,

and a quest for beauty,

the usefulness of which was irrelevant,

Pure Maths.

Then, of course, as you get further into the mathematical wilds,

you have to look backwards and re-evaluate where you came from,

to consider whether the mathematics of now

changes any of the prior assumptions

of the maths that got you here,

and with that to consider whether

the ground on which you are standing

is as solid as you thought it was,

Foundation Maths.

I wish I had more maths to hand,

but the fact that I don't do the work

doesn't mean that I can't love to see other people

using numbers with skills I don't possess

and in ways I don't understand.

I love to gaze in wonder

as I struggle to understand what it could mean.

I'm never ashamed to admit

that I don't understand something,

but at the same time,

if I think that conclusions and inferences drawn

are going an unjustifiable step too far

whoever it is,

I try not to be afraid to say

that I politely disagree.

So if at any time or place we meet,

please feel free to do the same to me.