[DoctorBeaver (OP)]

Well?  []

[Andrew K Fletcher]

One has half as many letters?

[Bored chemist]

57 points if you are playing scrabble.

The stuff you need to check if you are being ripped off by a credit card company is arithmetic.
Once you get to the level of sophistication where most of us can carry out our lives without remembering it- that's maths.

[blakestyger]

Arithmetic is mucking around with numbers whereas Maths deals with abstract ideas such as trig', algebra and calculus.

[lyner]

Arithmetic is even less than 'mucking about with numbers'; it is only what a straightforward digital calculator will do. You use Arithmetic to calculate things using formulae and procedures which someone else has already sorted out.
Maths is a huge field of study and can involve pretty well everything else. When a new problem in practical living or just 'thinking' comes up you may have to invent a new 'Maths' to cope with it.
Using Algebra to represent numbers by general symbols was a huge step forward but, before that, there was the inventions of the concepts of Zero, Negative, Pi, Irrational Numbers - all much more than Arithmetic.

I sometimes feel pretty smart when I find I can cope with some new Maths idea - then I feel really dumb, once I have found something I can't cope with. Then I feel better when I realise that someone, who I thought was much smarter than I, admits to struggling with some new Maths idea.
Basically, we all have our limit.

But questions need to be asked: What is maths - did it exist before we invented it? It's so 'powerful'; can we really take the credit for the invention? Are they doing the same Maths on Alpha Centauri? How fundamental is it? One day, will we invent a new maths which will make all existing problems clear as day? Is it the final solution?
What do YOU think?

[blakestyger]

I don't know what to think anymore but in the meantime here's a joke:

"There are 10 types of people in the world - those that understand binary and those that don't."

[LeeE]

Personally, I think that there is still further development to be done in maths.  It's interesting to think about the development from scalar maths, through vector and matrix maths, to tensor maths, and wonder what might come next.

[Bored chemist]

"Personally, I think that there is still further development to be done in maths."
So do mathematicians. They even offer prizes for some sorts of progress.
http://en.wikipedia.org/wiki/Millennium_Prize_Problems
Incidentally, It's really not my field but I always assumed that matricies, vectors and scalers could be treated as special cases of tensors. If that's right then all there are are tensors with higher dimensions.