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?