The Pure Mathematics graduate has all the strengths of the arts graduate although he or she may not spend so long in the coffee shop. And the Pure Mathematics graduate is SMART. This is widely recognised.
Students are often surprised to discover that the world outside doesn't care so much about what you know, but more about whether you have practised clear thinking. And Pure Mathematics is very much about clarity, and understanding why things are the way they are, and much less about merely knowing formulae and rules.
So the answer appears to be that Pure Mathematicians are highly regarded wherever an active. clear mind is wanted. Which minds are in very short supply.
In doing Pure Mathematics, you will learn the ways of thinking which have produced the most advanced software, you will learn the ideas beind computer graphics, behind theoretical physics, behind modern information engineering. So the stuff is useful, and you will get to play with powerful computers and construct algorithms. But more important to the world of industry and business is that you will have learnt to be clear, precise and succinct, you will have learnt how to learn.
Whether you will get rich is up to you; but the chances are good that you will have a job, and an interesting one which you enjoy.
