Modern day mathematician

I have always wanted to be a mathematician (weird I know). Their job is playing with pure ideas and solving hard problems. All a mathematician needs is paper, a pencil, and a waste basket.

There is an old proverb - "A mathematician never soils his hands with calculations." First, ignore the gender bias. Second, in the time before computers that perspective made sense. Actual calculations waste precious time. Now that world view is limiting. Testing ideas, at any scale, is computational efficient. However if there is little (or no thought) for Big O, it is difficult to compare multiple correct methods.

I'm pragmatic in choosing between abstract calculations of run time and Monte Carlo simulations. I choose the quickest, best time estimation method for a given problem. But I always makes estimates. A modern day mathematician has to realize the constraints of reality on pure solutions.