I seem to recall reading about a mathematician from antiquity whose view was, roughly, that to "apply" math was to do it violence (or indeed, to expedite violence) and so looked down on applications. Who/what might I be thinking of?
The sentiments you are describing are most likely those attributed to Plato. Although not primarily a mathematician, Plato is the figure who is credited with drawing the distinction between pure and applied mathematics - drawing a line between the theoretical and the computational aspects of mathematics, and instilling this in his followers.
According to Boyer's History of Mathematics :
[I]n geometry, he espoused the cause of pure mathematics as against the materialistic views of the artisan or technician.
Plutarch, in his Life of Marcellus, speaks of Plato's "indignation at the use of mechanical contrivances in geometry." According to Boyer, Plato may largely be responsible for the restriction in Greek geometric constructions to those that can be effected by straightedge and compass alone.
The reason for this restriction is not likely to have been only the simplicity of the instruments used in constructing lines and circles, but rather the symmetry of the configurations.
In arithmetic, Plato draws the line between those aspects of arithmetic that we now call number theory, and logistic as mere computation.
He regarded "logistic" as appropriate for business men and men of war who must learn the art of numbers or he will not know how to array his troops, while "arithmetic" was appropriate for philosophers because he has to arise out of the sea of change and lay hold of true being.
In the Republic, Plato says "Arithmetic has a very great and elevating effect, compelling the mind to reason about abstract number." Quoting Boyer :
So elevating are Plato's thoughts concerning number that they reach the realm of mysticism and apparent fantasy.