Viewpoint: Yes, mathematics should be pursued for its own sake, as doing so will eventually present practical benefits to society.

Viewpoint: No, mathematics should first be pursued by everyone for its societal utility, with the mathematically gifted being encouraged to continue the pursuit of math for math's sake at advanced levels.

One of the great problems in mathematics is not a "math problem" at all; rather, it is a question of the means by which the study of mathematics should be pursued. This may be characterized as a debate between "pure" mathematics, or mathematics for its own sake, and applied mathematics, the use of mathematics for a specific purpose, as in business or engineering. This is a concern that goes back to the historical...