Commentary. This is purely rhetorical question, because we all know that mathematicians invariably choose the former. And wonder why the rest of the world finds us strange.
Commentary. By which I mean that a student who likes problem-solving needs to be encouraged to read, and a student who likes reading needs to be encouraged to work on a problem. This is part of the training in "intellectual discipline" discussed above.
Commentary. What I tell my grad students. Just kidding, Fort Meade. The computer franchise of Evil Empire, passed from IBM to Microsoft around 1990, then to Google around 2012, and now to Facebook; where next?