I guess in bringing up those examples I didn’t so much mean “Vojta and Wiles didn’t do original work – it had already essentially been done by Mazur” as much as “the original contributions in math are more densely concentrated in a smaller number of people than one would guess from the outside,” which in turn bears on the question of how someone should assess his or her prospects for doing genuinely original work in a given field.
I agree with your assessment of things here, but I do think it’s worth taking a moment to honor people who take correct speculation and turn it into a full proof. This is useful cognitive specialization of labor, and I don’t think it makes much sense to value originality over usefulness.
I agree with your assessment of things here, but I do think it’s worth taking a moment to honor people who take correct speculation and turn it into a full proof. This is useful cognitive specialization of labor, and I don’t think it makes much sense to value originality over usefulness.