By "young" here Hardy probably means under 50. Hardy's own most productive years began at age 34, when he began his celebrated collaboration with J.E. Littlewood. (One mathematician said at the time, "There are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.") The boundary of "young" has crept down over the years; the Chronicle of Higher Education was recently moved to ask, "Are mathematicians past their prime at 35?"