At a certain age some people's minds close up; they live on their intellectual fat.

Phelps is criticizing a common form of intellectual complacency: the tendency, often in midlife or later, to stop learning and instead rely on accumulated knowledge, reputation, or past achievements—“intellectual fat.” The metaphor suggests stored reserves that can sustain a person for a time, but also implies stagnation and eventual decline if no new nourishment is taken in. The remark reflects a progressive, lifelong-learning ideal associated with Phelps’s public role as a celebrated Yale teacher and popularizer of literature: the mind should remain active, curious, and receptive rather than settling into fixed opinions. It also serves as a warning that mental closure is a choice or habit, not an inevitable consequence of aging.