We could imagine infinity but never actually achieve it. Post-Aristotle, infinity was always idealized, never realized - a philosophical construct at best. As something that could never be reached, infinity could never be treated as a proper mathematical object, most believed. Through the millennia, some of the top philosophical and mathematical minds of their day turned their attention to the concept, pondered it at length, and inevitably gave it up.
Its eclectic nature. I am trained in a style of research that places value in the faithful documentation and analysis of the actual practices of experts in certain technical fields. Sometimes this line of work runs the risk of being too removed from the immediate advancement of such fields. (The rather polemical analogy is "as useful as ornithology to birds," but I'd like to think of it as a kind of ethnography of certain specialized expertise.)
