Studying fruitlessly or achieving nothing can be discouraging, but there are several phrases and synonyms for the term "study at waste." Some options include "spinning wheels," "chasing one's tail," or "putting forth effort with little to no result." Another phrase to describe it would be "beating a dead horse" or "going down a rabbit hole." Overall, these synonyms all imply that the effort put into the task is ineffective or inefficient in achieving the desired outcome. It's important to recognize when one is studying or working at waste and redirect their efforts towards a more productive and beneficial endeavor.