The phrase "study at ruin" typically refers to an academic pursuit that ultimately leads to failure or disappointment. There are several synonyms for this phrase that convey similar meanings. For example, "study in vain" suggests that one's efforts are futile and unlikely to lead to success. "Study to no avail" conveys a similar idea, emphasizing the lack of positive outcomes despite diligent studying. "Study for naught" is another synonym that emphasizes the sense of wasted effort. Overall, these synonyms all convey a sense of disappointment and frustration with the outcome of one's academic efforts. They are useful for expressing the idea that academic success is not always guaranteed, despite one's best efforts.