When it comes to educational pursuits, there are many synonyms for the phrase "study at decay." Some may prefer to use "delve into deterioration," which conveys the sense of exploring the breakdown of knowledge or understanding. Others may opt for "examine erosion," which emphasizes the gradual loss of information or skills over time. Additionally, "investigate decrepitude" can evoke the sense of approaching a subject that has been neglected or fallen into disrepair. Regardless of which term one chooses, the goal remains the same: to gain a deeper understanding of a subject that is fading or deteriorating, and to do so with curiosity and determination.