Is zakat obligatory upon a poor person who owns books whose value reaches or exceeds the zakat threshold? And does the ruling differ if he is in need of these books (such as a student of knowledge) or not in need of them (such as a layperson or an elderly person)?

It is not permissible to give zakat to an owner of books whose value reaches the nisab, unless he is in need of them for learning, teaching, or issuing fatwas. Scholars have elaborated on this: if people of knowledge are in need of their books for teaching, memorizing, and correcting, then these books do not prevent them from being considered poor, even if their value reaches the nisab, and thus they are eligible to receive zakat. Books of fiqh (Islamic jurisprudence), hadith (prophetic traditions), and tafsir (Qur'anic exegesis) fall into this category, unlike books of medicine, grammar, and astronomy. Some Maliki scholars held that if a jurist has books that he needs, he may be given zakat. If these were historical books, they should be sold to him. If they were medical books, then if there is no other physician in the town besides him, they should not be sold to him, and he should be given zakat; but if another physician exists, they should be sold to him. If they were books of fiqh, and he is someone whose leadership is hoped for, they should be sold to him according to one opinion, and according to another opinion, they should not be sold, and he should be given zakat. The summary is to differentiate between the needy and the non-needy, and between the types of books, as each case is treated according to its specific details.