What is the ruling of the Sharia on a student's vow to do a certain thing if Allah fulfills a wish for him?

A vow is not established except with a formula that indicates commitment, such as "It is a duty upon me for Allah." If the formula does not imply commitment except with the intention, such as saying, "If this matter is realized, I will do such-and-such, by Allah's will," then it is not considered a vow unless you intended it to be a vow. In that case, it is obligatory to fulfill it. Scholars have differed on the ruling of conditioning a vow on Allah's will: the majority hold that it is nullified by conditioning it on Allah's will, while the Malikis hold that its fulfillment is obligatory. The more cautious approach is to fulfill it if you intended it as a vow, but if you do not, there is no blame upon you according to the majority.