Question: It is written in Se’adet-i Ebediyye that it is better to give zakat to those who learn and teach knowledge ('ilm). That is, does it mean that zakat can be given to today’s professors and university students even if they own nisab?
ANSWER
No, what is meant is not that. It can be given only to those who learn and teach Islamic knowledge.

Question: A local imam said that zakat can be given to any student even if he or she is rich. Is zakat not the right of the poor? How can a rich person be recipient of it? What is the privilege of being a student?
ANSWER
Zakat is not given to all students in a random manner. He or she must be Muslim and poor. Only exception is those who learn or teach Islamic knowledge. It is written in fiqh books:
"Those who learn or teach Islamic knowledge can receive zakat even if they are rich, because they do not have time to earn money." (Durr-ul-Mukhtar)

Hadrat Ibn Abidin explains aforementioned statements from Durr-ul-Mukhtar as follows:

It is stated in a hadith-i sharif written in Jami-ul-Fatawa, “It is permissible to give zakat to a person learning 'ilm even if he has forty years’ nafaqa.”

In another hadith-i sharif, it is stated that the following rich people can receive zakat:

A Muslim who performs jihad in the way of Allah,
An indebted wealthy Muslim who cannot pay off his debts,
A Muslim who is wealthy in his hometown but left without money wherever he is,
A needy Muslim who cannot receive money he is owed. (Abu Dawud)