What is the ruling on a father permanently preventing his daughter from memorizing the Qur'an?

Obedience to parents is confined to what is good and permissible. Preventing the memorization of the Quran does not fall under this category, so the father is not to be obeyed in preventing his child from memorizing the Quran. Even if his prevention stems from foolishness or paternal overprotectiveness, it should not be heeded. However, one should deal gently with the father and try to convince him. If he insists, then the Quran can be memorized without his knowledge.