Bismillah.
وَلَقَدْ يَسَّرْنَا الْقُرْآنَ لِلذِّكْرِ فَهَلْ مِن مُّدَّكِرٍ
And We have certainly made the Quran easy for remembrance, so is there any who will remember?
(Sūrat al-Qamar, No.54, Āyat 17)
The above verse has been repeated four times in Sūrat al-Qamar, emphasizing the fact that the Quran is easy for remembrance. The words ‘easy for remembrance’ have been interpreted differently by Mufassirūn. ‘Allāmah Tabātabā’ī says it means that elevated teachings and concepts have been made easy for the human being to understand. Others like al-Tabarsī say it means it is easy for recitation and memorization. Shahid Murtadhā Mutahharī in his book Ashnā’i bā Quran says it means that Quran is more amenable to memorization than other books. The brain can memorize its verses when exposed to them repeatedly, something that is harder to do with other prose or poetry.
Other verses of Quran also emphasize the memorization of Quran. In Sūrat al-Ahzāb verse 34, Allah tells the wives of the Prophet sallallāhu ‘alayhi wa-ālihi wasallam to remember the verses recited in their homes:
وَاذْكُرْنَ مَا يُتْلَىٰ فِي بُيُوتِكُنَّ مِنْ آيَاتِ اللَّهِ وَالْحِكْمَةِ ۚ
And remember what is recited in your houses of the verses of Allah and wisdom. The word used here is ‘wadhkurna’. Dhikr, as opposed to forgetfulness, implies to remember or to memorize. The Quran also talks about the chests being the receptacles of its verses:
بَلْ هُوَ آيَاتٌ بَيِّنَاتٌ فِي صُدُورِ الَّذِينَ أُوتُوا الْعِلْمَ ۚ
Rather, the Quran is distinct verses [preserved] within the chests of those who have been given knowledge (Q 29:49).
Many Hadith also emphasize the memorization of Quran. The Prophet (s) has said: The most honored servants with Allah after the Prophets are the scholars, then those who memorize the Quran. They will leave the world the way the Prophets left, be raised from their graves with the Prophets, pass on the Sirat with the Prophets, and receive the reward of the Prophets. (Majlisī, Bihārul Anwar, 92:17)
Reciters and memorizers of Quran were highly regarded by the Prophet (s) and Amirul Mu’minīn (a) and were respected and encouraged materially and spiritually by them. In the early days of Islam, the criterion for the precedence of individuals in important and sensitive social tasks was the knowledge of recitation and memorization of the Quran. Prophet Muhammad sallallāhu ‘alayhi wa-ālihi wasallam appointed reciters and memorizers to positions such as commanding and leading the congregation. He decreed that every Muslim who had learned, collected, or memorized the Quran more than others should command others and lead funeral prayers for the dead. In the battle of ‘Uhud when they wanted to bury the bodies of the martyrs, the martyr who knew more was placed in front. The burial place of the one who had memorized more verses was placed closer to Hamza.
One day, the Prophet of Islam (s) while sending a group on a journey, asked them: ‘How much do you know from the Quran?’ One of them, who was the youngest, replied: ‘I know Sūrat Al-Baqarah and a few other verses from the Quran’. The Prophet (s) told the group that he would be their leader. They protested, saying he was the youngest. The Prophet (s) replied: ‘He knows Sūrat Al-Baqarah’.
Memorization of Quran, whenever mentioned, does not imply the whole Quran. Memorization to whatever extent possible is good. We find in Islamic history that those who memorized sūrhas al-Baqarah and Āli ‘Imrān, were regarded among the prominent companions. The verses of the Quran remind us that it is possible and even easy to memorize the Quran, at least parts of it, if not the entire Quran. Even though it may seem difficult, once the journey of memorization begins and is constant, the human mind can become a receptacle of the verses of the Quran.
May the Almighty make us among those whose chests contain some verses of the Quran.
Sources: Darsname Hifz Quran, Dr. Muhammad Hajj Abul Qasim, Sayyid Mustafa Husayni and Ali Qasimi. hawzah.net/fa/goharenab/View/55325