Short answer
The hadith say the Prophet ﷺ was shown Aisha in a dream before the marriage, and the dreams of prophets are revelation. The marriage also joined him to Abu Bakr, his closest friend, and gave the ummah one of its greatest teachers.
Sunni scholars explain the marriage by the dream he was shown (a form of revelation for prophets), the tie it made with Abu Bakr, and the role Aisha went on to play in passing on the Sunnah, especially the Prophet's ﷺ private life and family rulings.
The four schools agree on this.
Explanation
The Prophet ﷺ told Aisha that he had seen her in a dream twice before the marriage, carried by an angel in a piece of silk, and that he said: if this is from Allah, He will bring it about. The dreams of prophets are a kind of revelation, so scholars see the marriage as something Allah chose.
The proposal came after the death of Khadijah, when the Prophet ﷺ was grieving and caring for his daughters alone. The biographers say Khawla bint Hakim suggested Aisha and Sawda to him. When the proposal reached Abu Bakr, he asked whether it was allowed, since the two of them called each other brothers. The answer was that they were brothers in faith, not by blood, so the marriage was lawful.
The marriage tied the Prophet ﷺ to his closest companion, as his later marriage to Hafsa tied him to Umar. Aisha also became a channel of knowledge. She was young, sharp and blessed with a strong memory. She lived for decades after him and narrated more than two thousand hadith, many about his home, worship, character and family life that only a wife could know. Senior Companions came to her with questions.
On her age, see How old was Aisha when she married the Prophet? For all his marriages, see Wives of the Prophet ﷺ.
The evidence
Quran, Surah Al-Ahzaab 33:6
ٱلنَّبِىُّ أَوْلَىٰ بِٱلْمُؤْمِنِينَ مِنْ أَنفُسِهِمْ ۖ وَأَزْوَٰجُهُۥٓ أُمَّهَٰتُهُمْ ۗ وَأُو۟لُوا۟ ٱلْأَرْحَامِ بَعْضُهُمْ أَوْلَىٰ بِبَعْضٍۢ فِى كِتَٰبِ ٱللَّهِ مِنَ ٱلْمُؤْمِنِينَ وَٱلْمُهَٰجِرِينَ إِلَّآ أَن تَفْعَلُوٓا۟ إِلَىٰٓ أَوْلِيَآئِكُم مَّعْرُوفًۭا ۚ كَانَ ذَٰلِكَ فِى ٱلْكِتَٰبِ مَسْطُورًۭا ﴿٦﴾
The Prophet is more worthy of the believers than themselves, and his wives are [in the position of] their mothers. And those of [blood] relationship are more entitled [to inheritance] in the decree of Allah than the [other] believers and the emigrants, except that you may do to your close associates a kindness [through bequest]. That was in the Book inscribed.
His wives hold a special rank for every believer.
Sahih al-Bukhari 3895
Sahih... أريتك في المنام مرتين ...
"You were shown to me in a dream twice."
The marriage was preceded by a dream, which for a prophet is revelation.
Sahih al-Bukhari 5081
Sahih... أنت أخي في دين الله وكتابه وهي لي حلال ...
"You are my brother in Allah's religion and His Book, and she is lawful for me."
His answer to Abu Bakr's question about the brotherhood between them.
Where the ruling is recorded
- Fath al-Bari (Ibn Hajar), Commentary on Kitab Manaqib al-Ansar, chapter on the Prophet's marriage to Aisha. Explains the dream and the meaning of the silk cloth.
- al-Bidaya wa al-Nihaya (Ibn Kathir), Events after the death of Khadijah, the Prophet's marriages to Sawda and Aisha. Gives the proposal through Khawla bint Hakim.
- al-Isaba fi Tamyiz al-Sahaba (Ibn Hajar), Entry on Aisha bint Abi Bakr. Her knowledge and the Companions who learned from her.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.