Question: Where can I find the ḥadīth about this ummah being illiterate? Is it found in any strong sources, and if so, weren’t there Companions who could read and write in the Prophet’s time (sallallāhu ʿalayhi wa sallam)?
Answer: The ḥadīth I believe you are referring to reads: “We are an unlettered nation (ummah). We do not write nor do we calculate.” This ḥadīth can be found in Ṣaḥīḥ Bukhārī (1814), Ṣaḥīḥ Muslim (1080), Sunan Abī Dāwūd (5319), Sunan al-Nasā’ī (2451), Musnad Aḥmad (5017,5137,6041, and 6129), and Muṣannaf Ibn Abī Shaybah (3:85).
The ḥadīth is ṣaḥīḥ, and as is apparent from the above-mentioned citations, is mentioned in authentic sources of ḥadīth with sound, unbroken chains of transmission.
About your last question, Ḥafiẓ Ibn Ḥajar provides a brief and valuable commentary on the narration inFatḥ al-Bārī that should suffice us here. He states, “No objection can be raised to the ḥadīth that (amongst the ummah at that time) were those who could write and calculate, since literacy was little and rare amongst them. As for “calculation”, what is meant here are astronomical calculations.” [Fatḥ al-Bārī 4:623]
My teacher, Shaykh Mohammed Amin Kholwadia also provides a fascinating commentary on this hadith, the summary of which is that Islam is not an elitist religion. Every Muslim, literate or illiterate, rich and poor, can practice fully upon its rules and regulations. It is a religion that applies as equally to the bedouin Arab as it does to the Harvard graduate or medical professional. In other words, the wisdom of the exclusion of complex calculations from Islamic law is that it would have restricted the applicability of its rulings. The unlettered desert nomad, therefore, can identify the beginning of the Islamic months as perfectly as a city-bred astronomer.
Additionally, the fact that this nation is ummi (or unlettered) indicates that the primary method of its preservation and transmission will be through praxis and aural tradition, a contrast to previous nations that depended heavily on written documentation and were perhaps thus termed “Ahl al-Kitab” by the Quran, or “the people of written tradition”. For the sake of brevity, I will not expand further on Shaykh Amin’s wonderful commentary on the hadith at this time. An expansion on the explanation of his theories can be found in numerous lectures of his on the topic.
And Allah knows best.