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Translation of "Unlettered"
The main source of thought for Muhammad being illiterate are several verses (7.157-158, 62.2) that describe Muhammad as the "an-nabi al-ummi." In modern Arabic, this means illiteracy but not in Qur'anic Arabic. Palmer translates "illiterate" and Yusuf Ali translates "can neither read nor write" but these are interpritative translations coming from the strong tradition of Muhammad's illiteracy.
Reasons For Literacy
The Value of Education in Islam
Because Islam emphasizes education, for Muhammad to have never tried to learn to read would give a strong anti-literacy message to Muslims.
Experience in the Caravan
Khadija hired Muhammad to work for her caravan which makes little sense if Muhammad was illiterate at the time. Further, he could not have made the caravan succeed if he could not work with records at all.