Sayyiduna Abu Sa'id Khudri (may Allah be pleased with him) narrates: The Prophet Muhammad (peace and blessings be upon him) said:
"Only record the Qur'an from me. Whoever has recorded anything from me other than that, let him erase it."
(Imam Ibn Hibban, may Allah have mercy on him, says:) The Prophet Muhammad's (peace and blessings be upon him) prohibition of recording anything other than the Qur'an means: He (peace and blessings be upon him) encouraged the memorization of hadiths, lest people record the hadiths and then not memorize them or reflect upon them.
The evidence for the correctness of this position is that the Prophet Muhammad (peace and blessings be upon him) allowed Sayyiduna Abu Shah Yamani to record the sermon of the Farewell Pilgrimage, which he had heard from the Prophet Muhammad (peace and blessings be upon him) himself.
Similarly, the Prophet Muhammad (peace and blessings be upon him) also allowed Sayyiduna Abdullah bin Amr (may Allah be pleased with him) to record hadiths.