No Permission to Write
Rav Nosson never wrote down his Torah or his chiddushim. He explained that the Rambam allows the Torah SheBaal Peh, the oral Torah, to be put in writing only because people forget it. "I, however, have no such permission to write down what I learned, because I do not forget it."
Source: Chut HaMeshulash, pp. 13–14, 16–17