(Ahou ni tsukeru kusuri wa nai; “There’s no medicine for stupidity.”)
There’s nothing that can be done to help a fool. Note that this saying isn’t about mere lack of education, or about people holding opinions or beliefs that you feel to be wrong, even stupid-wrong. It’s about how someone who doesn’t think about things much can’t be corrected because no matter what you do… they won’t think about it much. A special case of “you can lead a horse to water, but you can’t make it drink.” A wry version of “Against stupidity, the gods themselves contend in vain.”
A more positive interpretation emphasizes the fact that there is no quick fix, no simple medicine, to cure foolishness – the treatment indicated is thorough schooling, preferably chosen and pursued by the patient rather than imposed on them forcefully by others.
阿呆 (originally ahou but now often aho, commonly written using hiragana or katakana, rather than phonetic kanji, in modern orthography) is both a noun and an adjective. Here it functions as a noun, with に (ni), the directional particle, giving its relationship to the following verb 付ける (tsukeru) – which has many meanings such as “attach,” “fasten,” etc. but in this case refers to applying ointment. This verb in turn modifies the noun 薬 (kusuri, “medicine”). は (wa), the “topic marker” particle, seems a bit odd here. I suspect that its use is contrastive, emphasizing the difference between medicine for aho versus medicines for curable conditions like rashes. At the end comes the adjective of negation, ない (nai, in kanji 無い).
The saying can also end ～薬無し (kusuri nashi) without any significant change in meaning. Some versions substitute 馬鹿 (baka) for 阿呆.
This is the proverb given for あ in the Osaka/Nagoya Iroha Karuta set. (Oh, those Kansai people!) As one might guess, it’s relatively old.
(“Aaa, mata yacchimatta na, aitsu! Dou shiyoukka?” “Dou shiyou mo nai. Ahou ni tsukeru kusuri wa nai shi.”)
[“Argh, that idiot did it again! What do we do?” ”There’s nothing we can do. I mean, there’s no cure for dumb.”]