Proto-Indo-European *medʰu- "honey; also mead" became Greek μέθυ methu "wine". μεθύσκω methuskō meant "to get drunk" (with the iterative suffix *sḱo-) and ἀμέθυστος amethustos was "not intoxicating" (with the prefix α "not"). This was borrowed into Latin as amethystus, becoming Old French amatiste, then borrowed into English as amatiste, which was respelled as amethyst in the 16th century. The OED says the word was "applied subst. to this stone (as also to a herb), from a notion that it was a preventive of intoxication". Who exactly held this notion, and when was this word applied to the gemstone?
In Old English the PIE root became meodu, then mead. In Russian it became медведь medved' "bear" - etymologically "honey-eater".