Although "so surprised and confused that one is unsure how to react" is the original meaning of "nonplussed", the second, "unfazed", meaning arose in North America in the 1960s. It has become so pervasive that, in Canada at least, according to the surveys we did for the Canadian Oxford Dictionary, it has become the dominant meaning of the word. Indeed, many Canadians we asked were not even aware that there WAS a "confused" meaning of "nonplussed". When matters reach this point, it is clear that the word has changed its meaning, and no admonitions that "this is not standard" (as found in many dictionaries) can stop it.
However, because of these very divergent senses, I would recommend that you avoid using this word in writing unless the context makes the meaning absolutely unambiguous.
It's an odd word, isn't it? It comes from classical Latin nōn plūs (not more, no further). In the 1500s, when English speakers just adored making English more Latinate, we made this Latin phrase into an English noun, "non plus" (a state in which no more can be said or done; an inability to proceed in speech or action; a state of perplexity or puzzlement; a standstill). You could be at or in a nonplus, or reduced to a nonplus. As is usual with English, it didn't take long for this noun to be turned into a verb, so that by the 1600s, people who were paralyzed by perplexity were "nonplussed".
What does "nonplussed" mean to you?
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