Princeton's English Lexicon defines well-read as follows:
Quote:
S: (adj) well-read (well informed or deeply versed through reading) "respect for a well-read man"; "well-read in medieval history"
S: (adj) knowing, knowledgeable, learned, lettered, well-educated, well-read (highly educated; having extensive information or understanding) "knowing instructors"; "a knowledgeable critic"; "a knowledgeable audience"
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There is a massive difference between being well informed in one topic versus many, but someone can be well-read in both senses, of course. I would argue it is the difference between being an expert and a polymath.
I think all the negative connotations we put on the phrase are, as stated above, due in great part to wanting to be considered well-read, but know others wouldn't (due to perceived elitism).
I'd honestly go for the polymath method every time, with a good Zettelkasten to help me relate ideas and thoughts from across a universe of topics. I am an expert in my particular field, but it does not bring me the same pride as when I connect a phrase from a world war I memoir with a 2018 novel.