Yes, "man" is etymologically a person, "woman" is a female person, and "wereman" is a male person. Over time "were" got dropped, but "wo" got kept, so "man" is either a gender-neutral person or a male person, distinguished based on context. E.g. "mankind" is gender-neutral.

« mann » comes from Old English and stands for a human being.

« wïfmann », literally "female human", led to « wife ».

« were » means man and comes from Germanic and I don't think « weremann » has ever been a thing.

Blew my mind when I found out “world” is a direct derivative of the word “were”.

“world” is derived from “were” + “eald” (old), and meant “the age of humans”, which was distinguished from the age of the Gods, when the Æsir and Vanir dominated, and the age of the Jötnar.

I find it interesting how the term shifted from a (mythical) temporal concept to a spatial concept, to now often a social concept (e.g. the Fourth World).

yes

I was making a funny