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[[Come on you guys - you should know better than to post lazy internet ripostes to shallowly provocative titles. This is a fine and interesting historical article.]]
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Invented? Ancient Rome would like a word: the Vigiles Urbani date back to 6 AD.
https://en.wikipedia.org/wiki/Firefighting_in_ancient_Rome
And private firefighters were active even earlier, with Crassus particularly notorious:
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There were many private establishments going back to Ancient Rome.
Fully paid, professional municipal departments came in 1853 Cincinnati.
So I guess it depends on how you define it. US gets a lot of credit for the idea of a “fire department”