As title says, with the followup question whether your answer says anything about whether central banks have been successful (on average) in controlling inflation at a desirable level?
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There were certainly prolonged bouts of high inflation before central banking. EG in the 16th/17th centuries and in late Roman times. Fiat currencies have been around forever – the first currencies were temple notes (on clay pegs) in Sumer, and Bank of England notes were the bulk of local exchange in Britain from the mid 18th century (without prolonged inflation).
A prominent economist recently noted that quantity theories of money are clearly wrong – he just did not have an alternative. Also clearly, some central banks have been successful in controlling inflation, usually by suppressing the lower-classes.
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