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past, last, latest

Although these words are often used interchangeably, last can have the connotation of final whereas latest and past mean the most recent.

If the meaning of last is ambiguous, it is better to use past or latest:

            
"In his last article Mike Edwards described Scythian gold discoveries in Siberia"

could mean the last article he will ever write or the most recent one with the expectation he will write more, in which case using latest would be clearer.

"The past century" usually means a hundred years back from the present time; "the last century" means the previous numbered century, for instance the 20th century from the vantage point of the 21st.