A numismatist is a person who studies coins, to find out when they were made, and where, and by whom.
Numismatists can tell what kind of metal a coin is made of. They can use coins that were found in archaeological excavations to date the buildings that archaeologists have dug up.
Numismatists can also tell how the economy of a country was doing by whether the coin really has as much gold or silver in it as it was supposed to have. When the government starts to cheat on how much gold or silver is in the coins, that’s not a good sign.
For instance, in the 200s AD, the Roman emperors started to put out silver coins that really had only a thin coating of silver over bronze. They needed a lot of silver coins to pay the army, but they didn’t have enough silver to make all those coins. After a little while, though, the Roman soldiers realized that the government was cheating them. Cheating on your coins can only ever be a short-term solution to money problems.
Bibliography and further reading about ancient coins:
Ancient History from Coins, by C.J. Howgego (1995).