Step 1: Read the description carefully.
The clue is: one who studies ancient inscriptions and writings. The important words are inscriptions, that is, writing carved on stone, metal, or monuments.
Step 2: Look at the word root.
The root epi- with -graph means writing on a surface. So an epigraphist deals with carved writings and inscriptions.
Step 3: Check option Archaeologist.
An archaeologist studies past civilizations through digging up objects and remains. This is broader than inscriptions, so it is not the best fit.
Step 4: Check option Numismatist.
A numismatist studies coins and currency. Coins are not the same as inscriptions, so this is wrong.
Step 5: Check option Genealogist.
A genealogist studies family history and ancestry. This has nothing to do with inscriptions, so it is wrong.
Step 6: Pick the matching word.
Epigraphist is the person who studies ancient inscriptions and writings, which matches the clue exactly. \[ \boxed{\text{Epigraphist}} \]