The Greeks actually did write but they weren't really interested in it to a level where they would make a god for writing and also it's not as important as war, harvest or other importanat things. The closest Greek gods to it I would say is Dionysus, the god of wine, parties and festivals, madness, tragedy, drunkenness and pleasure. Because is a festival for him which involves authors writing plays, the one judged the most tragic and dramatic would win a prize. Though, yes, they don't really have a god or goddess of writing.
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He is Greek god, but he does have a roman version Jupiter
the greek god hermes the god of messages
The name of the greek writing system is Cuniform.
He is the Herald of the Gods, a God of merchants, travelers, thieves, he is also a trickster who likes to play pranks, he is also a God of writing (he invented it) and rhetoric.
There is no Greek god mercury, he was a roman god, and he was the god of war and weapons.