(I suspect that Atlantis was created specifically to appeal to fanfiction writers. As it's existed for ten days and there are already twenty-six fics in its AO3 tag (which is, incidentally, twenty-six times the number of stories in the last fandom I wrote for), it seems to have succeeded.)
Even if I manage to grasp the characters, writing fanfiction set in Ancient Greece is probably going to be tricky. Jason's from the modern day, of course, which makes things a bit easier, but writing from the perspective of Pythagoras would throw up all sorts of restrictions. I ran into similar problems when I was writing for Merlin; obviously Merlin's dialogue is 'translated' into Modern English, so you don't have to go 'oh no, can't use that word, that wasn't around until the Norman invasion', but there are other things you have to be aware of. I unthinkingly used the phrase 'when Merlin is out of the picture' in my Merlin-Gwen bodyswap fic and realised hours after posting it that that's almost certainly a photography metaphor. Nobody used photography metaphors in the Dark Ages.
Here's a terrible Merlin fic idea I noted down a while ago, incidentally:
Merlin fanfiction, set in the modern day, after the finale. Merlin is a thousand and something years old. Arthur is resurrected as a twenty-something-year-old. (They still have sexual tension.) The plot concerns their efforts to overthrow Queen Elizabeth II and install Arthur on the throne again.
Actually, while I'm talking about terrible fanfiction ideas: during an e-mail exchange with th_esaurus about Atlantis and The Great British Bake Off, I ended up ill-advisedly combining the two:
My first Atlantis fic is going to be about Pythagoras being suddenly flung into the modern day and appearing in the middle of the Bake Off tent, during an incredibly tense showstopper challenge.
It was a joke, but the more I think about this, the more I want to see it. The poor contestants only have four hours to make about six hundred elaborate pastries; they can't afford to be distracted by a confused mathematician from Ancient Greece! Mel and Sue, however, are amused and delighted and refuse to evict Pythagoras from the tent.
(Alternatively, Pythagoras turns up during the technical challenge, glances at the baking instructions and mutters, 'I can't read this; none of it's Greek to me.')
This is probably not something I should actually write.