Remember all those times in HoH when Percy did feats so amazing Annabeth couldn't understand how he was able to do so, but we never got to see Percy's narration of these events, and he and Annabeth never got to talk about how exactly he was able to do such things?
Well, I would like to show you something from SoM
First, we have Percy and Clarisse fighting Polyphemus, and barely scratching him. And then:
Mind you, Polyphemus is described as being at least fifteen feet tall.
Percy's anger in this scene seems to unlock something in him, allowing him to do things he wouldn't normally be able to. Or maybe he already could do that, but didn't know he could, or didn't know how to?
Is Percy stronger than he thinks he is? Did his anger make him stronger, or did it simply allow him to forget that he was "hopelessly outmatched", and attack without limiting himself?
There are a few moments during the saga where you get to see Percy doing things that require a greater amount of strength than what you would think he possesses (all while not being in contact with water)
What I find interesting about these scenes is that, in the fight with Polyphemus, despite knowing how impossible what he just did is, Percy either refuses to think about how the hell did he just defeat this giant cyclops all by himself, or he refuses to tell us what he thinks about it.
Then, in the fight with Antaeus, Percy seems to be trying to play it off, reasoning that his mother always said he had "a gift for getting stuff tangled up" — which doesn't explain at all how he had the strength to do any of it — and also implying that this was an extraordinary situation, since he was "desperate to save [his] friends", so, obviously, that's not something he could do in a normal context, right? Right.
Then, in the scene he kills Arachne and Annabeth asks him how he moved so fast, you can't really tell if he is deflecting the question on purpose. And at last, the most interesting thing about the jump scene isn't even the jump itself, but rather the fact that Percy knew that somehow he would be able to pull it off. It seems to me like at this point, Percy is finally able to admit to himself that he is capable of doing more than what is expected. In his narration we so often see him saying that the idea of doing something is "impossible", right before he does that exact same thing.
(I also like this scene bc Percy is still deluding himself into thinking he's not as powerful as he is but Michael knows he can do it)
When Percy allows himself to try, he always seems to be able to do impossible things. And I don't think he is comfortable with this idea, going so far as only letting himself attempt to control poison bc a) he was dying and b) well, surely that's only possible bc he's in Tartarus right? That's certainly not a power he has access to on a daily basis...
But I feel like as time goes on, Percy is less and less able to continue telling himself he isn't more powerful than he thinks he is.