Math vs Peace: which one is the one for Carmy?
There is a transcendental scene happening here: Carmy asks, "What is the opposite of chaos?. Claire (self-nominating herself as peace because the bozzos of the Faks told her she was) answers "Peace"
Carmy then smiles, maybe implying that, looking at Claire, he is trying not afraid of peace anymore, and therefore, he is now only really scared of math.
(Even though he could have been deflecting and running away from Claire, because she was making him feel like he was on fire, we are leaving that for later.)
Sydney joins in Carmy's joke, and remembering her intentions to teach Carmy math (which he cannot follow right now), we know Sydney is now "math". So, Carmy is apparently learning to be less afraid of Claire's "peace," but is still scared of Sydney's "math".
Here is my thing: the opposite of chaos is not peace, it is order
credits to @hamachibloodmagic
The most significant ongoing parallels that indicate that Sydney is "order" are her comparisons with Chef Terry, as seen in the video above; Carmy is aware of this comparison.
Now, why is it significant that Sydney is "order"? Because the order that both Chef Terry and Chef Sydney created in the spaces they worked in is a result of two things: accountability and respect.
Sydney respected all the people she worked with in S1, even if they were awful to her at the beginning. And because they have grown to admire her (and their own processes), people have made an effort to rise to the occasion, and every time, Sydney is there to guide them and encourage them. But even most importantly, Sydney is there when they mess up.
Now, let's examine the word' accountability'.
The root of the word 'accountability' is to count, so...math
Syd didn't tolerate bad behavior; she held people accountable, but she also forgave them when there was an effort to improve. It applied to most of the crew, including Carmy, and with Richie since season 2.
So, we know these attributes are the things that Carmy admires (loves) the most about Sydney, so why is he so afraid of them?
Well, because for a kid to grow up in an abusive household, respect and accountability are not only foreign concepts, but from the perspective of an abusive victim, you don't even deserve respect or accountability. In the house where Carmy grew up, with a mother like Donna, people weren't encouraged, supported, or forgiven; instead, there were just wounds that bottled up into resentment and toxic dynamics.
Even more, in Carmy's house, abusers didn't take accountability for their actions, and neither did the people who copied that toxic dynamic. None of them, not Donna, not Michael, not Lee, sometimes not even Cicero, Nat, or Richie.
So again, why Claire is peace?
Well, she isn't; there is something about Claire's double face that maybe is triggering Carmy's instincts, and that's why he has so many panic attacks around her. Carmy believes Claire is peaceful because, with her, there is no accountability either; she has never encouraged him to seek help for his issues, and they never discussed the challenging things when they were together. Claire just wants to have her cake (be Carmy's peace) and eat it too (cuddle Carmy into being whatever suits it at any given moment without actually caring for his wellbeing). She supposedly is peace for him because with her (fire), he doesn't have to feel the pain, like when he puts his hand on fire.
But she isn't peace really...
There have been 3/3 full panic attacks Carmy had that were either related to Claire, or that Carmy tried to calm down by thinking of Claire. It didn't work. Sydney is the one who actually saves him from the panic. See this post. and this post
So, Carmy doesn't realise Claire's true nature and lack of care (which also contributes to Claire's lack of accountability, as evident in her justification of committing malpractice with a very unjustifiable mistake).
And until he puts all these pieces in place, he won't be able to realise Claire is bad for him in all the ways Sydney is good for him. To be fair to the man, I think his heart knows; his mind just has to catch up.
