It is possible to become a social savant if you apply yourself and practice. Most social skills are a handful of routines and checklists coupled with practice in real life situations.
You shouldn't label yourself 'bad at social' or 'bad at math' because it'll hold your confident to improve in check.
If you keep a notebook, deliberately put yourself into social settings and keep score it'll be intimidating but you'll improve.
I hope so. Part of the problem is I think I'm a slow thinker, so when talking on technical concepts, people have a tendency to blow by me when I need clarification on the things they said three sentences ago. And once I finally get clarification, I have to retrace through their entire thought process with the new context.
Hard to manage this type of conversation without being a jerk.
That's quite alright. I've had similar experiences in social and technical settings from both sides of that interaction.
What you refer to as 'slow thinking' is likely being thoroughly analytical. I know quite a few programmers like this. It's System 1 and System 2 all over again (book title: thinking fast and slow).
Thinking from 'Elon Musk's First Principals' isn't fast, it's just really important, like how a CPU register is intrinsically more constrained than a HD but the role is differently important. Knowing when to context switch from Sys1 to Sys2 takes practice, not that I'm an expert at that either.
I often find it easy to bedazzle and bamboozle people with knowledge (or more like streams of consciousnesses!), but it's sometimes not that I'm good, so much as that I'm not communicating simple ideas properly to them. Geeks are often very bad at communicating for that reason, and when in groups it gets worse because we can fall into competing by being semi-obscurantist. As the guy who runs the Sante Fe Insitute points out: "You made that look easy" is a statement about intelligence. I highly recommend you examine David Krakauer's idea on intelligence, ignorance and stupidity:
The fact of the matter is that when dealing with new knowledge nearly everybody is slow and this is covered up through a variety of tricks. People who are very socially adept are exactly like construction workers in the trades. They actually make about the same number of mistakes as the newbs, it is just that they recover from them faster because they know what to do next....
So I'd encourage you to notebook your interactions and keep a self made score. Sounds simple but could be immensely important for you. The important bit is "I screwed that one up", "what next?", because knowing the answer to that will solve for most circumstances.
Humans are not the top predator because we're faster or stronger, we're on top because we're the most adaptable. It might not feel like it all the time to you and I, but we're in possession of AI super intelligence like powers in our brains and it's just a case of harnessing them, giving them training data... :-)
Personally I know I'm bad at correlating names and faces, so I intend to keep a record of name to face data for the right contexts.
You shouldn't label yourself 'bad at social' or 'bad at math' because it'll hold your confident to improve in check.
If you keep a notebook, deliberately put yourself into social settings and keep score it'll be intimidating but you'll improve.