For example, when I started college, I called someone on the phone I knew from high school, "How do you make friends?" He told me to invite people to do things with me. So my first semester in the dorm towers I called someone, on a different floor, on his dorm room phone. I asked him if he wanted to play ping pong. He said he would be busy. So I called him back a week later asking if he wanted to play ping pong. He then again said he was going to be busy. I tried this again for the next few weeks, then after a while thought maybe he might be getting annoyed, and then I stopped.
Later on someone told me you're supposed to try small talk with someone first so that they feel comfortable before asking them to do something. I tried doing that with roommates since you see them more often and it's less awkward, and it seemed like some were much warmer all of a sudden toward me and would do some activities, but then after asking them to do things a few times they seemed to be aloof while being friendly towards many other people instead. They'd also ask others to do things, but not really in return ask me even if I had asked them earlier. (There are many people who are analytical but are social because they know how to speak the other person's language, so the issue can't just be being analytical, plus I'd suppress being analytical with them so I know it's more to it than that. Even some people would all of a sudden seem extremely interested in something I was tfrom biology/physics I may have been thinking about at the time, but being interested in something together doesn't mean they want to hang out.)
Then I read in a book that sometimes people will ask people indirectly so that it comes across as less intrusive and if they say they're "busy" it's less of a rejection. So I would read examples of it, and if someone said they were interested in something or were doing something, I'd say something like, "I like doing that," etc. Then I found they'd sometimes they'd say something like, "You should come," or, "We should do that sometime" (before if they'd say, "We should do that sometime" I didn't do anything, because I didn't know how one was to respond to that until I read it in a book, and remember I read that late in life in college). However, after doing things together a few times, they'd seem to loose some interest. Worthwhile friendship I'd think would have much more to it than just doing some activities together, so maybe there's something I'm not doing?
If I talk to people from high school, they tell me that I seemed extremely extremely aloof and they thought it was weird, although from my perspective they wouldn't let me interact.
If I'm in social groups, it seems like people don't connect socially with me no matter how hard I try, although individual one on one doesn't seem to have the same issue. In social group settings they'll talk back and forth and seem interested in each other, but don't seem to notice me. I read in a book that people use body language to pass the conversation back and forth in group situations just like you throw a ball, so maybe if I learn more about it and use do it yourself exercises just like you learn to play the piano, maybe it'll help.
Mathematical models would allow me to visualize how it's all related (even if it's probability rather than certainty, it could give me a starting point to work from and then I could use experience to smooth out the edges).