What Do Mathematicians Do?

Back in the Dark Ages I was a member of MAA and loved their publications. I would share them with my students to prove that math was accessible to them as sharp high-school seniors and would be as college students. They were a very mathy crowd, but more of them became engineers (sigh).
I am with you completely about a math community and how it can improve both knowledge and teaching. When I was finished coaching (my own kids were in the high school, so I chased them around instead of everyone else's) I wished to get the next degree in math (at night). Every time I signed up for a math class it would get cancelled a week before the scheduled start.
Eventually I got a call from the office of the Dean of Graduate Studies and was informed that I was going to get booted out as I was "not making progress towards my degree". The caused me to write a sharply-worded letter that contained the term "insidious fraud".
This got me a call from the Dean himself. I had to explain myself: what fraud was I upset about?
"You offer this degree, do you not?"
"Yes, we do."
"Does anyone ever get one?"
"Uh, I believe two people got that degree last year."
"Well, what freakin' courses did they take????????"
"Uh, I believe they were largely self-directed."
"Well, I've been self-directed for 22 years! I want to hang out with the math people!"

I gave them one more chance, but three days before a class was to begin it was cancelled. I was out. In fact, I was so far out that I get zero mail from this school to this day.
Now I'm retired but hope to find some mathy people to hang with.

And here i am, thinking you mathematicians either aim to find a fool-proof method to win tic-tac-toe, or aim to change the rules of tic-tac-toe in order to then find a fool-proof method to win. Sheesh. What was i thinking?