[v64]

> Sometimes the best stuff have come out of something like "I was thinking about xyz, here are some things I noticed, thoughts?"

I think this is a matter of preference. I see where you're coming from, and there's a lot of value in that kind of unrestricted brainstorming, but I've always preferred to have those types of discussions in person with some whiteboards available for fleshing out ideas. When I'm brainstorming, I don't want to get caught up in LaTeX formatting issues, or to spend an hour writing out a response, only to have the discussion go in a completely different direction within that hour.

I enjoy reading MathOverflow because the Q&A format forces the question asker to take whatever vague idea they have and form it into an objective question that can be rigorously proven or refuted. The narrow focus keeps the discussion on topic, so even if it takes you a while to contribute, you can be assured that your response will still be relevant.

[whatshisface]

>I've always preferred to have those types of discussions in person with some whiteboards available for fleshing out ideas.

Not everyone has people to talk to in person that understand their subfield. In a small institution it might be 100 miles to the nearest person who could converse fluently in what it is you're thinking about, even if thousands of them exist.

[v64]

That's a great point. In that case, I would prefer a video conference call or an online service that allows collaborators to share a paint canvas or some other kind of unrestricted drawing board. Again, this is personal preference, but I prefer text for writing out proofs and something visual and more freeform for brainstorming.