I invited a collection of friends, not all of them knew each other, to meet every couple of weeks at a mediocre pizza shop in SF and discuss machine learning papers and articles. Some are PhD level experts, some are newbies, founders, all are engineers in industry or academia.
The group has devolved (or evolved) into lots of discussions of ethics in machine learning, online ads, etc. The last two sessions have been entirely centered around philosophy papers.
We've strayed a bit from math but it's a good group to learn with.
I think the choice of a shitty pizza shop is key. It's not popular so we always have room for the whole group of 9, we don't get distracted with exciting food options or drinking a lot. The only thing I don't like is that it's an all male group but hopefully that will change.