I think that the best way to study mathematics is through interactions with others studying similar things. For those who don’t live near a university, or simply feel like you want to meet more people and talk to them about math, here are some nice links:
- Gmail. No, I’m serious. Gmail is an amazing way to talk to mathematicians; I’ve talked to many using just this one resource!
- Math Stackexchange. This is for the more general and usually not research-level math questions, like questions that you may have when studying analysis, topology, abstract algebra, etc.
- MathOverflow. This is for the research questions. I use this site sometimes, and it’s a nice place to meet great people. I post as user Sanath.
- ErdosNinth. This is a blog which I started with a few friends I met at Intel ISEF 2015. We blog about various topics, and you can send us an email at (the logically correct form of) moc[tod]liamg[ta]htninsodre.