So a friend and I recently decided to start a little educational experiment. I unfortunately don’t have a lot of experience with writing proofs, and he suggested that we work through some simple proofs together so I could better see what was going on and the logical steps one takes when proving a theorem.
Reading a book or studying theorems is all fine and good, but I think that the real learning comes from interacting with others, sharing ideas, contributing insights to a final goal. While many people see mathematics as a solitary profession, I think that intimate collaboration with a few others can really be useful. In the current education system, we have professors lecturing to rooms of dozens if not hundreds of students. I know from my point of view, as someone who has little experience with “professional mathematics”, it is like having a mentor with which I can ask questions and learn together with. It’s really nice.
At my university, we had an academic mentoring system similar to this. I’ve been on both sides of the fence, mentoring and being mentored. Its definitely worth doing and a great experience if you have the chance. Find someone in your field that you can work with and learn from. It will be worth it, I promise.