Mass distribution of learning material has been around for a few centuries and has yet to replace the process of guided learning. While it’s possible to amass facts and skills from reading and listening, it’s much more difficult to produce complex works of value without feedback on the process.

Doing mathematics isn’t just applying rules and techniques. It’s about knowing how to reason, and writing a proof in a way which communicates your reasoning clearly to others. You can get started by following along with proofs from a lecture, but in order to really ingrain the techniques in your brain, you have to write proofs of things you’ve never encountered before. Someone has to read those proofs, and give feedback on where your reasoning was unclear, incomplete, or flawed. They can suggest a different notation, or a shorter path to the same solution. Good teachers will leave notes: “this is a cool idea you’ve developed here, and it points towards this area of complex analysis we haven’t talked about yet.”