Your remark that “learning is a process of information compression”, plus the math example, reminded me of anold post by Qiaochu Yuan written in 2009 on his blog Annoying Precision:
A little after that, I started reading math blogs, which was probably the best thing that happened to my mathematical education all of last year. It started with the master expositors Terence Tao and Tim Gowers. As I read through their archives, I marveled at how they were able to summarize and generalize technical arguments in non-technical but still enlightening ways. Once I learned that there’s more to mathematics than rigor, I realized that what Tao and Gowers do mentally is something like an enormous feat of compression. Rather than memorize the details of the proofs of the important results in their areas, it is both more efficient and ultimately more enlightening to compress an argument into a few important ideas, and provided you understand the subject well enough, you can (in principle) rewrite the entire argument from these big ideas. And the great thing about focusing on these big ideas rather than on the details of certain proofs is that you can apply these ideas to other situations where the details are different but the big ideas are the same.
Your remark that “learning is a process of information compression”, plus the math example, reminded me of an old post by Qiaochu Yuan written in 2009 on his blog Annoying Precision: