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DoctorOetkertoday at 3:40 PM0 repliesview on HN

I can find a kernel of truth in both statements:

As long as the literature contains insights a reader isn't aware about, reading the literature is low-hanging fruit compared to having to derive all the things yourself.

As soon as the literature no longer contains insights, it becomes more productive to explore mathematics oneself by trial and error.

Organized education will model this on a topic by topic basis: during class you're handed the more valuable insights on a silver platter, during an exam you are prevented from looking at your textbook.

Every time you read a chapter and do the exercises it's a small simulacrum of catching low hanging fruit followed by making sure you can derive similar statements with trial and error for fixing any gaps. The trial and error while you do problems does improve your intuition, but only trial and error is like having every student redevelop the frontier starting from antiquity.