Depth-first search is the right approach to reading a math textbook.
That’s a great point! I never explicitly thought of it like that but it’s clearly true now that you mention it. And not just math—nearly any scientific writing has the same quality where lack of knowledge about one idea or principle ruins your ability to understand any of it—these are examples of those “complex machines” which break if any part doesn’t work.
A friend of mine mentioned that reading Wikipedia tends to be like your second example—going depth-first (chasing links) instead of breadth-first when trying to learn about a topic. You end up with a hundred tabs and no smarter than you were before. That’s another failure mode where a breadth-first method like your note taking system presents advantages.
That’s a great point! I never explicitly thought of it like that but it’s clearly true now that you mention it. And not just math—nearly any scientific writing has the same quality where lack of knowledge about one idea or principle ruins your ability to understand any of it—these are examples of those “complex machines” which break if any part doesn’t work.
A friend of mine mentioned that reading Wikipedia tends to be like your second example—going depth-first (chasing links) instead of breadth-first when trying to learn about a topic. You end up with a hundred tabs and no smarter than you were before. That’s another failure mode where a breadth-first method like your note taking system presents advantages.