wiki/2020-06-27-18-31-40.org

:PROPERTIES:
:ID:       b318dc2b-5fa1-48ff-9d33-6fbbdee46a2f
:END:
#+title: When reading mathematical texts, write down the simplest possible example
#+date: "2020-06-27 18:31:40 +08:00"
#+date_modified: "2021-05-04 20:52:06 +08:00"
#+language: en


On practice, writing down the simplest possible examples allows you to get started working on the definitions.
When you're done with the simplest possible example, you can then start with a more complicated example (relative to the simplest one) until you worked your way to a real mind-boggling example that really made you bang your head to a wall.
This is one of the foundation to building mathematical intuition.

That said, this habit can mold well into writing [[id:431532c3-6506-4565-b193-dbfb60eac7d6][Evergreen notes]].
Since you're dealing with the simplest possible examples, you can write easy-to-understand notes which can help you retain information even more.
This also makes a good transition in writing more complex topics and more complex examples.

On the non-practical side, it is said to be a cultural thing for mathematicians.
It is an unwritten rule for a reader to immediately write down examples and not pass through the text until they have understood it.
Providing examples is not an obligation from the author but they may do so for the sake of easier understanding.
However, to make sure you are paying attention, it is a recommendation that you have to practice this habit.