We learned the goal-setting “understand” is that you can explain the concept with your own words without seeing anything. To achieve the goal, we need to “read” in principle of ”do not go ahead if you do not understand.”
The goal is a high hurdle. The reading is quite a time-consuming. It is necessary to train mathematicians, but in other circumstances, I think it is not always necessary.
The purpose of reading is what you should decide. For the purpose you want, what do you need to explain without seeing anything?
When it is necessary for your purpose or the purpose is itself to understand, there is no escape. No matter how long it takes, you have no other choice but to read textbooks, make concrete examples, and search for external reference until you can explain the concept with your own words.
On the other hand, if it is not necessary to understand, you can assume that the concept is correct. You can go ahead with the assumption. You need to remember that it is an assumption. Even if there is no guarantee of correctness, it can be beneficial to your life.#todo link to chapter 7
The choice depends on your purpose.
Whether it is reading of Akinori Takada or reading in mathematics department, we follows the principle of ”do not go ahead if you do not understand” in the end. The ”read from where you want to read” principle by Akinori Takada looks conflicting. However, this reading has two phases. The ”read from where you want to read” principle is for the first phase and the ”do not go ahead if you do not understand” principle is for the second phase.
Those slow reading leads to large loss of time when the contents of the book are incorrect, or when book selection is not appropriate for the purpose. The importance of book selection is high.