[joe_the_user]

The advice of one teacher of one moderately known mathematician hardly seems definitive.

The advice implies a completely linear process of learning. I think that works for some portion of learners and isn't useful at all for another portion.

Edit: never abandon a book you have chosen without working all the way through it

I've read a number of math books on my own. There are plenty of bad books out there. Some will have you wasting an awful long time if you never abandon them (since they are filled with extremely difficult problems or simply don't explain themselves well). This is advice for someone who, at minimum, has a teacher feeding them good books.

[jorgenveisdal]

How does Abel’s level of fame 200 years later matter?

[joe_the_user]

The post I responded to above cited the high school math teacher of Abel. As far as I can tell, the authority of the claim rested on Abel indeed having significant mathematical achievements ("A Norwegian high school teacher from from 200 years once said" doesn't sound convincing as claim by itself to me). My response was just pacing the situation - Niels Abel is just one example of someone achieving a lot, not insignificant but not the last word.

[watwut]

Not at all. There is reason no contemporary teachers give this particular advice.

Abel is famous because of his algebra results. He had awful good abstract thinking and was indeed very good at math. That does not only everything he ever said is correct. In particular, it does not imply general teaching skills.

Being good at proving theorems does not imply being good at teaching students.