unpopular opinion: imho there is no substitute for deep learning and doing problems. Math is unlike other subjects, where you have to actually do it head on; you cannot just passively consume it like listening to a history podcast or watching a video.
"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"
I think a lot of people, sadly, imply that they think this, even if they don't explicitly say it.
I recently tried to obliquely bring this up to a friend and he asked out loud, "Sometimes I do wonder if it's better to watch YouTube videos or do problems. I'm not sure."
This has been one piece of acedata representing an aggravating trend in my personal life. It could just be my attracting these types (which I've been fretting about since I'm thinking wtf is wrong with me then), but other examples are family members even expressing this bad habit with something as dumb as Marvel. They read forums about comics without ever reading them and feel possessive enough about the genre to get pissed when I, who...does read comics..., criticize the Disney Marvel movies.
I'm hoping it's just me over indexing for it since it bothers me, but yeah - I have found that there are certainly people who just consume content without practicing or implementing the thing they're supposedly learning about, and then think they've actually learned.
ofc ymmv - it could just be my strange social circles.
(2023)
unpopular opinion: imho there is no substitute for deep learning and doing problems. Math is unlike other subjects, where you have to actually do it head on; you cannot just passively consume it like listening to a history podcast or watching a video.
"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"
-The goat paul halmos
This is the single most popular opinion about learning math.
Learning nearly anything? You can’t learn to drive a car from YouTube. Or paint a house, or wash a dish, or code, or … Learning requires doing.
Who thinks otherwise?
I think a lot of people, sadly, imply that they think this, even if they don't explicitly say it.
I recently tried to obliquely bring this up to a friend and he asked out loud, "Sometimes I do wonder if it's better to watch YouTube videos or do problems. I'm not sure."
This has been one piece of acedata representing an aggravating trend in my personal life. It could just be my attracting these types (which I've been fretting about since I'm thinking wtf is wrong with me then), but other examples are family members even expressing this bad habit with something as dumb as Marvel. They read forums about comics without ever reading them and feel possessive enough about the genre to get pissed when I, who...does read comics..., criticize the Disney Marvel movies.
I'm hoping it's just me over indexing for it since it bothers me, but yeah - I have found that there are certainly people who just consume content without practicing or implementing the thing they're supposedly learning about, and then think they've actually learned.
ofc ymmv - it could just be my strange social circles.