Comment by chipdart
8 hours ago
> I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things.
I would argue something different. The "skill" angle is just thinly veiled ladder-pulling.
Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the cliche "X is left as an exercise for the reader" is just people rejoicing on the idea they can needlessly make life hard for the reader for no reason at all.
Everyone is familiar with the "Ivory tower" cliche, but what is not immediately obvious is how the tower aspect originates as a self-promotion and self-defense mechanism to sell the idea their particular role is critical and everyone who wishes to know something is obligated to go through them to reach their goals. This mindset trickles down from the top towards lower levels. And that's what ultimately makes math hard.
Case in point: linear algebra. The bulk of the material on the topic has been around for many decades, and the bulk of the course material,l used to teach that stuff, from beginner to advanced levels, is extraordinarily cryptic and mostly indecipherable. But then machine learning field started to take off and suddenly we started to see content addressing even advanced topics like dimensionality reduction using all kinds of subspace decomposition methods as someting clear and trivial. What changed? Only the type of people covering the topic.
I saw a lot of this when I went to college for engineering, some professors had this ability (or willingness) to make hard things simple, and others did the opposite, it was the same with the books, I dreaded the "exercise for the reader" shit, I don't think I ever did any of those, so those were all proofs I never got.
I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.
> I think the ML people want to get (a narrow band) of stuff done and ivory towered people want to understand a prove things. ML is applied mathematic. Both are needed.
I don't agree. First of all, ladder-pulling in math is observed at all levels, not only cutting-edge stuff. Secondly, it's in applied mathematics where pure math takes a queue onto where to focus effort. See how physics drives research into pure math.