Math is not a spectator sport
- george polya
when learning, it is really tempting to watch awe-inspiring youtube videos and tutorials, read in-depth blog posts and bookmark cheatsheets on twitter. as you listen/read/watch, you can feel yourself getting smarter. ‘wow that makes so much sense’, you say, as someone else does the work for you.
in no way do i mean to disparage the incredible work these people have done. i may never have switched from premed to math, if i hadn’t been inspired by 3blue1brown. i may never have thought i could be a machine learning engineer, if not for statquest’s explanations. i may not have even studied science at all if not for the stories of my 2nd grade science teacher Mr. Faber. beyond inspiration, karpathy’s tutorials were immensely helpful for debugging my own implementation of GPT-2. working alongside the hpc algorithmica textbook made learning about performance optimization much easier.
but those intuitions our teachers have passed down to us did not come from just the oral/visual tradition. they came from putting the reps in. it’ll be obvious where you need to apply conditional probability after doing the every problem in the AOPS chapter on it. previously nonsensical pandas operations will form bit by bit after you’ve wrangled with enough messy data. you’ll notice that confusing proof actually was trivial after questioning each and every step of it. lectures, blogs, tutorials are supplementary to the work that needs to be done.
you need to engage with, play with, fight with the material at hand in order to wrest away the understanding hidden inside.
and why not start now?