”The roots of education are bitter, but the fruit is sweet.” — Aristotle

> After scratching the itch of knowing that something's been written completely rigorously, it's easy to call a work done when maybe we shouldn't call it done yet. And there's contexts where this is maybe OK, research comes to mind...

It's funny, because all of the advice he gives in the rest of the video would be amazing to apply to research papers as well. I've had people discourage me from writing research papers pedagogically because it is "unusual," which really meant that it would be looked down upon. It's kind of tragic that the norm is to write research papers that strip away the human details of how a definition is motivated or how something was discovered. This kind of information is usually only shared through in-person discussions or occasionally research presentations, but it is often the core knowledge that enables one to do research in a given field.

It's a great video though. He gives a little checklist of ways to check if your work is clear:

- Do definitions have motivating examples?

- Do proofs [or other results] feel rediscoverable?

- Is there personality?

- Are core ideas illustrated with diagrams?

- Is relative importance highlighted?

...

He also gives a beautiful example of how powerful it is to give a motivating example for an abstraction before introducing it. I really got the sense from watching this of what makes him such a great math educator. Highly recommend his YouTube channel 3Blue1Brown for anyone who hasn't heard of him

Writing "3Blue1Brown" would be more recognizable than "Grant Sanderson" :)

(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.