Unfortunately there is no halfway with maths. Math is the language of logic, the purpose of mathematical formalism is to allow easy communication, not just naval gazing.
I strongly disagree. While rigorous mathematical proof (logic) is a big part of modern mathematical research output, it is an impenetrable barrier to learning for most students, including maths students. I doubt any mathematician ever learned their subject by mainly reading proofs. And I say that as someone who secretly enjoys reading and working through proofs of theorems. Understanding mathematics demands developing strong intuition of ideas before attempting their
logical justification. That rigour and intuition in mathematics education are largely contradictory goals is widely acknowledged by maths teachers; 3BlueBrown, for example, has often mentioned this duality in his videos. It was only in latter part of the twentieth century that the idea of abandoning intuition in teaching mathematics was seriously attempted, by the Bourbakists I believe, and was embraced for a while, before fading away.
> I doubt any mathematician ever learned their subject by mainly reading proofs. And I say that as someone who secretly enjoys reading and working through proofs of theorems. Understanding mathematics demands developing strong intuition of ideas before attempting their logical justification.
This is half right: you don't learn math by reading proofs, you learn it by writing proofs. Developing strong intuition without proofs is possible (albeit difficult) for applied topics, but not viable at all for pure math.
That's not really true, in several senses. Mathematics is not the language of logic. I'm not even sure what that was supposed to mean. Logic is the language of logic. Also, engineers and physicists can have rather intuitive understandings of various filters with almost no mathematical calculations being done, on paper or their head.
It's only supposed to be somewhat intuitive for those who already possess some intermediate level college math background.
And no, rejecting the notion that not every advanced topic is supposed to be accurately ELI5-ed with a cringy Redditesque tone, means neither there's any gatekeeping taking place nor there's lack of understanding from the potential explainer's side.
But I've seen both it and the alternative. It is literally easier to learn the math, and then use that to facilitate communication, than to attempt to directly communicate key concepts while avoiding the math.
