Well as a non mathematician all I saw in your description was opaque jargon. "locally euclidean hausdorff topological space" means nothing to me. It'd be like if I asked what the Spanish word "¡hola!" meant and the answer was in evocative Spanish poetry. Extremely unlikely to be helpful to that person who doesn't know basic greetings.

This article breaks that loop and it's refreshing to see a large topic not explained as an amalgamation of arcane jargon

If this article broke some loop, you could answer my question and tell me one thing you got out of it. What's a manifold?