[fpgamlirfanboy]

You skipped over the second sentence of what you're responding to:

> Say you’re reading a paper or trying to implement some technology that uses a mathematical concept you aren’t familiar with

In such a case you're not interested in either manifold or sub-manifold or group in and of itself. So a lack of familiarity with theorems isn't an impediment.

[Tainnor]

I didn't "skip over" anything. If it's irrelevant to you that something is a submanifold or group, you also don't need to look up the definition.

Reading mathematical definitions on their own just doesn't give you a whole lot of context about the objects they're describing.