There are two issues here, I think. One, as a layman in math you end up reading about / paying attention to the discoveries you can parse and understand, thus i

There are two issues here, I think. One, as a layman in math you end up reading about / paying attention to the discoveries you can parse and understand, thus introducing a bias by ignoring the results that require years of math training to understand. Second, the specific examples you listed are not entirely accurate or even comparable (one is a theorem, one an axiom). There is a risk of misunderstanding the results when they are presented in English, oversimplified and converted to common terms. This oversimplification may lose important details (not just formal stuff) and may end up with a common-sense sounding phrase that trivializes the result and doesn't really do it justice.