I agree, this kind of thing is awesome. Like in the original meaning of the term too... inspiring of awe.

You are just repeating a myth. A quick look from wikipedia:

Logicians and philosophers of logic reject the notion that it is intrinsically impossible to prove negative claims.[11][12][13][14][15][10][16][17] Philosophers Steven D. Hale and Stephen Law state that the phrase "you cannot prove a negative" is itself a negative claim that would not be true if it could be proven true.[10][18] Many negative claims can be rewritten into logically equivalent positive claims (for example, "No Jewish person was at the party" is logically equivalent to "Everyone at the party was a gentile").[19] In formal logic and mathematics, the negation of a proposition can be proven using procedures such as modus tollens and reductio ad absurdum.[15][10] In empirical contexts (such as the evaluating the existence or nonexistence of unicorns), inductive reasoning is often used for establishing the plausibility of a claim based on observed evidence.[20][10][21] Though inductive reasoning may not provide absolute certainty about negative claims, this is only due to the nature of inductive reasoning; inductive reasoning provides proof from probability rather than certainty. Inductive reasoning also does not provide absolute certainty about positive claims.[19][10]

The Rockies are actually relatively recent, 55M to 80M years old. The Appalachians are much older and part of the reason they aren't anywhere near as big as (for example) the Rockies, is because they have been eroded for so much longer. That said, they are still definitely not the oldest mountain range. It looks like the Makhonjwa Mountains win that one.