When people are initially confronted with TSP and similar optimization problems, the reaction is usually awe at the shear number of potential combinations. "A 48 city tour of the continental US has 10^61 possibilities!!".

Well, not really. Massive chunks of the search space can be eliminated through clever (but non-optimal) algorithms. The rest of the search space can usually be explored through heuristics. In practice, we can solve gigantic TSP problems "well enough" and "fast enough".

It reminds me of the Midwit meme. Both the low IQ and high IQ folks say "Heuristics are good enough". Only the mid IQ guy cares about NP-hard.

That's not to take away from the research into theoretical limits of computation. Just noting that's a completely different question from the practical concerns of actually solving those problems IRL