Earlier quoted context omitted.
> As soon as you need reliable outcomes, such as certainty whether an erroneous state can arise in a program, whether a proof for a mathematical conjecture exists, or whether a counterexample exists, exhaustive search is often necessary. Proof checking requires 100% reliability. But if you are searching the space of all possible proofs for a valid one, that process does not require 100% reliability. On the contrary,…
Finding a proof of a mathematical conjecture is much harder than NP-hard, it's undecidable (the Entscheidungsproblem) because the search space is infinite (and worse, doesn't necessarily include a proof even if the statement is true - Gödel's first incompleteness thm). So even if we restrict to conjectures that are actually machine-provable, it's still much harder than NP decision problems which are combinatorial so…
* - In Peano arithmetic, let's say