Let's say hypothetically, someone's discovered a heuristic to solve Sudoku puzzles of n x n sizes, as the size gets larger and larger the brute force search for a counterexample is not practical.

Unfortunately, it seems there is no easy way to generate a puzzle where the heuristic fails.

What if this heuristic was actually an unproven correct algorithm that solves every instance of n x n puzzles in polynomial time?

Even if the general consensus is that we don't think it works, we have searched for a very long time for a counterexample but haven't found one. Perhaps no counterexample exists.

Is it possible, that general consensus has prevented research into further exploration into heuristics?

Are there any known heuristics that haven't been formally proven?

What does that say about the limitations of modern mathematics, if a heuristic hasn't been disproven?