Does the 4 color theorem count? The problem with brute force proof is that proofs are supposed to bring understanding. They aren't supposed to just assert that

Does the 4 color theorem count? The problem with brute force proof is that proofs are supposed to bring understanding. They aren't supposed to just assert that something is true, but also explain why it is true, and by doing so, they open the door for further research. For this reason, a proof is often more valuable than the result itself. The proof of Fermat's Last Theorem is important because it exposes deep connections between previously disconnected disciplines, not because the identity itself is particularly useful. On the other hand, brute force proofs are inscrutable and offer none of that. While Goedelian Incompleteness garuantees that not everything can be understood this way, that is not an excuse to use brute force more than absolutely necessary.