For an exhaustive search, if you can explain to me:
- how to exhaustively list the cases that need to be checked, and why that method is exhaustive
- how to check each case, and why that works
and then conclude with "we've had a computer do this exhaustive search, and the result came up as X", for me that satisfies completely understanding the proof.
I could prove anything by claiming I completed a trivial-to-explain exhaustive search. The only support or refutation would be someone doing their own search. It's a very weak foundation.
We already had the ABC conjecture crisis: A theorem with a human-written proof so complex that no one besides the author can understand it. Some people claim to have refuted it. Most mathematicians are unqualified to decide.
