[tuhgdetzhh]

Lets assume the kenerl is correct and a mathematian trusts it, now what happens if it is the proof itself that he cannot understand anymore because it has gotten too sophisticated? I think that this would indeed be a difference, and a crossing point in history of mathematical proofs.

[zozbot234]

In principle, it's no different than failing to understand the details of any calculation. If the calculating process is executed correctly, you can still trust the outcome.