Not knowing what you are sure of: e.g. “π + e is irrational.”

It is as unexceptionable as philosophical principles ever are that we can claim to have knowledge if, in addition to belief, we have the proper sort of justification. It seems we can have excellent justification for believing that that π + e  is irrational, leading to high confidence that it is. Yet no mathematician would say that we know the sum is irrational. Why is that?