 With this interpretation, however, we run into a serious problem in the special case where \(Q\) is the negation, \(\neg P\), of \(P\). To assert \(\neg P\) is to show that \(P\) implies a contradiction (such as \(0 = 1)\). But it will often be that mathematicians have neither a proof of \(P\) nor one of \(\neg P\). To see this, we need only reflect on the following Goldbach conjecture (GC):