We can use the term 'Ulam's Dilemma' for the situation which he has described vivdly in his autobiography, Adventures of a Mathematician
At a talk I gave at a celebration of the twentyfifth anniversary of the construction of von Neumanns computer at Princeton a few years ago, I suddenly started estimating silently in my mind, how many theorems are published in mathematical journals each year...
He thus set the following question to his students