From Longman Dictionary of Contemporary Englishthe/your mind boggles, the/your mind bogglesthe/your mind boggles, (also something makes the/your mind boggle, something boggles the/your mind) informalBELIEVE if your mind boggles when you think of something, it is difficult for you to imagine or accept it The sheer amount of data makes the mind boggle.the/your mind boggles, at My mind boggles at the amount of work still to do. → boggle
Examples from the Corpus
boggle at• The mind boggles at the complexity of a system using twelve slide projectors producing 4,000 pictures during the 2¼ hour performance. 