The publication of Gödel’s incompleteness theorems has frequently been portrayed as a devastating event, from which mathematics has not yet recovered. Yet those same theorems have also been hailed as proving that the powers of the human mind surpass those of any computer. Both those views, however, are caricatures. Gödel’s impact on modern logic has been profound, but the incompleteness theorems did not cause widespread upset at the time of their publication, and subsequent mathematical work outside logic has hardly been affected by them. Nor is mathematics any less "secure" than it was before Gödel’s work.