Perhaps more than any other profession, science places a premium on being correct. Of course, most scientists—like most living humans—make plenty of mistakes along the way. Yet not all errors are created equal. Historians have unearthed a number of instances in which an incorrect idea proved far more potent than thousands of others that were trivially mistaken or narrowly correct. These are the productive mistakes: errors that touch on deep, fundamental features of the world around us and prompt further research that leads to major breakthroughs. Mistakes they certainly are. But science would be far worse off without them.