Despite mathematicians’ genuine quest for rigor and truth, various fictions infect math textbooks and classrooms. Old and charming stories about Pythagoras, Gauss, Galois, and the Golden Ratio are part of the folklore of mathematics but aren’t quite true. Invention infects the history, so what happens if we subtract it? Do we have to? I’ll argue that invention is not all bad; there’s a great place for invention in the history of math.