 The role of non-deductive methods in empirical science is readily apparent and relatively uncontroversial (pace Karl Popper). Indeed the canonical pattern of justification in science is a posteriori and inductive. What makes empirical science empirical is the crucial role played by observation, and—in particular—by experiment. A natural starting point, therefore, in a survey of non-deductive methods in mathematics, is to look at the rise of a genre known as “experimental mathematics.” The past 15 years or so have seen the appearance of journals (e.g., The Journal of Experimental Mathematics), institutes (e.g., the Institute for Experimental Mathematics at the University of Essen), colloquia (e.g., the Experimental Mathematics Colloquium at Rutgers University), and books (e.g., Borwein and Bailey 2003 and 2004) devoted to this theme. These latter authors also argue, in Borwein and Bailey (2015), for the significance of experimental mathematics within mathematical practice more generally, while Sorensen (2016) provides a broader historical and sociological analysis of experimental mathematics. 