 The upshot of the above discussion, albeit based on a single case study, is that mathematicians ought not to—and in general do not—give weight to enumerative induction per se in the justification of mathematical claims. (To what extent enumerative induction plays a role in the discovery of new hypotheses, or in the choice of what open problems mathematicians decide to work on, is a separate issue which has not been addressed here.) More precisely, the thesis is in two parts: