 One of the aspects of the enhanced indispensability argument that has generated much attention is that the argument seems to presuppose a form of inference to the best explanation. An inference to the best explanation licenses, when one is presented with several alternative explanations of the same phenomenon, the acceptance as true of the best among such explanations. In addition to raising the crucial issue of determining whether a certain argument is a mathematical explanation of a scientific fact, we are also confronted with the further issue of how to rank alternative explanations and of whether the appeal to inference to the best explanation in arguing for scientific realism carries over to an argument for mathematical realism. Such inferences have been at the center of much discussion in philosophy of science (see Lipton 2004). In the context of enhanced indispensability arguments, they were also discussed, in addition to several of the articles cited so far, in several articles contained in the special issue of Synthese (2016, n. 193) edited by Molinini, Pataut, and Sereni (see Molinini 2016, Sereni 2016, Busch and Morrison 2016, Hunt 2016, and Molinini, Pataut, and Sereni 2016 for a lucid introduction). Molinini 2016 uses alternative mathematical explanations of scientific facts in kinematics (using a case study from Euler studied in Molinini 2012) and special relativity (using a case study on the FitzGerald-Lorentz contraction studied in detail in Friend and Molinini 2015) to put pressure on the inference to the best explanation underlying the enhanced indispensability argument. The existence of alternative mathematical explanations of the same phenomenon, appealing to two different mathematical entities, speaks against the indispensability of any of those entities for providing an explanation of the phenomenon in question. He concludes: “the notion of explanatory power of mathematics in science has no ontological import and cannot be used in EIA [enhanced indispensability argument]” (pp. 420-421). Sereni 2016, a reply to Molinini 2016, offers some important reflections on the issue of the equivalent explanations problem. The issue of compatible mathematical explanations (positing the same physical ontology but appealing to different mathematical entities) is also central to Hunt 2016 where Hunt argues that ‘in cases of compatible mathematical explanations, IBE cannot establish ontological commitment to mathematical entities’ (p. 452). Hunt’s article is a reply to Busch and Morrison 2016 (see also Busch 2011), which focuses on the parity of reasoning, or lack thereof, between scientific and mathematical realists. Indeed, they claim that inference to the best explanation is used differently in arguments for scientific realism from the way it is used in arguments for mathematical realism (see also Colyvan 2001, 2006) and that this undermines the use of the enhanced indispensability argument as establishing Platonism. 