 A response to the easy-road view has been given by Colyvan (2002, 2010) and Baker (2005, 2009). They argue that mathematics doesn’t just play a descriptive role in science. It also plays an explanatory role. For instance, Baker considers a case involving various species of periodic cicadas in which the nymphal stage is either 13 or 17 years. Why are the nymphal stages 13 or 17 years? According to evolutionary biologists, the answer is that 13 and 17 are prime numbers, and this minimizes intersections with other periodic species. Colyvan and Baker argue that cases like this—cases in which mathematical objects play an indispensable role in the explanations of physical phenomena—provide us with a better and more powerful version of the indispensability argument. Indeed, they argue that if there really are cases involving genuinely mathematical explanations of physical phenomena, then easy-road versions of fictionalism cannot succeed. But this claim is open to debate, and responses to these explanatory versions of the indispensability argument have been given by Melia (2002), Leng (2005b), Bangu (2008), Daly and Langford (2009), and Yablo (2012).