 Among the most recent contributions arising from Baker’s 2005 article we have Daly and Langford 2009, Baker 2009a, 2015, 2016a, 2017a, 2017b, Baker and Colyvan 2011, Saatsi 2010, Rizza 2011, Pincock 2012, Bangu 2013, Baron 2014, Marcus 2013, Tallant 2013, and Wakil and Justus 2017. We can only provide here a very short summary of the main positions. Daly and Langford side with Melia to claim that the role of positing concrete unobservables in science allows the explanation of the behavior of observable facts. By contrast, mathematics has no such explanatory value: it merely ‘indexes’ physical facts. Against Baker they argue that the appearance of primes in the cicadas example is only due to the decision to measure those periods in years but that a different choice of measure (say, seasons or months) would give rise to non-prime numbers, thereby showing that Melia’s indexing strategy can also apply to the cicadas example. Baker and Colyvan 2011 reassert the claim on the existence of mathematical explanations of scientific phenomena and argue that Daly and Langford’s strategy is only plausible in extremely simple cases and that the ‘index strategy’ does not square with the complexities of mathematical and scientific practice. In particular, they also make appeal to the existence of mathematical explanations of mathematical facts, for which see below. Baker 2009a defends the ‘enhanced indispensability arguments’ against criticisms by Daly and Langford, Bangu, Leng, and Saatsi. Saatsi 2010 emphasizes the representational role of mathematics and criticizes the alleged explanatory role of mathematics in the explanation of empirical phenomena such as the honeycomb case (see below) and the cicadas case. Rizza 2011 is also deflationary about the alleged ontological consequence of the role of mathematics in the cicadas case; however he does not deny the centrality of mathematical concepts in constructing explanations. Finally, Pincock 2012, chapter 10, also rejects the cogency of various formulations of the enhanced indispensability argument. The objection is that inference to the best explanation for novel abstract entities requires that those new entities are needed to explain the phenomenon in question. But in the cases discussed in this debate, there is no explanatory value to adding the natural numbers or the real numbers to our theories, over and above nominalistically acceptable surrogates (see Pincock 2012, 212).