  One example of how mathematics might be thought to be explanatory is found in the periodic cicada case (Yoshimura 1997 and Baker 2005). North American Magicicadas are found to have life cycles of 13 or 17 years. It is proposed by some biologists that there is an evolutionary advantage in having such prime-numbered life cycles. Prime-numbered life cycles mean that the Magicicadas avoid competition, potential predators, and hybridisation. The idea is quite simple: because prime numbers have no non-trivial factors, there are very few other life cycles that can be synchronised with a prime-numbered life cycle. The Magicicadas thus have an effective avoidance strategy that, under certain conditions, will be selected for. While the explanation being advanced involves biology (e.g. evolutionary theory, theories of competition and predation), a crucial part of the explanation comes from number theory, namely, the fundamental fact about prime numbers. Baker (2005) argues that this is a genuinely mathematical explanation of a biological fact. There are other examples of alleged mathematical explanations in the literature but this remains the most widely discussed and is something of a poster child for mathematical explanation.