In this paper I shall adopt a possible reading of the notions of ‘explanatory indispensability’ and ‘genuine mathematical explanation in science’ on which the Enhanced Indispensability Argument (EIA) proposed by Alan Baker is based. Furthermore, I shall propose two examples of mathematical explanation in science and I shall show that, whether the EIA-partisans accept the reading I suggest, they are easily caught in a dilemma. To escape this dilemma they need to adopt some account of explanation and offer a plausible answer to the following ‘question of evidence’: What is a genuine mathematical explanation in empirical science and on what basis do we consider it as such? Finally, I shall suggest how a possible answer to the question of evidence might be given through a specific account of mathematical explanation in science. Nevertheless, the price of adopting this standpoint is that the genuineness of mathematical explanations of scientific facts turns out to be dependent on pragmatic constraints and therefore cannot be plugged in EIA and used to establish existential claims about mathematical objects.