This essay seeks to clarify the role played by poetic license in the triangular relationship involving mathematics, the history of mathematics, and mathematics in fiction. This relationship can be analyzed, in the first place, from the perspective offered by the wellknown Aristotelian distinction between "history" and "poetry." It can also be analyzed from the point of view of the kind of language typically used in texts produced in each of these realms, or, alternatively, from the point of view of the nature of their expected audiences. It will be seen, however, that the most illuminating perspective for this analysis is the one related to the kind of attitude that is expected from the reader in each case, whether critical or based on a suspension of disbelief. To the considerations that pertain to this latter perspective when it comes to texts of any kind, the peculiarities of mathematical texts add some unique twists.