In this talk, I present an overview of the recent literature on the dilemma of inference, a conflict between the following two theses: i) Non-informativeness: due to their deductive character, proofs cannot extend the mathematical information possessed beforehand. The semantic information carried by the conclusion of a proof is included in the information carried by its premises. ii) Epistemic usefulness: demonstrations improve our mathematical knowledge.This talk is divided in two parts. In the first part, we will examine Novaes' standpoint on this issue (Novaes, 2020). In her opinion, the dilemma of inference is a false dilemma, i.e., deductive reasoning is epistemic useful despite its non-informativeness. We will see that Novaes' solution is too restricted since it associates only a negative utility to logical knowledge. In the second part, we will survey a tradition of analysis of the informativeness of proofs in terms of a dichotomy between surface and depth information. In particular, we will consider D'Agostino and Floridi's treatment of the topic that ascribes a positive informational value specifically to hypothetical proofs (D'Agostino and Floridi, 2009). Then, I argue that, albeit D'Agostino and Floridi successfully delimit a large set of informative proofs, driven by a veridicalist conception of semantic information, they offer an implausible, hyper-realist explanation of the information displayed by such proofs. Finally, I claim that we might achieve a more parsimonious (anti-realist) account by paying attention to the pragmatic and dialogical dimensions of our use of dischargeable hypotheses.