# Explanatory value of proofs and the power of conviction

Explanatory value of proofs and the power of conviction. It is clear that explanation plays an important role for mathematicians. A mathematical proof that has explanatory power is usually preferred over a proof that lacks it. Any theory of mathematical practice should deal with this problem. So far a few approaches have been outlined but a lot of work remains to be done (see, e.g., Mancosu (2008)). The guiding hypothesis here is that, in contrast with the existing models that refer to purely internal characteristics, a broader idea of what explanation is, plays a central role. The task of this subproject is to go through existing theories of explanation and see whether these are applicable to mathematics. If none of these proves to be satisfactory, a bottom-up strategy will be followed: case studies will have to be gathered to arrive at insights and (a) proposal(s) for mathematical explanation.