Dimostrazioni Esplicative in Matematica

In recent times philosophers of mathematics have generated great interest in explanations in mathematics. They have focused their attention on mathematical practice and searched for special cases that seem to own some kind on explanatory power. The present thesis aims to discuss this issue. We firstly present a case study in the history of mathematics. Here we show the Cauchy problem and some solutions that were proposed in the 19th century. Then we focus on Peano's proof and we deal with his idea of explanatoriness. These historical remarks legitimate our philosophical investigations and the rest of the thesis is devoted to it. Two main views are presented, namely noneism and someism: the first is the view that no proof is explanatory, whereas the second is the view that some proofs are explanatory while others are not. Then we deal with this second view focusing on two proposals, Steiner's account and Frans and Weber's account. Hence, we argue that someism is a troublesome view whereas another view that we call allism seems to work better, i.e. the view that all proofs are explanatory, at least in some sense.