Abstract: According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view. I argue that certain fallacious mathematical arguments considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that, in order to be successful in transmitting justification, an argument must satisfy specific standards, some of which are social. The picture I delineate is a hybrid form of phenomenal conservatism. Although in this talk I focus on mathematical inferential beliefs, the view on offer generalizes straightforwardly to other inferential beliefs.