Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a proof to develop new representations for mathematical concepts. The second is identifying reasoning techniques that might be useful in mathematicians' own area of research. The mathematicians further contended that they have these goals when presenting proofs in the undergraduate mathematics courses that they teach.