Non-deductive Justification in Mathematics

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? The answer is an emphatic yes, as I explain in this chapter. I argue that non-deductive justification is in fact pervasive in mathematics, and that it is in good epistemic standing.