There are certain formulas for which only inductive proofs are known. But since we need to know the formula first to prove it using mathematical induction, how do they get the formula in the first place? Here is an example: - Euler's formula in graph theory states that v-e+f=2 for all planar graphs. I think only an inductive proof is currently known. So how did he come up with this formula without proving it first?...guessing?