In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?
Those mathematicians know to be cautious when working with their models. Because they know that no matter how useful and interesting their model, no matter how compelling the evidence they collect, there might be something out there about elliptic curves that they didn’t quite imagine. And if you can’t imagine it, your model can’t capture it, and that means the evidence won’t reflect it.