No Proof

Proof: I know the answer. I’m sitting here with the answer in my head – There is a maximum number of 2n-14 triangles in an admissible triangulation of a polygon with n sides. And I know why, too. It’s because such a polygon can contain no more than n-6 interior vertices, and I found a correlation between the number of interior vertices and the number of triangles. But my answer is useless. It’s useless because I can’t prove a whit of it. But I have faith in my answer. I worked to find it, went on a pilgrimage to this test, swallowed my libation of burnt coffee, tortured myself with equations too hard to solve, like an ascetic of mathematics. And this is the answer brought to me, an answer I know in my mathematical heart is right, but I have no evidence or proof. No proof? Without a proof, I might as well not have an answer at all. A proof by induction, using a smaller case to induce a larger, general case. A proof my contradiction, assuming the exact opposite to prove what can not possibly be. A proof by brute force, knocking down all obstructions, meeting and vanquishing each special case with methodical accuracy. But I have none of these. No proof. I sit here with an answer on my paper, in my head, in my heart, clutching firmly to this belief I can explain, but can’t begin to understand why it can’t be. And I understand now why science and religion will never get along. Until God can give a proof for himself, presented with graphs, typeset and ended with a careful square, our mathematical minds will remain in disbelief. Without a proof we might as well not have an answer at all, might as well not have a God at all. ■