At this point it should become apparent that I do not think that theorems are really proved. As G. H. Hardy said long ago, we emit some symbols, another person reads them, and they are either convinced or not by them. To simple people who believe whatever they read and do not question things for themselves, a proof is a proof is a proof, but to others a proof merely supplies a way of thinking about the theorem, and it is up to the individual to form an opinion. Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results obtained they themselves seem to deny any meaning. Is that to be the mathematics we are to use in understanding the world we live in?

-Richard Hamming, Mathematics on a Distant Planet