  We investigate the reasons of having confidence in mathematical theorems. The
formalist point of view maintains that formal derivations underlying proofs,
although usually not carried out in practice, contribute to this confidence.
Opposing this opinion, the main claim of the present paper is that such a gain
of confidence obtained from any link between proofs and formal derivations is,
even in principle, impossible in the present state of knowledge. Our argument
is based on considerations concerning length of formal derivations. We also
discuss psychological and social factors that contribute to building belief in
theorems.
