Theorems of Mathematical Proof

A mathematical proof is about abstract entities, but we use physical objects in order to represent those abstract entities. Proving a proposition means performing a computation which, if one has done it correctly, establishes that the proposition is true. Neither theorems of mathematics, nor the process of mathematical proof, nor the experience of mathematical intuition, confers any certainty. Our mathematical knowledge may, just like our scientific knowledge, be deep and broad. It may be uncontroversially accepted, but it cannot be certain. No one can guarantee that a proof that was previously thought to be valid will not one day turn out to contain a profound misconception.