Proofs – are they objective?

The concept of proof may be given a first approximate explanation by saying that a proof is a chain of valid inferences from known truths such that at each inference step the conclusion is seen to follow from the premisses. A natural reaction to this explanation is to say that whether something “is seen to follow” may depend on a subject, and to ask whether this does not make proofs subjective in character. We cannot simply skip the phrase “is seen to” in this explanation, if the validity of ...