This is true for almost all mathematicians: they are able to identify the correct proof and the invalidity of the incorrect proof, although they cannot define the precise meaning of a proof. From this, it can be inferred which of the following must be true? ['People who can identify correct and incorrect certifications may not be able to define the precise meaning of a certification.', 'Some mathematicians cannot identify the invalidity of incorrect proofs.', 'No mathematician can define the exact meaning of a proof.', 'Some mathematicians do not recognize the correct proof, but can recognize the incorrect proof.']