I don't think you are addressing the concern that the GP brought up. Mathematics: The Loss of Certainty is not an essay about nihilism.

Briefly,

[Mathematics] will be seen as the creation of finite human beings, liable to error in the same way as all other activities in which we indulge. Just as in engineering, mathematicians will have to declare their degree of confidence that certain results are reliable, rather than being able to declare flatly that the proofs are correct.