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then you should re-read the definition of a proof.

It's clear that you haven't read it at all:


The fact of the matter is that the sort of Platonic definition of proof that you fantasize is impossible because it depends on certainty, which itself cannot be proven. The best we can do is fail to find an error in an alleged proof.

Consider the proofreader's paradox: A proofreader can be prepared to swear, for any given page of a 1000 page book, that there are no typos on that page, but no proofreader is so foolish as to claim that there are no typos in the book.

What more are you hoping for?

Given a mathematical proof, the chance of an error in the proof is vastly larger than 10^-20.

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