What is a proof?

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A definition of proof is:
"The evidence or argument that compels the mind to accept an assertion as true."

This might seem simple and clear, but it gives rise to some natural questions, such as the following.

What is meant by "the mind" here? If it is only my mind, then proof would be well defined, but then it would only be a proof to me.

But what about a general proof? Would it have to compel all minds? Even the minds of fools? Or does it only have to compel the "sane" minds? But then, what is "sane"?

It is a well known fact that the idea or definition of sane has been changing throughout history.

So, what is a proof?