I think this is not the right way to look at it. You can think of mathematical proofs as computer program that is compiled by the mathematician by hand. There i

I think this is not the right way to look at it. You can think of mathematical proofs as computer program that is compiled by the mathematician by hand. There is a lot of room for error, but with practice and peer review, it's relatively easy to avoid the common errors. This human compiler also brings the benefit of error correcting, which commonly correct two types of errors: sometimes the proof makes syntactical mistakes that the human compiler fixes automatically, sometimes the proof claims something that's not fully justified (similar to calling a function that is not implemented), but the human compiler just fill in the detail themselves. The social part of mathematics is really about how much error the reviewer is willing to accept, because the reviewer can also be wrong with how they correct the proof.