The Finished mathematics reference article from the English Wikipedia on 24-Jul-2004
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Finished mathematics

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Finished mathematics is finished and published and accepted mathematical proof that has passed rigorous peer review (except that in mathematics, peer-review is called refereeing), and to which formal terms like "theorem" or "lemma" apply. It excludes "folk mathematics" in the sense of that term applied by mathematicians.

It implies that mathematicians believe that high standards of mathematical practice have been applied to these publications, partly but not primarily to find and correct errors.