Errors in math research papers

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  • In the history of mathematics, has there ever been a mistake?

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One egregious case recently analyzed in detail by Adrian Mathias is Bourbaki’s text Theory of sets and a couple of sequels published by Godement and others. Mathias’ paper is:

Mathias, A. R. D. Hilbert, Bourbaki and the scorning of logic. Infinity and truth, 47–156, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 25, World Sci. Publ., Hackensack, NJ, 2014.

Mathias analyzes several ubiquitous errors in the book, such as choosing an inappropriate foundation in Hilbert’s pre-Goedel epsilon (or tau) operator, confusion of language and metalanguage, missing hypotheses that make certain statements incorrect, and even more serious “editorial comments” suggesting to the reader that certain issues in logic are too complicated to be clarified completely.

The result was not merely perpetuation of errors in other papers, but the stagnation of logic in France for several generations that only recently has begun to be corrected.