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Introduction
2023pp. 1–14
Abstract
Abstract This is a methodological or philosophical introduction. It analyzes the nature of impossibility theorems (as opposed to other types of mathematical theorems), the difference between meta statements and proper mathematical theorems, the difference between impossibility statements in mathematics and elsewhere and impossibilities as a creative force. Moreover, it introduces a classification of impossibility statements and analyzes why impossibility results have often attracted a great number of amateurs, and why these amateurs have often misunderstood the nature of the impossibility claim.