Why Mathematicians Resist AI: Between Rigor, Risk, and Opportunity ?

Despite the rapid spread of artificial intelligence (AI) across science and technology, many mathematicians remain skeptical or indifferent toward its role in their discipline. Online mathematical communities such as \emph{MathOverflow} and \emph{StackExchange} explicitly discourage AI-generated content, arguing that such tools routinely provide convincing but incorrect answers, violating the strict standards of rigor on which mathematics depends. In this paper, we argue that this rejection is not merely cultural conservatism but reflects a deeper epistemological divide: the reliability of AI depends critically on the expertise of its user. For non-professionals---such as students or individuals with limited mathematical training---AI can be misleading, since they often lack the methodological skills to verify results, interpret errors, or connect outputs with established theory. By contrast, professional mathematicians may treat AI as an auxiliary tool, subjecting its suggestions to revision, numerical validation, and comparison with contemporary research. Furthermore, we show that the emerging practice of applying AI-detection software to research papers and theses is both unreliable and counterproductive. Such detectors often misclassify legitimate work, and their use risks discouraging scholars from responsibly adopting new technologies. Since most researchers possess sufficient background to employ AI as a tool for exploration and skill development, banning or penalizing its use does not strengthen mathematical practice but instead suppresses technological growth. We conclude that mathematicians' skepticism toward AI reflects both the discipline's culture of rigor and a misplaced institutional reliance on flawed detection methods.