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<p>Andrew Wiles’s resolution of Fermat’s Last Theorem offers a singular vantage point for reevaluating the mechanisms of high-level mathematical discovery. This article analyzes Wiles’s 8-year trajectory, characterized by non-linear processual transitions involving different modes of cognition, abrupt conceptual reframing, and intense affective demands sustained under extreme disciplinary pressure. By employing an analytical lens focused on the interface between cognitive flexibility and metacognitive self-regulation, the study dissects the underlying dynamics of the creative proving process. Findings suggest that field-changing creativity is not a matter of sporadic inspiration, but a highly regulated phenomenon grounded in epistemic mastery and requiring sustained control, a process exceeding the descriptive capacity of conventional creativity models. The article concludes with concrete pedagogical implications that prioritize the training of executive mechanisms, moving beyond idealized narratives to embrace the multifaceted complexity of mathematical invention.</p>

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Creativity in expert mathematics: insights from an analysis of Wiles’s proof of Fermat’s last theorem 

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Santiago Rementeria

摘要

Andrew Wiles’s resolution of Fermat’s Last Theorem offers a singular vantage point for reevaluating the mechanisms of high-level mathematical discovery. This article analyzes Wiles’s 8-year trajectory, characterized by non-linear processual transitions involving different modes of cognition, abrupt conceptual reframing, and intense affective demands sustained under extreme disciplinary pressure. By employing an analytical lens focused on the interface between cognitive flexibility and metacognitive self-regulation, the study dissects the underlying dynamics of the creative proving process. Findings suggest that field-changing creativity is not a matter of sporadic inspiration, but a highly regulated phenomenon grounded in epistemic mastery and requiring sustained control, a process exceeding the descriptive capacity of conventional creativity models. The article concludes with concrete pedagogical implications that prioritize the training of executive mechanisms, moving beyond idealized narratives to embrace the multifaceted complexity of mathematical invention.