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<p>Évariste Galois is celebrated for his groundbreaking contributions to algebra and group theory, but his last published paper, containing two essays, has been largely ignored by historians. We will show that the first essay contains an incorrect proof of the statement that continuous functions are differentiable, due to several very naive mistakes. We will see that the second essay contains an elegant and novel derivation of the formula for the curvature of space curves. While the formula itself was already known to Euler and Cauchy, Galois’s method, which uses a family of planes, is strikingly original and conceptually insightful. This paper reevaluates both the historical and mathematical significance of Galois’s last publication, comparing it with his other minor manuscripts and challenging Neumann’s dismissal of its value in his edition of Galois’s works (Neumann <CitationRef CitationID="CR21">2011</CitationRef>). By highlighting Galois’s overlooked contribution to differential geometry, this paper provides a fuller picture of his mathematical genius, thereby helping to avoid the Whiggish tendencies found in many studies of his work.</p>

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Galois’s lost insight: the overlooked brilliance of his last publication

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  • 发表日期：

    2025年12月4日

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  • Lizhen Ji

摘要

Évariste Galois is celebrated for his groundbreaking contributions to algebra and group theory, but his last published paper, containing two essays, has been largely ignored by historians. We will show that the first essay contains an incorrect proof of the statement that continuous functions are differentiable, due to several very naive mistakes. We will see that the second essay contains an elegant and novel derivation of the formula for the curvature of space curves. While the formula itself was already known to Euler and Cauchy, Galois’s method, which uses a family of planes, is strikingly original and conceptually insightful. This paper reevaluates both the historical and mathematical significance of Galois’s last publication, comparing it with his other minor manuscripts and challenging Neumann’s dismissal of its value in his edition of Galois’s works (Neumann 2011). By highlighting Galois’s overlooked contribution to differential geometry, this paper provides a fuller picture of his mathematical genius, thereby helping to avoid the Whiggish tendencies found in many studies of his work.