Réflexions sur la résolution algébrique des équations

work by Lagrange

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July 13, 2026

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In his 1770 work, "Réflexions sur la résolution algébrique des équations," Joseph-Louis Lagrange investigated why algebraic solutions for polynomial equations beyond the fourth degree had not been found. He analyzed known solutions for cubic and quartic equations, focusing on how certain algebraic expressions remained invariant when the equation's coefficients were permuted. Lagrange believed this analysis of invariance was key to solving higher-degree equations. While his work did not provide a general solution, it laid the groundwork for future algebraic developments and inspired Évariste Galois's group theory.123

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Joseph-Louis Lagrange, comte de l’Empire
In his long paper “Réflexions sur la résolution algébrique des équations” (1770; “Reflections on the Algebraic Resolution of Equations”), he inaugurated a new period in algebra and inspired Évariste Galois to his group theory.
Read More
In his long paper “Réflexions sur la résolution algébrique des équations” (1770; “Reflections on the Algebraic Resolution of Equations”), he inaugurated a new period in algebra and inspired Évariste Galois to his group theory.
Read More