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Abel and the Theory of Algebraic Equations

(Reflections Stimulated by the Letter Abel Sent to Crelle on September 25, 1828)

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The Abel Prize 2008-2012

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Abstract

A letter from Abel to Crelle dated 25 September 1828—uncovered by Mittag-Leffler more than seventy years later—is a poignant document which throws considerable light upon the last three months that Abel had left for doing mathematics before tuberculosis incapacitated him, sapping all his strength, and eventually killing him. The letter raises the intriguing question of how the theory of equations (later known as Galois Theory) would have evolved if Abel had been able to write up his discoveries in this area. With the Abel letter as resonant backdrop we reflect upon this, basing our reflections on Abel’s published as well as posthumous manuscripts. Of vital importance is his discoveries in the theory of elliptic functions. The latter provided him with an abudance of algebraic equations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, NTNU, 7491, Trondheim, Norway

    Christian Skau

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  1. Christian Skau
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Correspondence to Christian Skau .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Helge Holden

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Ragni Piene

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Skau, C. (2014). Abel and the Theory of Algebraic Equations. In: Holden, H., Piene, R. (eds) The Abel Prize 2008-2012. The Abel Prize. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39449-2_28

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