The Mittag-Leffler theorem: The origin, evolution, and reception of a mathematical result, 1876-1884

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(Thesis) M.Sc.
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The Swedish mathematician Gösta Mittag-Leffler (1846-1927) is well-known for founding Acta Mathematica, the first international mathematical journal. A "post-doctoral" student in Paris and Berlin (1873-76), Mittag-Leffler built on Karl Weierstrass' work by proving the Mittag-Leffler theorem, roughly: a meromorphic function is specified by its poles, their multiplicities, and the coefficients in the principal part of its Laurent expansion. In this thesis, I explore the evolution of the Mittag-Leffler theorem, from its initial (1876) state to its final (1884) version. Aspects of the details of Mittag-Leffler's work at various stages are analyzed to demonstrate the evolution of Mittag-Leffler's technique. A key finding of the thesis is that Mittag-Leffler's research on infinite sets of singular points attracted him to Georg Cantor's set-theoretic work. The incorporation of Cantor's theory was controversial, but demonstrates Mittag-Leffler's important role in the promotion of abstract mathematics over the more concrete mathematics of the previous era.
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