Article ID: CBB001252138

The Mittag-Leffler Theorem: The Origin, Evolution, and Reception of a Mathematical Result, 1876--1884 (2013)

unapi

The Swedish mathematician Gösta Mittag-Leffler (1846--1927) is well-known for founding Acta Mathematica, often touted as the first international journal of mathematics. A post-doctoral student in Paris and Berlin between 1873 and 1876, Mittag-Leffler built on Karl Weierstrass' work by proving the Mittag-Leffler Theorem, which states that a function of rational character (i.e. a meromorphic function) is specified by its poles, their multiplicities, and the coefficients in the principal part of its Laurent expansion. In this paper I explore the evolution of the Mittag-Leffler Theorem, from its initial state in 1876 to its final version, published in 1884. Mittag-Leffler's work contributed significantly to Weierstrass' program on the foundations of analysis. His interest in generalizing his results to functions having arbitrarily many essential singularities, however, which led to his research on infinite sets of singular points, attracted him to Georg Cantor's set-theoretic work. As we shall see, his use of Cantor's theorems and definitions was closely linked to his research efforts in the context of Weierstrass' program.

...More

Description On the Swedish mathematician Gösta Mittag-Leffler (1846--1927).


Citation URI
https://data.isiscb.org/isis/citation/CBB001252138/

Similar Citations

Article Heinonen, Riittamaija; (2006)
Ren och smutsig matematik. Gösta Mittag-Leffler och Stockholms högskola (/isis/citation/CBB001220359/)

Book Belna, Jean-Pierre; (2000)
Cantor (/isis/citation/CBB000771270/)

Article Moore, Gregory H.; (2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology (/isis/citation/CBB000950203/)

Book Cantor, Georg; Ferreirós, José; (2006)
Fundamentos para una teoría general de conjuntos: Escritos y correspondencia selecta (/isis/citation/CBB000930382/)

Article Ferreirós, José; (2004)
The Motives behind Cantor's Set Theory -- Physical, Biological, and Philosophical Questions (/isis/citation/CBB000500123/)

Article Moore, Matthew E.; (2002)
A Cantorian Argument Against Infinitesimals (/isis/citation/CBB000300363/)

Article Ausejo Martínez, Elena; Ausejo Lifante, Elena; (2017)
Correspondencia de Zoel García de Galdeano con matemáticos alemanes: Georg Cantor (/isis/citation/CBB631684117/)

Article Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David; (2013)
Ten Misconceptions from the History of Analysis and Their Debunking (/isis/citation/CBB001252715/)

Article Cobos Bueno, José M.; (2004)
Maimónides y la paradoja de Burali-Forti (/isis/citation/CBB000650510/)

Article Deisera, Oliver; (2010)
On the Development of the Notion of a Cardinal Number (/isis/citation/CBB001210973/)

Authors & Contributors
Grattan-Guinness, Ivor
Ferreirós, José
Ausejo Lifante, Elena
Wardhaugh, Benjamin
Turner, Laura E.
Tapp, Christian
Concepts
Mathematics
Set theory
Infinitesimals
Mathematical analysis
Infinity
Collected correspondence
Time Periods
19th century
20th century, early
Medieval
20th century
18th century
17th century
Places
Sweden
Germany
Stockholm (Sweden)
Europe
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment