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Zbl 0795.01012
Dixmier, Jacques
The history of Hilbert's 13th problem. (Histoire du $13\sp e$ problème de Hilbert.) (French)
[A] Chabert, Jean-Luc (ed.) et al., Analyse diophantienne et géométrie algébrique. Exposés du Séminaire d'Histoire des Mathématiques de l'Institut Henri Poincaré. Paris: Université Pierre et Marie Curie, Lab. de Mathématiques Fondamentales, Cah. Sémin. Hist. Math., 2. Sér. 3, 85-94 (1993).

The author presents the algebraic aspects of the 13th problem of Hilbert. He discusses results of E. S. Bring (1786), G. B. Jerrard (1834), W. R. Hamilton (1837), J. J. Sylvester (1887) and F. Klein (1877 and 1905) about the possibility of resolution of polynomial equations by superposition of algebraic functions. There are presented the contributions to the algebraic approach of Hilbert's 13th problem by Hilbert himself and N. Tschebotaröw, R. Brauer, B. Segre and A. Wiman. We mention the comments about the conjecture that the theorem Arnold- Kolmogorov is true in the algebraic case, i.e. ``$s(n)=1$'' for all $n$. The paper also includes an appendix with complete proofs of the results of Wiman published in Nova acta regiae societatis scientiarum Uppsaliensis 16, 3-8 (1927).
[D.Ştefănescu (Bucureşti)]

MSC 2000:: *01A60 Mathematics in the 20th century
12-03 Historical (field theory)
26-03 Historical (real functions)

Keywords: E. S. Bring; G. B. Jerrard; W. R. Hamilton; J. J. Sylvester; F. Klein

Cited in: Zbl 1016.01012

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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Zentralblatt MATH Berlin [Germany]