HILBERT, Uber das Dirichlet'sche Princip. [Bound, as issued, after] DEDEKIND, Ueber die Permutationen des Korpers aller algebraischen Zahlen. Offprint from: Festschrift zir Feier des 150 jahrigen Bestehens der Koniglichen Gesellschaft der Wissenschaften zu Gottingen 1901

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First edition, rare double-offprint, of these important papers by two of the leading mathematicians of the period. The Dirichlet principle, so-called by Riemann who learned it in lectures by Dirichlet, was due to Gauss - he showed that solving a boundary value problem for Laplace's equation (which arises in many areas of mathematical physics) reduces to the problem of finding a function that minimizes a certain double integral. Riemann used the principle extensively in his work on complex function theory, but this work was cast into doubt when Weierstrass showed by an example that functions making the integral a minimum may not exist. At the end of the 19th century Hilbert took up the problem of 'resuscitating' Dirichlet's principle. This he achieved in the present paper, which was reprinted in Mathematische Annalen in 1904. Hilbert's methods later proved spectacularly successful, mushrooming into a major new field of analysis which, together with the theory of integral equations, would become the dominant research areas for the many talented students who came to Gottingen to do their doctoral studies under Hilbert during his period of greatest fame, the crucial years from 1901 until the outbreak of the first world war. Hilbert presented his paper on the occasion of the 150th anniversary of the Gottingen Scientific Society. At the same meeting, Dedekind presented the accompanying paper in which he showed that classical Galois theory, developed by Galois and others for finite extension of the field of rational numbers, fails for infinite extensions. Dedekind's original work concerning infinite Galois Theory is in effect the genesis of a field whose beginning is generally credited to Wolfgang Krull, some quarter century later. 4to, pp. 17, [1]; 27, [1]. Original printed wrappers (with the titles of both papers on the front wrapper), perforated stamp on title page of Dedekind, repeated on contents page of Hilbert, otherwise near fine. N° de ref. del artículo ABE-1568583496770

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