Beschreibung:

RIEMANN, Georg Friedrich Bernhard (1826-1866) Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. [Bound With:] – Ueber die Fläche vom kleinsten Inhalt bei gegebener Begrenzung. [And:] – Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe. Göttingen: Dieterich, 1867. First edition, very rare offprint versions, of three foundational mathematical papers. The auction databases ABPC and RBH list only one copy of Ueber die Hypothesen (Reiss, October 23, 2007, lot 774, €23,200), no copy of Über die Darstellbarkeit, and one of Ueber die Fläche vom kleinsten Inhalt. Riemann’s celebrated Ueber die Hypothesen ‘did more to change our ideas about geometry and physical space than any work on the subject since Euclid’s Elements’ (Landmark Writings in Western Mathematics, p. 507). ‘Its reading on 10 June 1854 was one of the highlights in the history of mathematics’ (Freudenthal in DSB). ‘The importance of this treatise is not confined to pure mathematics. Without it, Einstein would not have been able to develop his general theory of relativity’ (PMM 293b). His famous Über die Darstellbarkeit, prepared for a doctoral defence in 1854 but published only after his death, ‘opened a new era in the handling of Fourier series’, leading to ‘new insights into functions and infinite series, and led to the creation of set theory’ (ibid., p. 491). The research first published in Ueber die Fläche was carried out in 1860-61; this delay in publication cost Riemann the credit for several fundamental discoveries contained in the present work. Most importantly, Riemann was the first to understand the intimate relationship between minimal surfaces and complex analytic functions, later credited to Karl Weierstrass (1815-97). Riemann did not have these papers published himself, but when his colleague Richard Dedekind did have them printed in 1867, shortly after Riemann’s early death, they excited great interest among mathematicians, opened new areas of research, and have had a profound influence on the development mathematics and theoretical physics from the 19th century through to the present day. Three works in one volume, quarto (259 x 207 mm). pp. [ii], 20 [Ueber die Hypothesen]; [ii], 50 [Ueber die Fläche]; [ii], 46 [Über die Darstellbarkeit] (some light dust soiling to the first and final pages of each work). Contemporary half roan over marbled boards (rubbed). Provenance: ‘Kabinet I. stolice mathematicky’ (stamps of the Czech Technical University in Prague on each title-page).