HILBERT, David (1862-1943). 'Grundlagen der Geometrie.' Offprint from: Festschrift zur Feier der Enthullung des Gauss-Weber-Denkmals in Göttingen. Leipzig: B.G. Teubner, 1899. [Sold with:] – Problems mathématiques. Paris: Imp. Gautier-Villars [?1902].

HILBERT, David (1862-1943). 'Grundlagen der Geometrie.' Offprint from: Festschrift zur Feier der Enthullung des Gauss-Weber-Denkmals in Göttingen. Leipzig: B.G. Teubner, 1899. [Sold with:] – Problems mathématiques. Paris: Imp. Gautier-Villars [?1902].

Two of the most influential mathematical publications ever published. The 'Grundlagen' proposes a formal set, called Hilbert's axioms, substituting for the traditional axioms of Euclid. It represents the realisation that, due to the advances in science as a whole in the 19th century, geometrical systems different from Euclid's could exist, and that in the modern separation of mathematics from science, it had become necessary to question whether Euclidean geometry was a complete and consistent whole. Hilbert's great advance, set out in this work, was that he succeeded in finding a system of axioms which he could prove would lead to all theorems of Euclidean geometry, without any appeal to the nature of the physical world. Accompanying this is the authorised French translation by Laugel of Hilbert’s famous declaration of his 23 problems in mathematics in his address to the International Congress of Mathematicians at Paris in 1900. The paper and its various printings and translations has a very complex history (see Ivor Grattan-Guiness, ‘A Sideways Look at Hilberts Twenty-Three Problems of 1900’ in Notices of the American Mathematical Society 47 (2000), pp. 752-757.

First work: octavo (237 x 167mm). [2], 92 pp. Text diagrams. Modern half sheep. Provenance: modern pencil marginalia in an unidentified hand to p. 17; second work: octavo (255 x 167mm). 56pp. Modern half leather. Provenance: a few pencil marginalia mainly cross-referencing pagination with the Congres printing of 1902 (pp. 58-114), with a photocopy of this latter title-page tipped on to head of first page.

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