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CASSOU-NOGUES PIERRE
HILBERT
LES BELLES LETTRES. 2005. In-12. Broché. Bon état, Couv. convenable, Dos satisfaisant, Intérieur frais. 169 pages. . . . Classification Dewey : 840-Littératures des langues romanes. Littérature française
Reference : R200047033
ISBN : 2251760369
Classification Dewey : 840-Littératures des langues romanes. Littérature française
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5 book(s) with the same title
Über die Grundlagen der Geometrie + Über die Grundlagen der Geometrie II. - [THE FREGE-HILBERT CONTROVERSY]
Leipzig, B. G. Teubner, 1903. 8vo. Bound with the original wrappers in contemporary half cloth with gilt lettering to spine. In ""Jahresbericht der Deutschen Mathematiker-Vereinigung"", 12. Band. 6. Heft. Juni. Bound with all issues from December 1902 till December 1903 (all issues with wrappers). Pp. 319-324"" Pp. 368-375. [Entire volume: VI, 602 pp.].
First appearance of Frege's important paper on the role of axioms in mathematical theories, describing the correct way to demonstrate consistency and independence results for such axioms.The two papers was Frege's response to Hilbert's ""Grundlagen der Geometrie"" which inaugurated the famous Frege-Hilbert Controversy. ""Hilbert's lecture [Grundlagen der Geometrie] inspired a sharp reaction from his contemporary Gottlob Frege, who found both Hilbert's understanding of axioms, and his approach to consistency and independence demonstrations, virtually incomprehensible and at any rate seriously flawed. Frege's reaction is first laid out in his correspondence with Hilbert from December 1899 to September 1900, and subsequently in two series of essays (both entitled ""On the Foundations of Geometry"") published in 1903 and 1906. Hilbert was never moved by Frege's criticisms, and did not respond to them after 1900. Frege, for his part, was never convinced of the reliability of Hilbert's methods, and held until the end that the latter's consistency and independence proofs were fatally flawed.""(SEP). ""Frege felt that his view represented a traditional understanding of this notion, and that Hilbert's departure from this understanding led to a confusion about axioms that undermined many of the sorts of results, in particular, the independence of the axioms of geometry, that Hilbert saw as major mathematical achievements. Symptomatic of Hilbert's confusion, according to Frege, was Hilbert's claiming that axioms could serve to define"" the reason that this is a confusion, according to Frege, is that axioms and definitions are statements of wholly different types."" (Antonelli, Frege's New Science).Friedrich Ludwig Gottlob Frege (1848 - 1925) was a German mathematician, but his main contributions lie in his becoming a logician and a philosopher, who influenced the fields of logic and analytic philosophy immensely. Together with Wittgenstein, Russel and Moore, Frege is considered the founder of analytic philosophy, and a main founder of modern mathematical logic. In the preface of the ""Principia Mathematica"" Russell and Whitehead state that ""In all questions of logical analysis our chief debt is to Frege"" (p. VIII). His influence on 20th century philosophy has been deeply profound, especially in the English speaking countries from the middle of the 20th century and onwards"" in this period most of his works were translated into English for the first time.The philosophical papers of Frege were published in Germany in scholarly journals, which were barely read outside of German speaking countries. The first collections of his writings did not appear until after the Second World War, and Frege was little known as a philosopher during his lifetime. He greatly influenced the likes of Russel, wittgenstein and Carnap, though, and bears a great responsibility for the turn modern philosophical thought has taken. Due to his contributions to the philosophy of language, analytic philosophy could be founded as it were. Instead of answering the question about meaning, Frege here sets out to explore the foundations of arithmetic, beginning with questions such as ""What is a number?"" In his solutions the answer to the question of meaning could also be found, though, and he permitted himself ""the hope that even the philosophers, if they examine what I have written without prejudice, will find in it something of use to them."" (p. XIi - Introduction).
Ueber die gerade Linie als kürzeste Verbindung zweier Punkte. (Aus einem an Herrn F. Klein gerichteten Briefe). - [FIRST PUBLICATION OF THE HILBERT METRIC]
Leipzig, B.G. Teubner, 1895. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 46. Band. 1. Heft.""Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 91-96. [Entire issue: IV, 160 pp].
First printing of Hilbert's groundbreaking paper in which ""Hilbert's Metric"" (or Hilbert's projective metric) - and the metric in general - was introduced. The Hilbert metric an a closed convex cone that can be applied to various purposed in non-Euclidean geometryThe usefulness of Hilbert's metric were made clear in 1957 by Garrett Birkhoff who showed that the Perron-Frobenius theorem for non-negative matrices and Jentzch's theorem for integral operators with positive kernel could both be proved by an application of the Banach contraction mapping theorem in suitable metric spaces. (Serrin. Hilbert's Matric. P. 1).
Rapport sur le Prix Bolyai. - [POINCARÉ APPRAISAL OF HILBERT]
Berlin, G. Reimer, 1912. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 35, 1912. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 1-28. [Entire volume: (4), 398, (1), 27, 19 pp].
First appearance of Poincaré's report on 1910 Bolyai Prize which was awarded to David Hilbert in recognition of his work in fields of invariant theory, transcendent number (e constant after Lindemann), arithmetic, the (Hilbert-)Waring theorem, geometry, integral equations and the Dirichlet’s principle.In 1910, Hilbert became only the second winner of the Bolyai Prize of the Hungarian Academy of Sciences. It was the recognition of the fact that Hilbert was one of the leading mathematicians of his time. The first winner of the prize in 1905 was Henri Poincare, the most prolific mathematician of the 19th century.Poincaré about the works and achievements of David Hilbert in fields of invariant theory, transcendent number (e constant after Lindemann), arithmetic, the (Hilbert-)Waring theorem, geometry, integral equations and the Dirichlet’s principle.
Ein Beitrag zur Theorie des Legendre'schen Polynoms. - [HILBERT MATRIX]
Berlin, Stockholm, Paris, Almqvist & Wiksell, 1894. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 18, 1894. Entire volume offered. Stamps to title page and light wear to extremities, otherwise a fine and clean copy. Pp. 155-59.[Entire volume: (4), 421, (2) pp].
First printing of Hilbert's paper in which he introduced The Hilbert Matrix. In linear algebra, a Hilbert matrix is a square matrix with entries being the unit fractions. The Hilbert matrix is symmetric and positive definite and is also totally positive (meaning the determinant of every submatrix is positive). The Hilbert matrix is an example of a Hankel matrix.
Über die Transcendenz der Zahlen e und pi. - [ANTICIPATION OF HILBERT'S SEVENTH PROBLEM]
Leipzig, B.G. Teubner, 1893. 8vo. Original printed wrappers, no backstrip and a small nick to front wrapper. In ""Mathematische Annalen. Begründet 1868 durch Rudolf Friedrich Alfred Clebsch. 43. Band. 2. und 3. (Doppel-)Heft.""Entire issue offered. Internally very fine and clean. [Hilbert:] Pp. 216-19. [Entire issue: Pp. 145-456].
First publication of Hilbert's important contribution to transcendental number theory which anticipates Hilbert's seventh problem, the seventh of twenty-three problems proposed by Hilbert in 1900 which became of seminal importance to 20th century mathematics. A transcendental number is a number which is not algebraic-that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are pi and e. Euler was the first person to define transcendental numbers - The name ""transcendentals"" comes from Leibniz in his 1682 paper where he proved sin x is not an algebraic function of x.
