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Otto Hölder’s Interpretation of David Hilbert’s Axiomatic Method
Published 2013-03-01“…My reconstruction focuses on Hölder’s critical assessment of David Hilbert’s account of axiomatics in general, and of Hilbert’s conception of metamathematics in particular. …”
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Current problems in mathematical phisics: the original contribution of David Hilbert
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Geometry, Formalism and Intuition: David Hilbert and the formal Axiomatic Method (1891-1905)
Published 2014-12-01“…The paper presents and analyzes a set of unpublished notes for lecture courses on geometry, which David Hilbert gave between 1891 and 1905. it will be argued that in these lecture courses the author elaborates the<span style="text-decoration: underline;"> conception of geometry </span>which underlies his axiomatic investigations in <em>Foundations of Geometry </em>(1899). on the one hand, it is claimed that this conception of geometry can be characterized by: <em>i</em>) an abstract or formal axiomatic view; <em>ii</em>) an empiricist stance regarding the origins of geometry and its place among the different mathematical theories. on the other hand, it is asserted that the role that Hilbert assigns to geometrical intuition in the process of the (formal) axiomatization of this theory, can be used to perceive his clear opposition with regard to (radical) formalist views which he is often identified with.…”
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Intuición y método axiomático en la concepción temprana de la geometría de David Hilbert
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El enfoque epistemológico de David Hilbert: el a priori del conocimiento y el papel de la lógica en la fundamentación de la ciencia
Published 2019-08-01“…En este trabajo se exploran los principales planteamientos filosóficos de la teoría de la prueba de David Hilbert. Específicamente, el trabajo se centra en sus ideas respecto de la lógica, el concepto de prueba, la axiomática, el concepto de verdad, la metamatemática, el conocimiento a priori y la naturaleza general del conocimiento científico. …”
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Hilbert e la logica
Published 2000-10-01“…David Hilbert ha coltivato un profondo interesse per i fondamenti, ...…”
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Hilbert e i fondamenti della matematica: il metodo assiomatico
Published 2000-10-01“…Il ruolo esercitato da David Hilbert nel campo dei fondamenti della matematica è insigne.…”
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Mathematics as a love of wisdom: Saunders Mac Lane as philosopher
Published 2020-12-01“…But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.…”
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Pro and Contra Hilbert: Zermelo’s Set Theories
Published 2005-08-01“…They correspond to two specific periods of research on the foundations of mathematics by David Hilbert and his collaborators in Göttingen. In the first period Hilbert elaborated his early axiomatic program, and Zermelo’s work is clearly along the lines proposed by Hilbert, it is pro Hilbert. …”
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Le concept d’espace chez Veronese
Published 2009-10-01“…Giuseppe Veronese is known for his studies on spaces with more dimensions; less known are his “philosophical” writings, that concern the foundations of geometry and mathematics and explain the reasons for constructing a non-Archimedean geometry (several years before David Hilbert’s Grundlagen) and the formulation of a concept of continuity that admits infinitely big and small quantities. …”
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Matematyka nie opisuje świata, lecz wychodzi mu naprzeciw
Published 2015-06-01“…In everyday experience mathematics rarely appears to us as a whole, and certainly never as a system in the sense of David Hilbert’s considerations from early 20th Century. …”
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Understanding Mathematical Logic and its Applications /
Published 2012“…In the early 20th century it was shaped by David Hilbert's program to provide the consistency of foundational theories. …”
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Conjecture of twin primes (Still unsolved problem in Number Theory). An expository essay
Published 2017-12-01“…The purpose of this paper is to gather as much results of advances, recent and previous works as possible concerning the oldest outstanding still unsolved problem in Number Theory (and the most elusive open problem in prime numbers) called "Twin primes conjecture" (8th problem of David Hilbert, stated in 1900) which has eluded many gifted mathematicians. …”
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Hugo Dionizy Steinhaus – a Way to Contemporary Probability
Published 2018-09-01“…Since 1905 he stayed in Göttingen where in 1911 he obtained his PhD under David Hilbert. In 1920 he became professor of the Lwow University. …”
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The Hilbert Edition: What is it and what is it good for?
Published 2010-04-01“…The Mathematical Institute (MI) of the University of Göttingen and the Niedersächsische Staats- und Universitätsbibliothek (SUB) together possess an impressive collection of documents by David Hilbert, perhaps the most important mathematicians of the period 1885-1930, and a very significant mathematical physicist. …”
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