David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Bernard Riemann (1900). On Psychology and Metaphysics. The Monist 10 (2):198-215.
William I. McLaughlin & Sylvia L. Miller (1992). An Epistemological Use of Nonstandard Analysis to Answer Zeno's Objections Against Motion. Synthese 92 (3):371 - 384.
Mark Colyvan (2005). (Book Review) Ontological Independence as the Mark of the Real. [REVIEW] Philosophia Mathematica 13 (2):216-225.
James Hope Moulton (1903). Riemann and Goelzer's Comparative Grammar of Greek and Latin Grammaire Comparée du Grec Et du Latin. Première Partie: Phonétique Et Étude des Formes Grecques Et Latines. Par O. Riemann Et H. Goelzer. Paris, Librairie Armand Colin. 1901. Pp. 540. 20 Fr. [REVIEW] The Classical Review 17 (07):361-362.
E. A. Sonnenschein (1900). Riemann and Goelzer's Comparison of Greek and Latin Syntax Grammaire Comparée du Grec Et du Latin—Syntaxe, Par O. Riemann Et H. Goelzer. (Paris, Colin Et Cie., 1897) 893 Pp. Price 25 Francs. [REVIEW] The Classical Review 14 (06):313-315.
Erik C. Banks (2005). Kant, Herbart and Riemann. Kant-Studien 96 (2):208-234.
George J. Stack (1989). Riemann's Geometry and Eternal Recurrence as Cosmological Hypothesis. International Studies in Philosophy 21 (2):37-40.
James Franklin (1987). Non-Deductive Logic in Mathematics. British Journal for the Philosophy of Science 38 (1):1-18.
Werner Ehm (2010). Broad Views of the Philosophy of Nature: Riemann, Herbart, and the “Matter of the Mind”. Philosophical Psychology 23 (2):141 – 162.
José Ferreiros Domínguez (1992). Sobre los orígenes de la Matemática abstracta. Theoria 7 (1-2):473-498.
Added to index2009-03-04
Total downloads27 ( #61,291 of 1,096,519 )
Recent downloads (6 months)4 ( #64,935 of 1,096,519 )
How can I increase my downloads?