From Kant to Hilbert Volume 2, Volum 2OUP Oxford, 21 d’abr. 2005 - 709 pàgines Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics—algebra, geometry, number theory, analysis, logic and set theory—with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics. |
Continguts
649 | |
662 | |
18 JULIUS WILHELM RICHARD DEDEKIND 18311916 | 753 |
19 GEORG CANTOR 18451918 | 838 |
20 LEOPOLD KRONECKER 18231891 | 941 |
21 CHRISTIAN FELIX KLEIN 18491925 | 956 |
22 JULES HENRI POINCARÉ 18541912 | 972 |
23 THE FRENCH ANALYSTS | 1075 |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
A₁ A₂ aleph algebraic numbers Anzahl applied arithmetic axiom of choice axiomatic axiomatic method axioms boundary number Brouwer called Cantor cardinal number commutative law complete induction concept consistency consistency proof contained continuous continuum contradiction convergent corresponding Couturat Dedekind defined definition determinate displacement elements equation example existence expressed fact finite number formal formula foundations function geometry given Hilbert inference infinite infinity integers interval intuition intuitionism intuitionistic investigation irrational numbers Kronecker logical magnitudes manifold mapping mathematicians mathematics means natural numbers normal domain notion number theory number-class objects ordinal philosophical physical Poincaré positive possible principle problem proof theory propositions proved pure question rational numbers real numbers relations Riemann Russell sensations sense sequence set theory space straight line surface theorem is true tion transfinite translation uniform convergence urelements variable well-ordered well-ordered set Zermelo