From Kant to Hilbert, Volume 2
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.
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aleph algebraic numbers alike analysis Anzahl applied arithmetic axiom of choice axiomatic method axioms boundary number Brouwer called Cantor cardinal number commutative law complete induction concept consistency consistency proof contained continuous continuum contradiction convergent corresponds 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 lecture logic magnitudes manifold mapping mathematical induction mathematicians mathematics means multiplication natural numbers normal domain notion number theory number-class objects ordinal philosophical physical positive possible principle problem proof theory propositions proved pure question rational numbers real numbers reason relations Riemann Russell sensations sense set theory space straight line surface symbols theorem is true things tion transfinite translation uniform convergence urelements variable well-ordered well-ordered set Zermelo