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The book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
First published in the series Science Networks Historical Studies, Vol. 17 (1996).
In the second rev. edition the author has eliminated misprints, revised the chapter on Richard Dedekind, and updated the bibliographical index.
List of contents
Introduction: Structures in Mathematics.- One: Structures in the Images of Mathematics.- 1 Structures in Algebra: Changing Images.- 2 Richard Dedekind: Numbers and Ideals.- 3 David Hilbert: Algebra and Axiomatics.- 4 Concrete and Abstract: Numbers, Polynomials, Rings.- 5 Emmy Noether: Ideals and Structures.- Two: Structures in the Body of Mathematics.- 6 Oystein Ore: Algebraic Structures.- 7 Nicolas Bourbaki: Theory ofStructures.- 8 Category Theory: Early Stages.- 9 Categories and Images of Mathematics.- Author Index.
Summary
The book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
First published in the series Science Networks Historical Studies, Vol. 17 (1996).
In the second rev. edition the author has eliminated misprints, revised the chapter on Richard Dedekind, and updated the bibliographical index.
