Chapter

Introduction

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print August 2008 | ISBN: 9780199550470
Published online September 2011 | e-ISBN: 9780191701559 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199550470.003.0001
Introduction

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Constructivism in mathematics is usually said to have its origin in the reaction of Leopold Kronecker, the great 19th-century German mathematician, to the rise of Georg Ferdinand Ludwig Philipp Cantor's set theory. This is in a sense misleading: Kronecker was not so much the first constructivist as the greatest representative at the time of a tradition of algebraists which includes Isaac Newton, Pierre de Fermat, Leonhard Euler, Carl Gustav Jacob Jacobi, Jacques Charles Francois Sturm – all responsible, as Kronecker was, for the discovery of powerful algorithms – and which has continued since with names such as Adolf Hurwitz, Denes Konig, and Francis Macaulay. Kronecker obtained deep results in arithmetic of modular functions and the theory of elliptic functions with complex multiplication which turned out to be of fundamental importance for 20th-century mathematics. This fact is known to mathematicians.

Keywords: constructivism; mathematics; Leopold Kronecker; set theory; algebra; modular functions

Chapter.  8427 words. 

Subjects: History of Western Philosophy ; Philosophy of Mathematics and Logic

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