General Topology, in Particular Dimension Theory, in the Netherlands: The Decisive Influence of Brouwer’s Intuitionism

Koetsier, Teun; Mill, Jan van

doi:10.1007/978-94-017-0468-7_12

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…Also implicit in his paper [48] is the notion of degree of a mapping, an idea that he made more explicit in [50]. 80 We refer to Koetsier [140] and to the comments in Brouwer's Collected Works edition by Freudenthal for summaries of Brouwer's works on topology.…”

Section: Brouwer and The Methods Of Continuitymentioning

confidence: 99%

On the early history of moduli and Teichmüller spaces

A'Campo

Papadopoulos

2015

Lipman Bers, a Life in Mathematics

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We survey some major contributions to Riemann's moduli space and Teichmüller space. Our report has a historical character, but the stress is on the chain of mathematical ideas. We start with the introduction of Riemann surfaces, and we end with the discovery of some of the basic structures of Riemann's moduli space and Teichmüller space. We point out several facts which seem to be unknown to many algebraic geometers and analysts working in the theory. The period we are interested in starts with Riemann, in 1851, and ends in the early 1960s, when Ahlfors and Bers confirmed that Teichmüller's results were correct.This paper was written for the book Lipman Bers, a life in Mathematics, edited by Linda Keen , Irwin Kra and Rubi Rodriguez (Amercian Mathematical Society, 2015). It is dedicated to the memory of Lipman Bers who was above all a complex analyst and spent a large part of his life and energy working on the analytic structure of Teichmüller space. His work on analysis is nevertheless inseparable from geometry and topology. In this survey, we highlight the relations and the logical dependence between this work and the works of Riemann, Poincaré, Klein, Brouwer, Siegel, Teichmüller, Weil, Grothendieck and others. We explain the motivation behind the ideas. In doing so, we point out several facts which seem to be unknown to many Teichmüller theorists.

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Section: Brouwer and The Methods Of Continuitymentioning

confidence: 99%

On the early history of moduli and Teichmüller spaces

A'Campo

Papadopoulos

2015

Lipman Bers, a Life in Mathematics

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“…28 For a more extensive treatment of Brouwer's work in dimension theory we refer to Johnson [94,95]. See also Koetsier and van Mill [104]. For Brouwer's topological work as a whole we refer to Freudenthal [64].…”

Section: Intermezzo: the Golden Agementioning

confidence: 99%

By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics

Koetsier

Mill

1999

History of Topology

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“…Some historians and mathematicians argue that Brouwer’s topological work is utterly separated from his intuitionistic endeavor, while others, such as Arend Heyting and Dirk van Dalen, remain unsure as to the unity or disunity in Brouwer’s work. Jan van Mill and Teun Koetsier claim that the dividing line in Brouwer’s work does not run through topology and intuitionism, but separates his research into pre-1917 and post-1917 works (Koetsier and Van Mill 1997). They show that there is more that links Brouwer’s intuitionistic work to his topology in the years up to 1917 than separates it, and conclude that Brouwer’s topological work derives naturally from the same basic principles.…”

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confidence: 99%

Towards a new philosophical perspective on Hermann Weyl’s turn to intuitionism

Bar-On

2021

Sci Context

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ArgumentThe paper explores Hermann Weyl’s turn to intuitionism through a philosophical prism of normative framework transitions. It focuses on three central themes that occupied Weyl’s thought: the notion of the continuum, logical existence, and the necessity of intuitionism, constructivism, and formalism to adequately address the foundational crisis of mathematics. The analysis of these themes reveals Weyl’s continuous endeavor to deal with such fundamental problems and suggests a view that provides a different perspective concerning Weyl’s wavering foundational positions. Building on a philosophical model of scientific framework transitions and the special role that normative indecision or ambivalence plays in the process, the paper examines Weyl’s motives for considering such a radical shift in the first place. It concludes by showing that Weyl’s shifting stances should be regarded as symptoms of a deep, convoluted intrapersonal process of self-deliberation induced by exposure to external criticism.

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General Topology, in Particular Dimension Theory, in the Netherlands: The Decisive Influence of Brouwer’s Intuitionism

Cited by 8 publications

References 27 publications

On the early history of moduli and Teichmüller spaces

On the early history of moduli and Teichmüller spaces

By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics

Towards a new philosophical perspective on Hermann Weyl’s turn to intuitionism

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