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Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 1447146166
Category : Mathematics
Languages : en
Pages : 877
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Book Description
Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.
Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 1447146166
Category : Mathematics
Languages : en
Pages : 877
Get Book Here
Book Description
Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.
Author: Luitzen Egbertus Jan Brouwer
Publisher: Cambridge University Press
ISBN: 9780521177368
Category : Mathematics
Languages : en
Pages : 130
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Book Description
Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.
Author: Walter P. van Stigt
Publisher: North Holland
ISBN: 9780444883841
Category : Mathematics
Languages : en
Pages : 530
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Book Description
Dutch Mathematician Luitzen Egbertus Jan Brouwer (1881-1966) was a rebel. His doctoral thesis... was the manifesto of an angry young man taking on the mathematical establishment on all fronts. In a short time he established a world-wide reputation for himself; his genius and originality were acknowledged by the great mathematicians of his time... The Intuitionist-Formalist debate became a personal feud between the mathematical giants Brouwer and Hilbert, and ended in 1928 with the expulsion of Brouwer from the editorial board of the Mathematische Annalen by dictat of Hilbert. Forsaken, humiliated and disillusioned Brouwer abandoned his Intuitionist Programme and withdrew into silence just about the time when the Formalist Programme appeared to be fundamentally flawed and major opposition collapsed... This book attempts to follow the `genetic' development of Brouwer's ideas, linking the man Brouwer, his Weltanschauung, his philosophy of mathematics and his reconstruction of mathematics. Brouwer's own writings, his publications as well as his unpublished papers, are its immediate and main source of reference. It is the second volume in the new series Studies in the History and Philosophy of Mathematics, and is written for the specialist as well as for the general reader interested in mathematics and the interpretation of its status and function.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
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Book Description
Author: Vladimir Tasic
Publisher: Oxford University Press
ISBN: 0199881510
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.
Author: Ekkehard Kopp
Publisher: Open Book Publishers
ISBN: 1800640978
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Author: Mark van Atten
Publisher: Springer
ISBN: 3319100319
Category : Philosophy
Languages : en
Pages : 336
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Book Description
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Author: Ole Skovsmose
Publisher: Springer Nature
ISBN: 3031713753
Category :
Languages : en
Pages : 270
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Book Description
Author: Loren Graham
Publisher: Harvard University Press
ISBN: 0674032934
Category : History
Languages : en
Pages : 252
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Book Description
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
Author: Dirk von Dalen
Publisher: Springer Science & Business Media
ISBN: 0857295373
Category : Mathematics
Languages : en
Pages : 531
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Book Description
L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.
