Lej Brouwer Topologist Intuitionist Philosopher

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L.E.J. Brouwer – Topologist, Intuitionist, Philosopher

Author : Dirk van Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 1447146166
Total Pages : 877 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis L.E.J. Brouwer – Topologist, Intuitionist, Philosopher by : Dirk van Dalen

Download or read book L.E.J. Brouwer – Topologist, Intuitionist, Philosopher written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mystic, Geometer, and Intuitionist

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (873 download)

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Download or read book Mystic, Geometer, and Intuitionist written by and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mystic, Geometer, and Intuitionist

Author : Dirk van Dalen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (263 download)

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Book Synopsis Mystic, Geometer, and Intuitionist by : Dirk van Dalen

Download or read book Mystic, Geometer, and Intuitionist written by Dirk van Dalen and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Selected Correspondence of L.E.J. Brouwer

Author : Dirk von Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 0857295373
Total Pages : 531 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis The Selected Correspondence of L.E.J. Brouwer by : Dirk von Dalen

Download or read book The Selected Correspondence of L.E.J. Brouwer written by Dirk von Dalen and published by Springer Science & Business Media. This book was released on 2011-07-25 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Selected Correspondence of L.E.J. Brouwer

Author : Dirk von Dalen
Publisher : Springer
ISBN 13 : 9780857295279
Total Pages : 532 pages
Book Rating : 4.2/5 (952 download)

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Book Synopsis The Selected Correspondence of L.E.J. Brouwer by : Dirk von Dalen

Download or read book The Selected Correspondence of L.E.J. Brouwer written by Dirk von Dalen and published by Springer. This book was released on 2011-07-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mystic, Geometer, and Intuitionist

Author : Dirk van Dalen
Publisher : Oxford University Press
ISBN 13 : 9780198516200
Total Pages : 10 pages
Book Rating : 4.5/5 (162 download)

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Book Synopsis Mystic, Geometer, and Intuitionist by : Dirk van Dalen

Download or read book Mystic, Geometer, and Intuitionist written by Dirk van Dalen and published by Oxford University Press. This book was released on 2005 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio-linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland. Although his abilities won him offers from prestigious universities such as Berlin and Gottingen, he preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in the artist community at Laren. This book, the second in a two-volume set, provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved.

Handbook of the History and Philosophy of Mathematical Practice

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman

Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Critical Philosophy of Mathematics

Author : Ole Skovsmose
Publisher : Springer Nature
ISBN 13 : 3031713753
Total Pages : 270 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Critical Philosophy of Mathematics by : Ole Skovsmose

Download or read book Critical Philosophy of Mathematics written by Ole Skovsmose and published by Springer Nature. This book was released on with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Brouwer's Intuitionism

Author : Walter P. van Stigt
Publisher : North Holland
ISBN 13 : 9780444883841
Total Pages : 530 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Brouwer's Intuitionism by : Walter P. van Stigt

Download or read book Brouwer's Intuitionism written by Walter P. van Stigt and published by North Holland. This book was released on 1990-01-01 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer

Author : Mark van Atten
Publisher : Springer
ISBN 13 : 3319100319
Total Pages : 336 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer by : Mark van Atten

Download or read book Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer written by Mark van Atten and published by Springer. This book was released on 2014-11-21 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics and the Roots of Postmodern Thought

Author : Vladimir Tasić
Publisher : Oxford University Press, USA
ISBN 13 : 9780195139679
Total Pages : 208 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis Mathematics and the Roots of Postmodern Thought by : Vladimir Tasić

Download or read book Mathematics and the Roots of Postmodern Thought written by Vladimir Tasić and published by Oxford University Press, USA. This book was released on 2001 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 2. Around the Cartesian Circuit. 2.1. Imagination. 2.2. Intuition. 2.3. Counting to One. 3. Space Oddity and Linguistic Turn. 4. Wound of Language. 4.1. Being and Time Continuum. 4.2. Language and Will. 5. Beyond the Code. 5.1. Medium of Free Becoming. 5.2. Nonpresence of Identity. 6. The Expired Subject. 6.1. Empire of Signs. 6.2. Mechanical Bride. 7. The Vanishing Author. 8. Say Hello to the Structure Bubble. 8.1. Algebra of Language. 8.2. Functionalism Chic. 9. Don't Think, Look. 9.1. Interpolating the Self. 9.2. Language Games. 9.3. Thermostats "R" Us. 10. Postmo.

Rediscovering Léon Brunschvicg’s Critical Idealism

Author : Pietro Terzi
Publisher : Bloomsbury Publishing
ISBN 13 : 1350171689
Total Pages : 352 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Rediscovering Léon Brunschvicg’s Critical Idealism by : Pietro Terzi

Download or read book Rediscovering Léon Brunschvicg’s Critical Idealism written by Pietro Terzi and published by Bloomsbury Publishing. This book was released on 2022-01-13 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Léon Brunschvicg's contribution to philosophical thought in fin-de-siècle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including Lévinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship.

Conceptual Mathematics

Author : F. William Lawvere
Publisher : Cambridge University Press
ISBN 13 : 0521894859
Total Pages : 409 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Conceptual Mathematics by : F. William Lawvere

Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Connecting with Computability

Author : Liesbeth De Mol
Publisher : Springer Nature
ISBN 13 : 3030800490
Total Pages : 506 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Connecting with Computability by : Liesbeth De Mol

Download or read book Connecting with Computability written by Liesbeth De Mol and published by Springer Nature. This book was released on 2021-07-01 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.

Making up Numbers: A History of Invention in Mathematics

Author : Ekkehard Kopp
Publisher : Open Book Publishers
ISBN 13 : 1800640978
Total Pages : 280 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Making up Numbers: A History of Invention in Mathematics by : Ekkehard Kopp

Download or read book Making up Numbers: A History of Invention in Mathematics written by Ekkehard Kopp and published by Open Book Publishers. This book was released on 2020-10-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Communities in the Reconstruction After the Great War 1918–1928

Author : Laurent Mazliak
Publisher : Springer Nature
ISBN 13 : 3030616835
Total Pages : 373 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Communities in the Reconstruction After the Great War 1918–1928 by : Laurent Mazliak

Download or read book Mathematical Communities in the Reconstruction After the Great War 1918–1928 written by Laurent Mazliak and published by Springer Nature. This book was released on 2021-03-27 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a consequence of the international meeting organized in Marseilles in November 2018 devoted to the aftermath of the Great War for mathematical communities. It features selected original research presented at the meeting offering a new perspective on a period, the 1920s, not extensively considered by historiography. After 1918, new countries were created, and borders of several others were modified. Territories were annexed while some countries lost entire regions. These territorial changes bear witness to the massive and varied upheavals with which European societies were confronted in the aftermath of the Great War. The reconfiguration of political Europe was accompanied by new alliances and a redistribution of trade – commercial, intellectual, artistic, military, and so on – which largely shaped international life during the interwar period. These changes also had an enormous impact on scientific life, not only in practice, but also in its organization and communication strategies. The mathematical sciences, which from the late 19th century to the 1920s experienced a deep disciplinary evolution, were thus facing a double movement, internal and external, which led to a sustainable restructuring of research and teaching. Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. This was accompanied by an explosion of new international or national associations of mathematicians with for instance the founding, in 1918, of the International Mathematical Union and the controversial creation of the International Research Council. Therefore, the central idea for the articulation of the various chapters of the book is to present case studies illustrating how in the aftermath of the war, many mathematicians had to organize their personal trajectories taking into account the evolution of the political, social and scientific environment which had taken place at the end of the conflict.

Brouwer's Cambridge Lectures on Intuitionism

Author : Luitzen Egbertus Jan Brouwer
Publisher : Cambridge University Press
ISBN 13 : 9780521177368
Total Pages : 130 pages
Book Rating : 4.1/5 (773 download)

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Book Synopsis Brouwer's Cambridge Lectures on Intuitionism by : Luitzen Egbertus Jan Brouwer

Download or read book Brouwer's Cambridge Lectures on Intuitionism written by Luitzen Egbertus Jan Brouwer and published by Cambridge University Press. This book was released on 1981 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.