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14 results on '"Lützen, Jesper"'

11. Kant, Helmholtz and the Determinacy of Physical Notes.

Author

Cohen, Robert S., Renn, Jürgen, Gavroglu, Kostas, Glick, Thomas F., Grünbaum, Adolf, Schweber, Sylvan S., Stachel, John H., Wartofsky, Marx W., Hendricks, Vincent F., Jørgensen, Klaus Frovin, Lützen, Jesper, Pedersen, Stig Andur, and Hyder, David

Published
2006
Full Text
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12. The Physical Origin of Physically Useful Mathematics.

Author

Lützen, Jesper

Subjects
*WIGNER distribution, *MATHEMATICS, *NATURAL history, *SCIENCE, *PHILOSOPHY
Abstract

When Wigner claimed that the effectiveness of mathematics in the natural sciences was unreasonable it was due to a dogmatic formalist view of mathematics according to which higher mathematics is developed solely with a view to formal beauty. I shall argue that this philosophy is not in agreement with the actual practice of mathematics. Indeed, I shall briefly illustrate how physics has influenced the development of mathematics from antiquity up to the twentieth century. If this influence is taken into account, the effectiveness of mathematics is far more reasonable. [ABSTRACT FROM AUTHOR] </p></dd> <dt class="blacklight-eds_authors col-md-3">Published</dt> <dd class="col-md-9 blacklight-eds_authors">2011</dd> <dt class="blacklight-eds_authors col-md-3"><span class="tags-custom">Full Text</span></dt> <dd class="col-md-9 blacklight-eds_authors"><a class="pdf-blue-icon" target="_blank" href="https://doi.org/10.1179/030801811X13082311482609">View/download PDF</a></dd> </dl> </article><article data-document-id="asx__47696611" data-document-counter="13" itemscope="itemscope" itemtype="http://schema.org/Thing" class="blacklight-academic-journal document document-position-13"> <header class="documentHeader row"> <h3 class="index_title document-title-heading col-sm-9 col-lg-10"> <span class="document-counter"> 13. </span> <a data-context-href="/articles/asx__47696611/track?counter=13&document_id=asx__47696611&search_id=40503471" href="/articles/asx__47696611">The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of the Angle.</a> </h3> <div class="index-document-functions col-sm-3 col-lg-2"> <form class="bookmark-toggle" data-doc-id="asx__47696611" data-present="In Bookmarks" data-absent="Bookmark" data-inprogress="Saving..." action="/bookmarks/asx__47696611" accept-charset="UTF-8" method="post"><input type="hidden" name="_method" value="put" /><input type="hidden" name="authenticity_token" value="VuC0AYe1az8CrTZ0DrJcDD6EC2rCWuGvD6MiwBomlXVly1G5gzLs/VhQy/C0Gtk97ztO2SPywXGPaOeTwKXolQ==" /> <input type="hidden" name="catalog_type" id="catalog_type" value="articles" /> <input type="submit" name="commit" value="Bookmark" id="bookmark_toggle_asx__47696611" class="bookmark-add btn btn-outline-secondary" data-disable-with="Bookmark" /> </form> </div> </header> <dl class="document-metadata dl-invert row"> <dt class="blacklight-eds_authors col-md-3">Author</dt> <dd class="col-md-9 blacklight-eds_authors mb-0"> <p class="truncate-text"> Lützen, Jesper</p></dd> <dt class="blacklight-eds_authors col-md-3">Subjects</dt> <dd class="col-md-9 blacklight-eds_authors">*<searchLink fieldCode="DE" term="%22HISTORY+of+mathematics%22">HISTORY of mathematics</searchLink>, *<searchLink fieldCode="DE" term="%22MATHEMATICAL+proofs%22">MATHEMATICAL proofs</searchLink>, *<searchLink fieldCode="DE" term="%22CUBES%22">CUBES</searchLink></dd> <dt class="blacklight-eds_languages col-md-3">Abstract</dt> <dd class="col-md-9 blacklight-eds_languages"><p class="truncate-text"> Today we credit Pierre Wantzel with the first proof (1837) of the impossibility of doubling a cube and trisecting an arbitrary angle by ruler and compass. However two centuries earlier Descartes had put forward what probably counts as the first proof of these impossibilities. In this paper I analyze this proof, as well as the later related proof given by Montucla (1754) and the brief version of this proof published by Condorcet (1775) . I discuss the many novelties of these early arguments and highlight the problematic points addressed by Gauss (1801) and Wantzel. In particular I show that although Descartes developed many of the algebraic techniques used in later proofs he failed to provide an algebraic impossibility proof and resorted to a geometric argument. Montucla and Condorcet turned this proof into an algebraic one. I situate the analysis of the early proof of the impossibility of the two classical problems in the general context of early modern mathematics where mathematics was primarily viewed as a problem solving activity. Within such a paradigm of mathematics impossibility results arguably do not play the role of proper mathematical results, but rather the role of meta-results limiting the problem solving activity. [ABSTRACT FROM AUTHOR] </p></dd> <dt class="blacklight-eds_authors col-md-3">Published</dt> <dd class="col-md-9 blacklight-eds_authors">2010</dd> <dt class="blacklight-eds_authors col-md-3"><span class="tags-custom">Full Text</span></dt> <dd class="col-md-9 blacklight-eds_authors"><a class="pdf-blue-icon" target="_blank" href="https://doi.org/10.1111/j.1600-0498.2009.00160.x">View/download PDF</a></dd> </dl> </article><article data-document-id="asx__145629344" data-document-counter="14" itemscope="itemscope" itemtype="http://schema.org/Thing" class="blacklight-review document document-position-14"> <header class="documentHeader row"> <h3 class="index_title document-title-heading col-sm-9 col-lg-10"> <span class="document-counter"> 14. </span> <a data-context-href="/articles/asx__145629344/track?counter=14&document_id=asx__145629344&search_id=40503471" href="/articles/asx__145629344">The Impossibility of Squaring the Circle in the 17th Century. A Debate Among Gregory, Huygens and Leibniz.</a> </h3> <div class="index-document-functions col-sm-3 col-lg-2"> <form class="bookmark-toggle" data-doc-id="asx__145629344" data-present="In Bookmarks" data-absent="Bookmark" data-inprogress="Saving..." action="/bookmarks/asx__145629344" accept-charset="UTF-8" method="post"><input type="hidden" name="_method" value="put" /><input type="hidden" name="authenticity_token" value="XeYnbKJ7ijj+ABGcqZ14EliRiOQ4fgcC40oF51Jgs2xeM88bD0d7LjdYOIDnnAgGq+VYmLfZ1fLlYxxnXAP3zg==" /> <input type="hidden" name="catalog_type" id="catalog_type" value="articles" /> <input type="submit" name="commit" value="Bookmark" id="bookmark_toggle_asx__145629344" class="bookmark-add btn btn-outline-secondary" data-disable-with="Bookmark" /> </form> </div> </header> <dl class="document-metadata dl-invert row"> <dt class="blacklight-eds_authors col-md-3">Author</dt> <dd class="col-md-9 blacklight-eds_authors mb-0"> <p class="truncate-text"> Lützen, Jesper</p></dd> <dt class="blacklight-eds_authors col-md-3">Subjects</dt> <dd class="col-md-9 blacklight-eds_authors">*<searchLink fieldCode="DE" term="%22SEVENTEENTH+century%22">SEVENTEENTH century</searchLink>, *<searchLink fieldCode="DE" term="%22CIRCLE%22">CIRCLE</searchLink>, *<searchLink fieldCode="DE" term="%22CALCULUS%22">CALCULUS</searchLink>, *<searchLink fieldCode="DE" term="%22HISTORY+of+mathematics%22">HISTORY of mathematics</searchLink>, *<searchLink fieldCode="DE" term="%22CONIC+sections%22">CONIC sections</searchLink>, *<searchLink fieldCode="DE" term="%22GAUSSIAN+quadrature+formulas%22">GAUSSIAN quadrature formulas</searchLink></dd> <dt class="blacklight-eds_authors col-md-3">Published</dt> <dd class="col-md-9 blacklight-eds_authors">2020</dd> <dt class="blacklight-eds_authors col-md-3"><span class="tags-custom">Full Text</span></dt> <dd class="col-md-9 blacklight-eds_authors"><a class="pdf-blue-icon" target="_blank" href="https://doi.org/10.1016/j.hm.2020.01.004">View/download 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