On “Space” and “Geometry” in the Nineteenth Century

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On “Space” and “Geometry” in the Nineteenth Century. / Lützen, Jesper.

The Richness of the History of Mathematic: A Tribute to Jeremy Gray. Springer, 2023. s. 317 - 339 (Archimedes, Bind 66).

Publikation: Bidrag til bog/antologi/rapport › Bidrag til bog/antologi › Forskning › fagfællebedømt

Harvard

Lützen, J 2023, On “Space” and “Geometry” in the Nineteenth Century. i The Richness of the History of Mathematic: A Tribute to Jeremy Gray. Springer, Archimedes, bind 66, s. 317 - 339. https://doi.org/10.1007/978-3-031-40855-7_13

APA

Lützen, J. (2023). On “Space” and “Geometry” in the Nineteenth Century. I The Richness of the History of Mathematic: A Tribute to Jeremy Gray (s. 317 - 339). Springer. Archimedes Bind 66 https://doi.org/10.1007/978-3-031-40855-7_13

Vancouver

Lützen J. On “Space” and “Geometry” in the Nineteenth Century. I The Richness of the History of Mathematic: A Tribute to Jeremy Gray. Springer. 2023. s. 317 - 339. (Archimedes, Bind 66). https://doi.org/10.1007/978-3-031-40855-7_13

Author

Lützen, Jesper. / On “Space” and “Geometry” in the Nineteenth Century. The Richness of the History of Mathematic: A Tribute to Jeremy Gray. Springer, 2023. s. 317 - 339 (Archimedes, Bind 66).

Bibtex

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abstract = "What did mathematicians mean by the words “space” and “geometry” in the nineteenth century? This chapter will try to answer this question, starting with an analysis of Hertz{\textquoteright}s, Lipschitz{\textquoteright} and Darboux{\textquoteright}s geometrization of mechanics and continuing with a discussion of the use of the words by mathematicians who are usually credited as the principal inventors of non-Euclidean and higher dimensional geometries. The conclusion is that most mathematicians prior to 1880 used the words to denote (intuited) physical space and the geometry describing that space. This is the background against which one should evaluate the sometimes confusing nineteenth century discussions about the existence of geometries other than Euclid{\textquoteright}s geometry. The question was radically changed with the advent of modernist structuralist mathematics, as described in (Gray, Plato{\textquoteright}s Ghost: the modernist transformation of mathematics. Princeton University Press, Princeton, 1994). {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

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AB - What did mathematicians mean by the words “space” and “geometry” in the nineteenth century? This chapter will try to answer this question, starting with an analysis of Hertz’s, Lipschitz’ and Darboux’s geometrization of mechanics and continuing with a discussion of the use of the words by mathematicians who are usually credited as the principal inventors of non-Euclidean and higher dimensional geometries. The conclusion is that most mathematicians prior to 1880 used the words to denote (intuited) physical space and the geometry describing that space. This is the background against which one should evaluate the sometimes confusing nineteenth century discussions about the existence of geometries other than Euclid’s geometry. The question was radically changed with the advent of modernist structuralist mathematics, as described in (Gray, Plato’s Ghost: the modernist transformation of mathematics. Princeton University Press, Princeton, 1994). © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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