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

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Standard

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

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

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Harvard

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

Vancouver

Lützen J. On “Space” and “Geometry” in the Nineteenth Century. In The Richness of the History of Mathematic: A Tribute to Jeremy Gray. Springer. 2023. p. 317 - 339. (Archimedes, Vol. 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. pp. 317 - 339 (Archimedes, Vol. 66).

Bibtex

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title = "On “Space” and “Geometry” in the Nineteenth Century",
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.",
author = "Jesper L{\"u}tzen",
year = "2023",
doi = "10.1007/978-3-031-40855-7_13",
language = "English",
series = "Archimedes",
publisher = "Springer",
pages = "317 -- 339",
booktitle = "The Richness of the History of Mathematic",
address = "Switzerland",

}

RIS

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T1 - On “Space” and “Geometry” in the Nineteenth Century

AU - Lützen, Jesper

PY - 2023

Y1 - 2023

N2 - 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.

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.

U2 - 10.1007/978-3-031-40855-7_13

DO - 10.1007/978-3-031-40855-7_13

M3 - Book chapter

T3 - Archimedes

SP - 317

EP - 339

BT - The Richness of the History of Mathematic

PB - Springer

ER -

ID: 380358962