Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T20:22:48.279Z Has data issue: false hasContentIssue false
  • English
  • Français

CERTAIN MODERN IDEAS AND METHODS: “GEOMETRIC REALITY” IN THE MATHEMATICS OF CHARLOTTE ANGAS SCOTT

Published online by Cambridge University Press:  05 March 2019

JEMMA LORENAT
JEMMA LORENAT*
Affiliation:
Pitzer College
*
*PITZER COLLEGE 1050 N MILLS AVENUE CLAREMONT, CA 91711, USA Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Charlotte Angas Scott (1858–1932) was an internationally renowned geometer, the first British woman to earn a doctorate in mathematics, and the chair of the Bryn Mawr mathematics department for forty years. There she helped shape the burgeoning mathematics community in the United States. Scott often motivated her research as providing a “geometric treatment” of results that had previously been derived algebraically. The adjective “geometric” likely entailed many things for Scott, from her careful illustration of diagrams to her choice of references and citations. This article will focus on Scott’s striking and consistent use of geometric to describe a reality of dynamic points, lines, planes, and spaces that could be manipulated analogously to physical objects. By providing geometric interpretations of algebraic derivations, Scott committed to an early-nineteenth-century aesthetic vision of a “whole” analytical geometry that she adapted to modern research areas.

Keywords

010200A30Charlotte Angus Scottgeometrymathematical aestheticsmathematical ontologyvisualizationnineteenth century
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 681 - 719
Check for updates
Copyright
Copyright © Association for Symbolic Logic 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Anonymous (1911). Geometry. In Chisholm, H., editor. Encyclopaedia Britannica: A Dictionary of Arts, Sciences, and General Literature, Volume 11. Franciscans to Gibson. Cambridge: Cambridge University Press, pp. 675–735.Google Scholar
Arana, A. & Mancosu, P. (2012). On the relationship between plane and solid geometry. Review of Symbolic Logic, 5 (2), 294–353.CrossRefGoogle Scholar
Barrow-Green, J. & Gray, J. (2006). Geometry at Cambridge, 1863–1940. Historia Mathematica, 33, 315–356.CrossRefGoogle Scholar
Brigaglia, A. & Ciliberto, C. (2003). Remarks on the relations between the Italian and American schools of algebraic geometry in the first decades of the 20th century. Historia Mathematica, 31(3), 310–319.CrossRefGoogle Scholar
Cayley, A. (1859). A sixth memoire upon quantics. Philosophical Transactions of the Royal Society of London, 149, 61–90.Google Scholar
Cayley, A. (1866). On the higher singularities of a plane curve. Quarterly Journal of Pure and Applied Mathematics, 7, 212–222.Google Scholar
Cayley, A. (1877). Curve. In Baynes, T. S. and Smith, W. R., editors. Encyclopaedia Britannica: A Dictionary of Arts, Sciences, and General Literature, Ninth Edition, Vol. 6. Edinburgh: A & C Black, pp. 716–728.Google Scholar
Cayley, A. (1896). Presidential address to the british association, southport, september 1883. In Press, C. U., editor. Mathematical Papers, Vol. XI. Cambridge: A. R. Forsyth, pp. 429–459.Google Scholar
Clebsch, A. (1872). Zum Gedächtnis an Julius Plücker. Göttingen: Dieterichschen Buchhandlung.Google Scholar
Cole, F. N. (1896). Modern methods of analytical geometry. Bulletin of the American Mathematical Society, 2(8), 265–271.CrossRefGoogle Scholar
College, B. M. (1903). Bryn Mawr College Calendar 1900–1903.Google Scholar
Crilly, T. (2005). Arthur Cayley: Mathematician Laureate of the Victorian Age. Baltimore: Johns Hopkins University Press.Google Scholar
Detlefsen, M. & Arana, A. (2011). Purity of methods. Philosopher’s Imprint, 11(2), 1–20.Google Scholar
Dunham, W. (2016). Bertrand Russell at Bryn Mawr. The Mathematical Intelligencer, 38(3), 30–40.CrossRefGoogle Scholar
Goldstein, C. (2016). “Découvrir des principes en classant”: la classification des formes quadratiques selon Charles Hermite. Cahiers François Viète, III(1), 103–135.Google Scholar
Gray, J. (2008). Plato’s Ghost: The Modernist Transformation of Mathematics. Princeton: Princeton University Press.CrossRefGoogle Scholar
Henrici, O. (1877). Geometry. In Baynes, T. S. and Smith, W. R., editors. Encyclopaedia Britannica: A Dictionary of Arts, Sciences, and General Literature, Volume 10 G. – Got. Edinburgh: A & C Black, pp. 376–420.Google Scholar
Henrici, O. (1883). Opening address in section a (mathematics) at the meeting of the british association at southport. Nature, 28, 497–500.Google Scholar
Hilbert, D. (1899). Grundlagen der Geometrie. Leipzig: B. G. Teubner.Google Scholar
Hirst, T. A. (1865). On the quadric inversion of plane curves. Proceedings of the Royal Society London, 14, 91–106.Google Scholar
Kenschaft, P. C. (1982a). The students of Charlotte Angas Scott. Mathematics in College, Fall 1982, 16–20.Google Scholar
Kenschaft, P. C. (1982b). Women in mathematics around 1900. Signs, 7(4), 906–909.CrossRefGoogle Scholar
Kenschaft, P. C. (1987). Charlotte Angas Scott, 1858–1931. The College Mathematics Journal, 18(2), 98–110.CrossRefGoogle Scholar
Klein, F. (1893a). A comparative review of recent researches in geometry. Bulletin of the New York Mathematical Society, 2, 215–249.CrossRefGoogle Scholar
Klein, F. (1893b). The Evanston Colloquium: Lectures on Mathematics. New York: The American Mathematical Society.Google Scholar
Klein, F. (1893c). Vergleichende Betrachtungen über neuere geometrische Forschungen. Mathematische Annalen, 43, 460–497.Google Scholar
Klein, F. (1926). In Courant, R. and Neugebauer, O., editors. Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. Berlin: Springer.Google Scholar
Lê, F. & Paumier, A.-S. (2016a). De la science comme classification à la classification comme pratique scientifique: quelques réflexions à partir de deux cas mathématiques. Cahiers François Viète, III(1), 9–34.Google Scholar
Lê, F. & Paumier, A.-S. (2016b). La classification comme pratique scientifique. Cahiers François Viète, III(1).Google Scholar
Loria, G. (1893). A few remarks on the ‘Syllabus of Modern Plane Geometry,’ issued by the A.I.G.T. General Report (Association for the Improvement of Geometrical Teaching), 19, 49–53.Google Scholar
Luciano, E. & Roero, C. S. (2016). Corrado Segre and His Disciples: the Construction of an International Identity for the Italian School of Algebraic Geometry. In Casnati, G., Conte, A., Gatto, L., Giacardi, L., Marchisio, M., and Verra, A., editors. From Classical to Modern Algebraic Geometry, Corrado Segre’s Mastership and Legacy. Cham: Springer, pp. 93–242.CrossRefGoogle Scholar
M., E. N. (1897). The Russell lectures. The Lantern Bryn Mawr, 137–138.Google Scholar
Macaulay, F. S. (1932). Dr. Charlotte Angas Scott. Journal of the London Mathematical Society, 1–7(3), 230–240.CrossRefGoogle Scholar
Mach, E. (1902). On the psychology and natural development of geometry. The Monist, 12(4), 481–515.CrossRefGoogle Scholar
Maddison, I. & Lehr, M. (1932). Charlotte Angas Scott: An appreciation. Bryn Mawr Alumnae Bulletin, 12, 9–12.Google Scholar
Mancosu, P., Jørgensen, K. F., & Pedersen, S. A. (editors) (2005). Visualization, Explanation and Reasoning Styles in Mathematics. Dordrecht: Springer.CrossRefGoogle Scholar
Marchisotto, E. A. C. (2006). The projective geometry of Mario Pieri: A legacy of Georg Karl Christian von Staudt. Historia Mathematica, 33, 277–314.CrossRefGoogle Scholar
Maurizio Avellone, A. B. & Zappulla, C. (2002). The foundations of projective geometry in Italy from De Paolis to Pieri. Archive for the History of Exact Sciences, 56(5), 363–425.CrossRefGoogle Scholar
Morgan, A. D. (1849). Trigonometry and Double Algebra. London: Taylor, Walton and Maberly.Google Scholar
Netz, R. (1999). The Shaping of Deduction in Greek Mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Nöther, M. (1875). Ueber die singulӓren Werthsysteme einer algebraischen Function und die singulären Punkte einer algebraischen Curve. Mathematische Annalen, 9, 166–182.CrossRefGoogle Scholar
Parshall, K. H. (2011). Victorian algebra: The freedom to create new mathematical entities. In Raymond Flood, A. R. and Wilson, R., editors. Mathematics in Victorian Britain. Oxford: Oxford University Press, pp. 339–356.Google Scholar
Parshall, K. H. (2015). Training Women in Mathematical Research: The First Fifty Years of Bryn Mawr College (1885–1935). Mathematical Intelligencer, 37(2), 71–83.CrossRefGoogle Scholar
Parshall, K. H. & Fenster, D. (1994). Women in the American Mathematical Research Community: 1891–1906. In David, E. Rowe, J. M., and Knobloch, E., editors. The History of Modern Mathematics. 3: Images, Ideas, and Communities. London: Academic Press, pp. 179–227.Google Scholar
Plücker, J. (1827). Géométrie analytique. Mémoire sur les contacts et sur les intersections des cercles. Annales de mathématiques pures et appliquées, XVIII, 29–47.Google Scholar
Plücker, J. (1828). Analytisch-geometrische Entwicklungen, Vol. 1. Essen: G. D. Baedeker.Google Scholar
Plücker, J. (1839). Theorie der algebraischen Curven gegründet auf eine neue Behandlungsweise der analytischen Geometrie. Bonn: Adolph Marcus.Google Scholar
Poincaré, H. (1902). Du rôle de l’intuition et de la logique en mathématiques. In Duporcq, E., editor. Compte rendu du deuxième Congrès international des Mathématiciens tenu à Paris du 6 au 12 août 1900. Paris: Gauthier-Villars, pp. 115–130.Google Scholar
Poncelet, J. V. (1817). Philosophie mathématique. Réflexions sur l’usage de l’analise algébrique dans la géométrie; suivies de la solution de quelques problèmes dépendant de la géométrie de la règle. Annales de mathématiques pures et appliquées, 8, 141–155.Google Scholar
Putnam, E. J. (1922). Celebration in Honor of Professor Scott. Bryn Mawr Alumnae Bulletin, 2(5), 12–14.Google Scholar
Richards, J. (1988). Mathematical Visions: The Pursuit of Geometry in Victorian England. San Diego: Academic Press.Google Scholar
Russell, B. (1897). An Essay on the Foundations of Geometry. Cambridge: Cambridge University Press.Google Scholar
Salmon, G. (1848). A Treatise on Conic Sections. London: Longmans, Green.Google Scholar
Salmon, G. & Cayley, A. (1879). A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic Sections (1852) (third edition). Dublin: Hodges, Foster, and Figgis.Google Scholar
Scott, C. A. (1886). The Binomial equation x p - 1 = 0. American Journal of mathematics, 8(3), 261–264.CrossRefGoogle Scholar
Scott, C. A. (1892). Edwards’ differential calculus. Bulletin of the New York Mathematical Society, 1(2), 217–223.CrossRefGoogle Scholar
Scott, C. A. (1892b). On the higher singularities of plane curves. American Journal of mathematics, 14(4), 301–325.CrossRefGoogle Scholar
Scott, C. A. (1893). The nature and effect of singularities. American Journal of mathematics, 15(3), 221–243.CrossRefGoogle Scholar
Scott, C. A. (1894). An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry. London: Macmillan.Google Scholar
Scott, C. A. (1895). Arthur Cayley. Bulletin of the American Mathematical Society, 1(6), 133–141.CrossRefGoogle Scholar
Scott, C. A. (1897a). Letter to Felix Klein. April 14, 1897. Georg-August-Universität Göttingen Niedersächsische Staats- und Universitätsbibliothek. Ms F. Klein 11:948.Google Scholar
Scott, C. A. (1897b). Letter to Felix Klein. March 19, 1897. Georg-August-Universität Göttingen Niedersächsische Staats- und Universitätsbibliothek. Ms F. Klein 11:947.Google Scholar
Scott, C. A. (1897c). On Cayley’s theory of the absolute. Bulletin of the American Mathematical Society, 3(7), 235–246.CrossRefGoogle Scholar
Scott, C. A. (1897d). Plücker’s collected papers. Bulletin of the American Mathematical Society, 4(3), 121–126.CrossRefGoogle Scholar
Scott, C. A. (1899a). A proof of Noether’s fundamental theorem. Mathematische Annalen, 52, 593–597.CrossRefGoogle Scholar
Scott, C. A. (1899b). Studies in the transformation of plane algebraic curves. Quarterly Journal of Pure and Applied Mathematics, 29, 329–381.Google Scholar
Scott, C. A. (1900a). Note on the geometrical treatment of conics. Annals of Mathematics, 2(1), 64–72.CrossRefGoogle Scholar
Scott, C. A. (1900b). On a Memoir by Riccardo de Paolis. Bulletin of the American Mathematical Society, 7(1), 24–38.CrossRefGoogle Scholar
Scott, C. A. (1900c). On Von Staudt’s “Geometrie der Lage”. The Mathematical Gazette, 1(19), 307–314.CrossRefGoogle Scholar
Scott, C. A. (1900d). On Von Staudt’s “Geometrie der Lage” (Continued). The Mathematical Gazette, 1(20), 323–331.CrossRefGoogle Scholar
Scott, C. A. (1900e). On Von Staudt’s “Geometrie der Lage” (Continued). The Mathematical Gazette, 1(22), 363–370.CrossRefGoogle Scholar
Scott, C. A. (1900f). The international congress of mathematicians in Paris. Bulletin of the American Mathematical Society, 7(2), 57–79.CrossRefGoogle Scholar
Scott, C. A. (1903a). Compte rendu du deuxième Congrès international des Mathématiciens tenu à Paris du 6 au 12 août 1900. Procès-verbaux et Communications publiés par E. Duporcq. Bulletin of the American Mathematical Society, 9(4), 214–215.CrossRefGoogle Scholar
Scott, C. A. (1903b). Letter to M. Carey Thomas. August 1, 1896. Bryn Mawr College Archives. Box 153.Google Scholar
Scott, C. A. (1903c). Letter to M. Carey Thomas. August 2, 1903. Bryn Mawr College Archives. Box 155.Google Scholar
Scott, C. A. (1926). On the higher singularities of plane algebraic curves. Proceedings of the Cambridge Philosophical Society, 23, 206–232.CrossRefGoogle Scholar
Shapiro, S. (editor) (2007). The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford: Oxford University Press.Google Scholar
Smith, H. J. S. (1876). On the higher singularities of plane curves. Proceedings of the London Mathematical Society, 6(1), 153–182.Google Scholar
Toffoli, S. D. & Giardino, V. (2014). Forms and Rroles of diagrams in knot theory. Erkenn, 79, 829–842.CrossRefGoogle Scholar