Petsche, Hans-Joachim (Author)
Annals of Science: The History of Science and Technology
Volume: 71, no. 4
Issue: 4
Pages: 522-576
Albert Lewis's article (Annals of Science, 1977) analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra. Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that: i. Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein. ii. Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways. iii. Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a `chemical conjunction`, which was developed largely dialectically by Hermann.
...MoreSimilar Citations
Article
Schubring, Gert;
(2010)
Hermann Graßmann -- Zwei sich unterscheidende Lebensläufe
(/isis/citation/CBB001033963/)
Book
Petsche, Hans-Joachim;
Kannenberg, Lloyd;
Keßler, Gottfried;
Liskowacka, Jolanta;
(2009)
Hermann Graßmann. Roots and Traces. Autographs and Unknown Documents
(/isis/citation/CBB001022166/)
Book
Petsche, Hans-Joachim;
(2006)
Graßmann
(/isis/citation/CBB000953012/)
Book
Petsche, Hans-Joachim;
(2009)
Herman Graßmann
(/isis/citation/CBB001022164/)
Article
Lewis, Albert C.;
(2004)
The Unity of Logic, Pedagogy and Foundations in Grassmann's Mathematical Work
(/isis/citation/CBB000740608/)
Chapter
Lewis, Albert C.;
(1981)
F. Schleiermacher's influence on H. Grassmann's mathematics
(/isis/citation/CBB000020260/)
Article
Lewis, Albert C.;
(1977)
H. Grassmann's 1844 Ausdehnungslehre and Schleiermacher's Dialektik
(/isis/citation/CBB000027158/)
Article
Hyder, David Jalal;
(2001)
Physiological Optics and Physical Geometry
(/isis/citation/CBB000102561/)
Book
Grassmann, Hermann;
(2000)
Extension Theory
(/isis/citation/CBB000471625/)
Article
Manning, Gideon;
(2013)
The History of “Hylomorphism”
(/isis/citation/CBB001212818/)
Book
Lützen, Jesper;
(2001)
Around Caspar Wessel and The Geometric Representation of Complex Numbers
(/isis/citation/CBB000550714/)
Article
Echeverria, Javier;
(1979)
L'analyse géométrique de Grassmann et ses rapports avec la caractéristique géométrique de Leibniz
(/isis/citation/CBB000006125/)
Article
Fearnley-Sander, Desmond;
(1979)
Hermann Grassmann and the creation of linear algebra
(/isis/citation/CBB000014442/)
Chapter
Lewis, Albert C.;
(1981)
Justus Grassmann's school programs as mathematical antecedents of Hermann Grassmann's 1844 Ausdehnungslehre
(/isis/citation/CBB000008949/)
Article
Pedrazzi, Maino;
(1980)
Spazio e movimento da Hermann Grassmann a Felix Klein
(/isis/citation/CBB000003874/)
Article
Darrigol, Olivier;
(2003)
Number and Measure: Hermann von Helmholtz at the Crossroads of Mathematics, Physics, and Psychology
(/isis/citation/CBB000340891/)
Article
Alberto Cogliati;
(2018)
Sulla ricezione del "Theorema Egregium," 1828-1868
(/isis/citation/CBB513903674/)
Article
Ferreirós, José;
(2004)
The Motives behind Cantor's Set Theory -- Physical, Biological, and Philosophical Questions
(/isis/citation/CBB000500123/)
Article
Adrian Rice;
Ezra Brown;
(2016)
Commutativity and Collinearity: A Historical Case Study of the Interconnection of Mathematical Ideas. Part Ii
(/isis/citation/CBB506323405/)
Book
Remmert, Volker R.;
Schneider, Ute;
(2008)
Publikationsstrategien einer Disziplin: Mathematik in Kaiserreich und Weimarer Republik
(/isis/citation/CBB000951941/)
Be the first to comment!