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Graßmann’s sources of inspiration

  • Hans-Joachim Petsche

Abstract

As we have already learned in previous sections, Hermann Graßmann and his father shared a common approach to scientific research. Unfortunately, this relationship has received little attention in scientific literature. Apart from the author’s dissertation from 1978 (Petsche 1979a), on which we will largely rely here, recent publications have discussed the influence of the Romantic philosophy of nature on Justus Graßmann (Heuser 1996) and the influence of Justus Graßmann’s vector algebraic approaches on the work of Hermann Graßmann (Scholz 1996). An analysis of Justus Graßmann’s ideas concerning the structure of mathematics and the foundations of arithmetic, and of the subsequent impact of these ideas on his son, has also been published (Radu 2000).

Keywords

Natural Science Extension Theory French Revolution Pure Theory Emphasis Mine 
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Notes

  1. 1.
    This textbook would never have been published “had it not been the will of the highest authority to use one single textbook for the entire mathematical curriculum in all secondary schools. Therefore, we either needed to put together such a book, or we needed to choose among the ones we already had.” (1835, p. iv) Given the fact that this textbook contains, more than any prior work, interesting thoughts on the negative magnitude in mathematics and on the sum and the product in geometry, phenomena which Hermann Graßmann intensely worked on in 1830/31 and 1834, it is quite surprising that M. Radu’s (2000) remarkable analysis ignores the textbook completely.Google Scholar
  2. 2.
    M. Radu links Bartholdy (and, as a consequence, J. Graßmann) only to Humboldt’s secondary-school reforms, in which Bartholdy played a significant part (Radu 2000, p. 87sq.). But concerning their two books, this connection was irrelevant because they had been written with the schools for the poor in mind. Also, it is risky to connect J. Graßmann to Kant and Fichte via Humboldt (ibidem, p. 88sq.) because, in fact, Bartholdy and Schleiermacher were close friends. Therefore, since Bartholdy was a follower of Pestalozzi, his theories on individuality, intuition and construction (as in the case of J. Graßmann) probably were inspired by the latter. This fact reduces the force of all arguments claiming that Graßmann was inspired by I. Kant, J. Schultz and J. F. Fries.Google Scholar
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    J. Graßmann 1824, p. iv.Google Scholar
  4. 4.
    It is surprising that in her excellent analysis of the contemporary concept of mathematics, M. Radu (2000) mentioned neither J. Schmid, nor Pestalozzi. Many of Graßmann’s ideas were taken from J. Schmid and were not originally his own.Google Scholar
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    In On the Concept and Extent of the Pure Theory of Number, J. Graßmann remarked in a footnote that he was currently working on a treatise “on general and geometric combination theory” (ZL, p. 2).Google Scholar
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    Apart from Robert Graßmann, the later minister of defence, G. von Kameke, a teacher from the “Friedrich-Wilhelmschule” ( Jungklaß) and Graßmann’s brother-in-law Scheibert, the headmaster of the “Friedrich-Wilhelmschule”, belonged to this circle. See BIO, p. 92.Google Scholar
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    Gert Schubring (1996d) answers all these questions affirmatively.Google Scholar
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Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Hans-Joachim Petsche
    • 1
  1. 1.PotsdamGermany

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