Subject: Re: [HM] Caratheodory, Klein & Grassman
From: Dominique Flament (flament@msh-paris.fr)
Date: Tue Mar 21 2000 - 03:00:18 EST
[Bill Everdell]
>
> No argument on the _Ausdehnungslehre_'s importance (which seems to grow
> with every mathematical innovation I look at in the period 1872-1913),
> but that importance was not recognized when Grassmann published it in
> 1844. So, it had occurred to me that, given the book's "geometrization"
> of so much of then current mathematics, the relative clout given to
> geometry with respect to algebra and arithmetic in German schools in the
> generation between Grassmann's and Frege's might help explain the book's
> circuitously extra-academic fate.
[John Conway]
>
> I doubt this very much. I think the book's fate was quite a likely
> one, given its content and the time and style in which it was written.
> The book was filled not only with new ideas, but also with new language
> (I think necessarily so) for explaining those ideas, which readers had to
> absorb before they could see whether they were valuable or not. So it's
> not surprising that there were so few people who read very much of it.
Dear John,
Thank you very much for your reply.
Concerning Hermann G\"unther Grassmann, it could be of special interest to
have a look at :
G. Ch\^atelet, ``Capture de l'Extension comme Dialectique G\'eom\'etrique :
Dimension et Puissance Selon l'Ausdehnung de Grassmann",
{\it Lectures Notes in Physics}, {\bf 402} (1992), {\it 1830-1930~:
A Century of Geometry},222-244.
D. Flament, ``La `lineale Ausdehnungslehre' (1844) de Hermann G\"unther
Grassmann", {\it Lectures Notes in Physics}, {\bf 402} (1992), {\it
1830-1930 : A Century of Geometry}, 205-221.
D. Flament, Hermann G\"unther Grassmann. La science de la grandeur
extensive. La {\it lineale Ausdehnungslehre} (Trad. B. Bekemeier et D.
Flament, Preface de D. Flament), Librairie Scientifique et Technique Albert
Blanchard, Paris, 1994.
D. Flament (s.d.) Le nombre une hydre \' a n visages ; entre nombres et
vecteurs. Editions de la Maison des Sciences de l'Homme, Paris, 1997.
Lloyd. C. Kannenberg, A New Branch of Mathematics. The {\it
Ausdehnungslehre} of 1844, and Others Works. Hermann Grassmann. (Translated
by Lloyd. C. Kannenberg ; Forword by Albert C. Lewis). Open Court, Chicago
and La Salle, Ilinois, 1995.
Gert Schubring (ed.), Hermann G\"unther Grassmann (1809-1877): Visionary
Mathematician, Scientist and Neohumanist Scholar. {\it Papers from a
Sesquicentennial Conference}, Boston Studies in the Philosophy of Science
(BSPS), Volume 187, Kluwer Academic Publishers,
Dordrecht/Boston/London,1996.
Arno Zaddach, Grassmanns Algebra in der Geometrie, mit Seitenblicken auf
verwandte Strukturen. Mannheim; Leipzig; Wien; Z\¨urich:
BI-Wissenschaftsverlag, 1994.
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