Subject: Re: [HM] Caratheodory, Klein & Grassman
From: John Conway (conway@math.Princeton.EDU)
Date: Mon Mar 20 2000 - 14:02:35 EST
On Mon, 20 Mar 2000, Bill Everdell wrote:
> 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.
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.
The world just wasn't ready for this book at that time. Later, when
the simpler ones of Grassman's ideas had been to some extent absorbed from
the more easily-read works of Gibbs, Cayley, Hamilton, Sylvester, ... ,
it became much easier to read, and its pioneering value became evident.
> I assume that _Lineale Ausdehnungslehre_ was reviewed
> when it first came out, and perhaps again when it was enlarged in 1862, and
> (now that John Conway has given me a second excuse to waddle over to NYU's
> Courant Institute library) I shall go and find out; but I would appreciate
> anyone's help on where to look.
This would be interesting - let me know what you find out. I seem to
remember reading of a rather dismissive review, and it would be nice to
hear exactly what it said.
John Conway
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