[FOM] Gauss and non-Euclidean geometry
S. S. Kutateladze
sskut at math.nsc.ru
Sat Oct 20 21:05:14 EDT 2007
Gauss wrote to Schumacher on Novermber 28, 1846 (I apologize for
a rough translation):
Recently I have a chance to look again through the Lobachevsky
book ... , Berlin 1840.... You know that I have the same
beliefs (since 1792) during 54 years (with some later enrichment
that I am disinclined to dwell upon here); so, as far as the
contents is concerned, I found nothing new for me in the
composition of Lobachevsky; however, the author, developing this
approach, travels in an another way completely different
from mine. I feel myself obliged to draw your attention to thus
book that will surely bring to you a quite exceptional
pleasure.
If you recall that Gauss was in full possession of surface theory
as its inventor (the ``Gauss curvature'' in particular) in contrast
to Lobachevsky and Bolyau who stood farther from differential geometry,
you will see that Gauss's technique and understanding of surface theory were at a higher level
than those by Lobachevsky and Bolyai. He was sincere and polite in his
views of the contributions by Lobachevsky and Bolyai as
appropriate for a great master appreciating the gems of genius of younger
persons but knowing much more about the area.
Gauss does not deserve a shade of reproach in my opinion.
S. Kutateladze
10/20/2007, you wrote to me:
Alasdair Urquhart> As for Gauss, there is no doubt that he anticipated Lobachevsky
Alasdair Urquhart> and Bolyai, but his dog-in-the-manger attitude to the discoveries
Alasdair Urquhart> of Bolyai and Lobachevsky did him little credit.
Alasdair Urquhart> Alasdair Urquhart
---------------------------------------------
Sobolev Institute of Mathematics
Novosibirsk State University
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