[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
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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