[FOM] Gauss and non-Euclidean geometry

S. S. Kutateladze sskut at math.nsc.ru
Thu Oct 25 14:14:15 EDT 2007

10/25/2007, Alasdair Urquhart wrote:

Alasdair Urquhart> of Janos Bolyai.  I was simply referring to his apparently
Alasdair Urquhart> grudging and ungenerous reactions to the ideas and
Alasdair Urquhart> results of other mathematicians in the area.  Here is a quote
Alasdair Urquhart> from W.K. Buhler:

Alasdair Urquhart>         From 1815 on, Gauss's attitude throughout the discussion
Alasdair Urquhart>         appears strangely rigid and indifferent; he seems to
Alasdair Urquhart>         confine himself to variations on the theme that everything
Alasdair Urquhart>         which others sent him had long been known to him.  Janos
Alasdair Urquhart>         Bolyai was particularly hurt when Gauss wrote to his father
Alasdair Urquhart>         that he had been familiar with Janos's results for the
Alasdair Urquhart>         last 30-50 years, a statement which was misleading if not
Alasdair Urquhart>         false.  It was in this context (letter to Bolyai of
Alasdair Urquhart>         March 6, 1832) that Gauss used the ominous phrase that
Alasdair Urquhart>         he must not praise Janos's work for "to praise it, would
Alasdair Urquhart>         mean to praise himself."
Alasdair Urquhart>                         Gauss, A Biographical Study, p. 102.

Alasdair Urquhart> Alasdair Urquhart

That is  just an opinionated interpretation of W.K. Buhler neglecting, for example, the
following  fact:

On February 14 ,1832 Gauss wrote to Gerling (Werke,VIII, p.290):

“I would also note that I have in the
last days received a small paper from
Hungary on Non-Euclidean geometry,
wherein I find reflected all of my
own ideas and results, developed with
great elegance—although for someone
to whom the subject is unknown,
in a form somewhat hard to follow,
because of the density. The author is a
very young Austrian officer, the son of
a friend of my youth, with whom I discussed
this theme very much in 1798,
although then my ideas were much
further from the development and
maturity, that they have attained
through this young man’s own reflection.
I hold this young geometer v.
Bolyai for a genius of the first order.”

Alasdair Urquhart> _______________________________________________
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Sobolev Institute of Mathematics
Novosibirsk State University
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