[FOM] Gauss and non-Euclidean geometry

S. S. Kutateladze sskut at math.nsc.ru
Sun Oct 21 21:24:03 EDT 2007

Antonino Drago wrote:
Antonino Drago> Moreover, Gauss promoted Lobachevsky in the Goettengen Academy.
Antonino Drago> But he never manifested his knowledge about
Antonino Drago> non-Eclidean geometries, not 
Antonino Drago> even when he maliciously chose the third subject out of the three subjects
Antonino Drago> Riemann submitted for his Habilitation thesis...
Antonino Drago> Riemann was obliged to employ 
Antonino Drago> a long time for having an idea of non-Euclidean
Antonino Drago> geometries and then he chose 
Antonino Drago> a different viewpoint with respect  to both
Antonino Drago> Lobachevsky and Bolyai. Gauss 
Antonino Drago> exited form the room of the discussion of this thesis by rubbing his hands.
Antonino Drago> At present Gauss' covert attitude about this subject is known by his 
Antonino Drago> correspondence he had with several mathematicians of his time. When the
Antonino Drago> father of Bolyai sent his geometrical work including the appendix wrote by
Antonino Drago> his son about the so-alled absolute geometry, Gauss answered: I cannot
Antonino Drago> praise your son because I would prise myself, since I had the same ideas
Antonino Drago> since so long time..." A very starnge semtence, that led Bolyai son to think
Antonino Drago> a Gauss' plagiarism; so that he abandoned his researches.

I think that we should distinguish between the traditional view if
what happened in the past from  what did  happen in  reality. 
The general  view of the story which is mostly unfavorable to Gauss 
was born ten decades ago  in the times when only a few understood the 
true mathematics behind  the works of Gauss, Bolyai, and  Lobachevsky.  
This is no denying that Gauss understood not less that Lobachevsky or
Bolyai in mathematics. The converse is false.

Gauss rubbed his hands or Bolyai thought about plagiarism
are  what we know by hearsay and evidence. I fo not dispute these
fact, buy I question their importance.
For me these details mean much less than the indisputable differences
of the participants in the mathematical technique and understanding
of the geometry of surfaces if variable curvature. 
Gauss was undoubtedly more knowledgeable and saw all
non-Euclidean effects locally before Lobachevsky and Bolyai.

He had  never plagiarized anything from Bolyai or
Lobachevsky. Moreover,  he had little if anything new to find from
their writings mathematically.
He might reveal some discontent or even envy that he underestimated 
the topical question of non-Euclidean geometry.  These things are
human follies and happen every now and then. 

The unfavorable comments on Gauss belong to the
public domain and stem from the times when the mathematics 
of the story was completely unknown to the public. 
The mathematical and logical backgrounds 
of this matter are of relevance and convince much more than 
the common  explanations in terms of human follies.

Gauss was accused primarily by the general habit of
the  presumption of guiltiness and the immortal public ignorance 
of mathematics. I see not a bit of prejudice or immorality
in his comments on the papers of Lobachevsky and Bolyai.

Sobolev Institute of Mathematics
Novosibirsk State University
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