[FOM] Gauss and non-Euclidean geometry
S. S. Kutateladze
sskut at math.nsc.ru
Mon Oct 22 22:13:01 EDT 2007
Please READ:
CAUCHY WAS NOT SUCCESSFUL
in my previous post:
For instance, you write that Cauchy tried to expel
infinitesimals but we know now definitely that he was NOT successful and
Robinson explained that the approach of Cauchy to analysis was based
intrinsically on actual infinities. Cauchy had never made the so-called
Cauchy error in pointwise convergence he was accused for about two and
a half centuries. However, the same "Beothians' cries" as in the times of
Gauss made him acknowledge the "error" he had never
committed and he even presented the same proof as excuse in fact
after the Abel criticism. We now see the whole story about Cauchy and
infinitesimals in better proportions than prior to Robinson.
The modern views of Cantor's set theory is much subtler and deeper
that the point of view implied in your question. The present
knowledge enables us to see Cantors immortal revelations in much
better proportion than it was possible for Russell.
It is an easy matter to expatiate about this and other of your
questions along the same lines.
Sincerely yours, S. S. Kutateladze
_____________________________________________________
Sobolev Institute of Mathematics
Novosibirsk State University
mailto: sskut at math.nsc.ru
copyto: sskut at academ.org
homepages: http://www.math.nsc.ru/LBRT/g2/english/ssk/cv.html (in English)
http://www.math.nsc.ru/LBRT/g2/ruswin/ssk/index.html (in Russian)
More information about the FOM
mailing list