Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
email: rylov@ipmnet.ru
Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm
Updated
The reasons of
the crisis in the contemporary (Riemannian) geometry are discussed. The
conventional method of the generalized geometries construction, based on a use
of the topology, leads to a overdetermination
of the Riemannian geometry. In other words, at the Riemannian geometry
construction one uses the needless information (topology), which disagrees with
other original axioms. The crisis manifests in the fact, that the mathematical
community cannot see and does not want to see the overdetermination of the
Riemannian geometry. The most geometers-topologists deny the alternative method
of the generalized geometry construction, which does not uses the topology,
because it does not contain theorems. Most geometers see the geometry
presentation as a set of definitions and theorems. They cannot imagine the
geometry presentation without customary theorems. As a result the most clever
topologists, which have acknowledged the negligible role of the topology in the
geometry construction and inconsistency of the conventional method of the
generalized geometry construction, appear in the difficult situation (conflict
with the mathematical community).
There is
text of the paper in English (ps, pdf ) and in Russian (ps, pdf)