Reminiscences of International Congresses of Mathematicians
By Dr. Mohsen Hashtroudi
This congress was the last international congress of mathematicians before the World War
II. One night after finishing the session of differential geometry and topology, the late
Cartan (Élie Cartan) and Schouten (who is now the president of Amsterdam mathematics
center) and Hermann Weyl and a group of researchers in tensor calculus and connection
theory negotiated and discussed. Alleys in Moscow in vicinity of Kremlin almost all lead to
Kremlin, indeed they are centralized. The late Weyl propounded this question that: “is there
a geometrical measure that its all geodesics (the shortest distance, here it should be pointed
out that in all measure spaces, geodesics and straight lines don not coincide with each other,
namely, between two points, there exist a straight line and a shortest curve that are distinct)
are centralized?” That night, after separation of this group Schouten overnight found this
connection that at present in his name in Russia it is known as Schouten connection. Strangely
in western countries this connection is called sometimes as Moscow connection.
The author of this lines determined intimate properties of this connection about 15 years ago
and simultaneously André Lichnerowicz, the professor in Collége de France, proved also
that among point spaces (spaces which are introduced just with point not with a point and a
line nor a point and a plane), the only space that are connected to nonholonomic analytical
mechanics, is the same semi-symmetric Schouten connection. This connection is called semi-
symmetric since torsion of space is determined by a vector just by using main tensor (this
space is obviously is nor a usual space, namely, it has curvature and torsion of space is related
to transportation of the origin of coordinates).
Such as this issue has happened in many congresses that a problem has been posed in a
session of a field or even out of that and an overnight it has been solved by one of mighty
mathematician.
Translated by Fariba Elliee
By Dr. Mohsen Hashtroudi
This congress was the last international congress of mathematicians before the World War
II. One night after finishing the session of differential geometry and topology, the late
Cartan (Élie Cartan) and Schouten (who is now the president of Amsterdam mathematics
center) and Hermann Weyl and a group of researchers in tensor calculus and connection
theory negotiated and discussed. Alleys in Moscow in vicinity of Kremlin almost all lead to
Kremlin, indeed they are centralized. The late Weyl propounded this question that: “is there
a geometrical measure that its all geodesics (the shortest distance, here it should be pointed
out that in all measure spaces, geodesics and straight lines don not coincide with each other,
namely, between two points, there exist a straight line and a shortest curve that are distinct)
are centralized?” That night, after separation of this group Schouten overnight found this
connection that at present in his name in Russia it is known as Schouten connection. Strangely
in western countries this connection is called sometimes as Moscow connection.
The author of this lines determined intimate properties of this connection about 15 years ago
and simultaneously André Lichnerowicz, the professor in Collége de France, proved also
that among point spaces (spaces which are introduced just with point not with a point and a
line nor a point and a plane), the only space that are connected to nonholonomic analytical
mechanics, is the same semi-symmetric Schouten connection. This connection is called semi-
symmetric since torsion of space is determined by a vector just by using main tensor (this
space is obviously is nor a usual space, namely, it has curvature and torsion of space is related
to transportation of the origin of coordinates).
Such as this issue has happened in many congresses that a problem has been posed in a
session of a field or even out of that and an overnight it has been solved by one of mighty
mathematician.
Translated by Fariba Elliee
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