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Across the centuries, the development and growth of mathematical
concepts have been strongly stimulated by the needs of mechanics.
Vector algebra was developed to describe the equilibrium of force
systems and originated from Stevin's experiments (1548-1620).
Vector analysis was then introduced to study velocity fields and
force fields. Classical dynamics required the differential calculus
developed by Newton (1687). Nevertheless, the concept of particle
acceleration was the starting point for introducing a structured
spacetime. Instantaneous velocity involved the set of particle
positions in space. Vector algebra theory was not sufficient to
compare the different velocities of a particle in the course of
time. There was a need to (parallel) transport these velocities at
a single point before any vector algebraic operation. The
appropriate mathematical structure for this transport was the
connection. I The Euclidean connection derived from the metric
tensor of the referential body was the only connection used in
mechanics for over two centuries. Then, major steps in the
evolution of spacetime concepts were made by Einstein in 1905
(special relativity) and 1915 (general relativity) by using
Riemannian connection. Slightly later, nonrelativistic spacetime
which includes the main features of general relativity I It took
about one and a half centuries for connection theory to be accepted
as an independent theory in mathematics. Major steps for the
connection concept are attributed to a series of findings: Riemann
1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918,
Cartan 1923, Eshermann 1950.
Across the centuries, the development and growth of mathematical
concepts have been strongly stimulated by the needs of mechanics.
Vector algebra was developed to describe the equilibrium of force
systems and originated from Stevin's experiments (1548-1620).
Vector analysis was then introduced to study velocity fields and
force fields. Classical dynamics required the differential calculus
developed by Newton (1687). Nevertheless, the concept of particle
acceleration was the starting point for introducing a structured
spacetime. Instantaneous velocity involved the set of particle
positions in space. Vector algebra theory was not sufficient to
compare the different velocities of a particle in the course of
time. There was a need to (parallel) transport these velocities at
a single point before any vector algebraic operation. The
appropriate mathematical structure for this transport was the
connection. I The Euclidean connection derived from the metric
tensor of the referential body was the only connection used in
mechanics for over two centuries. Then, major steps in the
evolution of spacetime concepts were made by Einstein in 1905
(special relativity) and 1915 (general relativity) by using
Riemannian connection. Slightly later, nonrelativistic spacetime
which includes the main features of general relativity I It took
about one and a half centuries for connection theory to be accepted
as an independent theory in mathematics. Major steps for the
connection concept are attributed to a series of findings: Riemann
1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918,
Cartan 1923, Eshermann 1950.
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