Question: Who helped reconcile the peculiarities of classical electromagnetism?
About the article "Electromagnetism", section "Classical electrodynamics".

Candidate passages:
The scientist William Gilbert proposed, in his "De Magnete" (1600), that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects.
Mariners had noticed that lightning strikes had the ability to disturb a compass needle, but the link between lightning and electricity was not confirmed until Benjamin Franklin's proposed experiments in 1752.
One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle.
However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment.
Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.
A theory of electromagnetism, known as classical electromagnetism, was developed by various physicists over the course of the 19th century, culminating in the work of James Clerk Maxwell, who unified the preceding developments into a single theory and discovered the electromagnetic nature of light.
In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.
One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity.
According to Maxwell's equations, the speed of light in a vacuum is a universal constant, dependent only on the electrical permittivity and magnetic permeability of free space.
This violates Galilean invariance, a long-standing cornerstone of classical mechanics.
One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume the existence of a luminiferous aether through which the light propagates.
However, subsequent experimental efforts failed to detect the presence of the aether.
After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism.
(For more information, see History of special relativity.
)In addition, relativity theory shows that in moving frames of reference a magnetic field transforms to a field with a nonzero electric component and vice versa; thus firmly showing that they are two sides of the same coin, and thus the term "electromagnetism".
(For more information, see Classical electromagnetism and special relativity and Covariant formulation of classical electromagnetism.
Timeline of electromagnetism and classical optics 
Examples of four-vectors in electromagnetism include the following. 
General classical equations 
 Permeability (electromagnetism), the degree of magnetization of a material in response to a magnetic field.
Vacuum permeability, permeability of free space or magnetic constant, a physical constant, the value of magnetic permeability in a classical vacuum.