“The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity.”

as quoted by Dennis Overbye, Einstein in Love: A Scientific Romance (2001)

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Hermann Minkowski11

German mathematician and physicist 1864–1909

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“After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the bases of experience or according to Maxwell's equations.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

1940s, "Autobiographical Notes" (1949)
Context: Reflections of this type made it clear to me as long ago as shortly after 1900, i. e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. By and by I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results.... How, then, could such a universal principle be found? After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the bases of experience or according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the stand-point of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest.