Many people assume that Einstein was a leader in this movement, but he was not. When Minkowski popularized the spacetime geometry in 1908, Einstein rejected it. When Grossmann figured out to geometrize gravity with the Ricci tensor, Einstein wrote papers in 1914 saying that covariance is impossible. When a relativity textbook described the geometrization of gravity, Einstein attacked it as wrongheaded.
I credit Poincare and Minkowski with the geometrization of relativity. In 1905, Poincare had the Lorentz group and the spacetime metric, and at the time a Klein geometry was understood in terms of a transformation group or an invariant metric. He also implicitly used the covariance of Maxwell's equations, thereby integrating the geometry with electromagnetism. Minkowski followed where Poincare left off, explicitly treating world-lines, non-Eudlidean geometry, and covariance. Einstein had none of that. He only had an exposition of Lorentz's theorem, not covariance or spacetime or geometry.
For a historian's detailed summary of how Poincare and Minkowski developed the geometric view of relativity, see Minkowski, Mathematicians and the Mathematical Theory of
Relativity and The Non-Euclidean Style of Minkowskian Relativity by Scott Walter.
In 1900, physics textbooks were not even using vector notation. That is how far we have come. Today vectors are indispensable, but they are also more subtle than the average student realizes. Most physics books don't explain the geometry adequately.
Carlo Rovelli writes:
WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?This essay is included in a new book, This Idea Must Die: Scientific Theories That Are Blocking Progress (Edge Question Series), has a curious collection of opinions. It was promoted on a Science Friday broadcast.
We will continue to use geometry as a useful branch of mathematics, but is time to abandon the longstanding idea of geometry as the description of physical space. The idea that geometry is the description of physical space is engrained in us, and might sound hard to get rid of it, but it is unavoidable; it is just a matter of time. Better get rid of it soon.
Geometry developed at first as a description of the properties of parcels of agricultural land. In the hands of ancient Greeks it became a powerful tool for dealing with abstract triangles, lines, circles, and similar, and was applied to describe paths of light and movements of celestial bodies with very great efficacy. ...
In reality, they are quantum entities that are discrete and fluctuating. Therefore the physical space in which we are immersed is in reality a quantum dynamical entity, which shares very little with what we call "geometry". It is a pullulating process of finite interacting quanta.
I don't know what he has against geometry. Geometry is central to most of XX century physics, and no good alternative has been found.
There is no evidence that physical space is discrete or fluctuating. We do not even have proof that electrons are discrete. Sure, some observables have discrete spectrum. But our theories for nature itself are continuous, not discrete, and make heavy use of geometry.
I have previously commented on Rovelli's defense of Aristotle, Einstein, and free will.