Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics.Symmetry was crucial to XX century physics, but not exactly as described in this paper.
Einstein changed physics forever by taking these ideas in a novel direction. He showed that rather than looking for symmetries that given laws satisfy, physicists should use symmetries to construct the laws of nature. This makes symmetries the defining property of the laws instead of an accidental feature. These ideas were taken very seriously by particle physicists. Their search for forces and particles are essentially searches for various types of symmetries.This is nonsense. Einstein did not do that. The particle physicists learned about symmetries from Noether and Weyl.
One of the most significant changes in the role of symmetry in physics was Einstein’s formulation of the Special Theory of Relativity (STR). When considering the Maxwell equations that describe electromagnetic waves Einstein realized that regardless of the velocity of the frame of reference, the speed of light will always appear to be traveling at the same rate. Einstein went further with this insight and devised the laws of STR by postulating an invariance: the laws are the same even when the frame of reference is moving close to the speed of light. He found the equations by first assuming the symmetry. Einstein’s radical insight was to use symmetry considerations to formulate laws of physics.No, that is more or less what Lorentz did in his 1895 paper. Lorentz used the Michelson-Morley experiment to deduce that light had the same speed regardless of the frame, and then proved his theorem of the corresponding states to show that Maxwell's equations had the same form after suitable transformations. He extended the theorem to frames going close to the speed of light in 1904. Einstein's famous 1905 paper added nothing to this picture.
Einstein’s revolutionary step is worth dwelling upon. Before him, physicists took symmetry to be a property of the laws of physics: the laws happened to exhibit symmetries. It was only with Einstein and STR that symmetries were used to characterize relevant physical laws. The symmetries became a priori constraints on a physical theory. Symmetry in physics thereby went from being an a posteriori sufficient condition for being a law of nature to an a priori necessary condition. After Einstein, physicists made observations and picked out those phenomena that remained invariant when the frame of reference was moving close to the speed of light and subsumed them under a law of nature. In this sense, the physicist acts as a sieve, capturing the invariant phenomena, describing them under a law of physics, and letting the other phenomena go.This sounds more like Poincare's 1905 relativity paper. It was the first to treat the Lorentz transformations as a symmetry group, and to look for laws of physics invariant under that group. He presented an invariant Lagrangian for electromagnetism, and a couple of new laws of gravity that obeyed the symmetry.
Einstein did not do any of this, and did not even understand what Poincare had done until several years later, at least.
The paper goes on to explain why symmetry is so important in mathematics.
A. Zee, completely independent of our concerns, has re-described the problem as the question of “the unreasonable effectiveness of symmetry considerations in understanding nature.” Though our notions of symmetry differ, he comes closest to articulating the way we approach Wigner’s problem when he writes that “Symmetry and mathematics are closely intertwined. Structures heavy with symmetries would also naturally be rich in mathematics” ([Zee90]:319).The Erlangen program was published in 1872, and would have been well-known to mathematicians like Poincare and Minkowski.
Understanding the role of symmetry however makes the applicability of mathematics to physics not only unsurprising, but completely expected. Physics discovers some phenomenon and seeks to create a law of nature that subsumes the behavior of that phenomenon. The law must not only encompass the phenomenon but a wide range of phenomena. The range of phenomena that is encompassed defines a set and it is that set which symmetry of applicability operates on. ...
All these ideas can perhaps be traced back to Felix Klein’s Erlangen Program which determines properties of a geometric object by looking at the symmetries of that object. Klein was originally only interested in geometric objects, but mathematicians have taken his ideas in many directions.
The preferred mathematical view of special relativity is that of non-Euclidean geometry. It can be understood in terms of geometrical invariants, like metric distances (proper time) and world lines, or in terms of the symmetries of that geometry, the Lorentz group. This was all very clearly spelled out by Poincare and Minkowski.
Separately, I see that Einstein score No. 2 on The 40 smartest people of all time.