Poincaré is a pre-eminent figure: as one of the greatest of mathematicians; as a contributor of prime importance to the development of physical theory at a time when physics was undergoing a profound transformation; and as a philosopher. However, I think that Poincaré, with all this virtue, made a serious philosophical mistake. In Poincaré’s own work, this error seems to me to have kept him from several fundamental discoveries in physics.As Stein admits, claiming that Poincare did not understand what he was saying is to hypothesize something that has never happened in the entire history of physics.
It quotes Poincare making the following points.
1. Poincare presents a relativity theory with electromagnetic and gravitational force both propagate at the speed of light. This remarkable coincidence has two possible explanations. Lorentz would say that it is because gravity and everything else has an electromagnetic origin.
2. Poincare proposes a more radical explanation, which he analogizes to Copernicus differing from Ptolemy. His idea is that relativity is about how we do spacetime measurements, and therefore applies to all forces.
Stein quotes Poincare saying all this, and is baffled by it, because it is about eight years ahead of Einstein.
Here is another silly argument:
No one referred to Poincare's 1905/6 papers in subsequent years and Einstein was unaware of them until the 1950s. Minkowski did not reference Poincare's work. Poincare wrote a semi-popular article in 1908, and that was all. Without the controversy started by E. T. Whitaker and discussed in this WP article, Poincare's 1905/6/8 papers might have languished in obscurity.No, Poincare's papers were more influential than Einstein's, at the time. Here is Minkowski's big paper on relativity, and as you can see, it references Poincare's big 1905/6 paper twice. These two papers were the most important relativity papers after Lorentz's, and formed the basis of all subsequent work. They were known to Einstein at the time, and to everyone else with an interest in relativity.
Poincare's paper was in French, but Einstein was fluent in French, as he had attended a French-speaking university. Relativity quickly became widely accepted because of these papers, not Einstein's. Both papers would have been tough reading for physicists of the day, but both had shorter summary versions that were widely distributed and read. See translations here: Poincare and Minkowski.
There is still a question that begs for explanation. It may be unique in the history of science. In 1905, Poincare was maybe the most respected scientist or mathematician in all of Europe. Certainly one of the most famous and respected. In 1904 he wrote a paper declaring an entirely new mechanics based on the speed of light. In 1905 he published a long paper on his relativity, comparing it to Copernican heliocentrism, and the work immediately became the basis of all XX century physics.
And yet there are scholars today who claim that no one ever noticed Poincare's papers, and that all the credit should belong to Einstein instead. None of them can tell us anything that Einstein did that was original, so they resort to arguments that Lorentz and Poincare did not know what they were doing!
This is like saying that Copernicus should not get any credit for heliocentrism because he did not understand that the Earth revolved around the Sun in his model.
Einstein went on to spend most of his post-1920 career arguing against quantum mechanics and pursuing silly unified field theories. Other physicists accomplishment many great things, but there is a signiticant faction even today that says goofy things about quantum mechanics and proposes grand untestable theories.
Update: The Wikipedia discussion ended without adding the remarks about Poincare not knowing what he was doing, or that Minkowski failed cite Poincare. The article remains heavily biased towards the views of Einstein scholars who favor crediting Einstein, but the facts presented are quite historically accurate, and you can decide for yourself.