http://www.bibliotecapleyades.net/esp_einstein.htm This site makes such claims including:

Jules Henri Poincaré (1854 - 1912) was a great scientist who made a significant contribution to special relativity theory. The Internet Encyclopedia of Philosophy website says that Poincaré: "sketched a preliminary version of the special theory of relativity" "stated that the velocity of light is a limit velocity" (in his 1904 paper from the Bull. of Sci. Math. 28, Poincaré indicated "a whole new mechanics, where the inertia increasing with the velocity of light would become a limit and not be exceeded") suggested that "mass depends on speed" ("formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest" "derived the Lorentz transformation" It is evident how deeply involved with special relativity Poincaré was.

Even Keswani (1965) was prompted to say that, "As far back as 1895, Poincaré, the innovator, had conjectured that it is impossible to detect absolute motion", and that "In 1900, he introduced 'the principle of relative motion' which he later called by the equivalent terms 'the law of relativity' and 'the principle of relativity' in his book, Science and Hypothesis, published in 1902". Einstein acknowledged none of this preceding theoretical work when he wrote his unreferenced 1905 paper.

In addition to having sketched the preliminary version of relativity, Poincaré provided a critical part of the whole concept - namely, his treatment of local time. He also originated the idea of clock synchronization, which is critical to special relativity.

Are these claims incorrect? I already know Hilbert was wrong. Edit: more info from quora: http://www.quora.com/Did-Einstein-plagiarize-Henri-Poincar%C3%A9?no_redirect=1

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    $\begingroup$ That is not the kind of website I'd expect to get reliable information from. This is not a physics question, anyway. Skeptics SE, maybe? $\endgroup$ – Hritik Narayan Sep 14 '15 at 5:50
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    $\begingroup$ Galileo and Newton already knew that absolute motion was not detectable, and so did Mach, they just couldn't make peace with that knowledge, for whatever reason. The Lorentz transformations were long known and established when Einstein wrote his paper and none of that was the problem. It doesn't seem like the author of your quote even understands what the problem was at that time. $\endgroup$ – CuriousOne Sep 14 '15 at 5:58
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    $\begingroup$ I'm voting to close this question as off-topic because it's about the history of science not physics. You might consider asking on the HSM SE. $\endgroup$ – John Rennie Sep 14 '15 at 6:08
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    $\begingroup$ @CuriousOne I'm not sure it's accurate to say Galileo didn't make peace with that knowledge. My impression, on reading the Dialogue Concerning the Two Chief World Systems (admittedly in modern English translation, since I don't read Italian), was that Galileo actively embraced the relativity principle as a wonderfully simplifying and organizing principle. $\endgroup$ – Selene Routley Sep 14 '15 at 6:18
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    $\begingroup$ Beware: the "Einstein was a fraud" meme has been rather fashionable in the last five years, particularly as either a kind of teenage nerd counterculture idea, an idea to simply annoy scientists (both silly IMO, but harmless) or, believe it or not, with anti-Semitic undertones. I think (for the sake of countering the last) it is important therefore to repudiate these ideas roundly, but I think real historians are the people to do this. You will find many knowledgeable physicists on History of SCience SE. In summary, I reject outright the notion of Einstein as a fraud, but if you study this ... $\endgroup$ – Selene Routley Sep 14 '15 at 6:27

I think you have to read "Science and hypothesis". It's a little book, easy and pleasant to read. And yes, Poincaré was SO close of special relativity. He did the mathematical work, he certainly wrote E=MC2 before Einstein (maybe some others like Hamilton did since you can find this formula with Hamilton Mechanic, but we will never know), and in his book, he was carefully and slowly going in the right direction. BUT he kept the Ether. And Einstein in his 1905's paper, first page wrote :

"The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."

And that is why Einstein took the credit. As a French guy, I really think that Poincaré was close and definitely in the right direction. But Einstein is the father of Special Relativity because he went further when Lorentz or Poincaré didn't dare. The reason I think can be because Einstein was a total outsider, nobody knew him in 1905, he was living an anonymous life and was not afraid of anything, when Poincaré was a famous guy, with more to lose and also older than Einstein. I guess when you get older, it's harder to break foundation of your knowledge.

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