In the Biography of Henri PoincarÃ© it is said http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Poincare.html "He is acknowledged as a co-discoverer, with Albert Einstein and Hendrik Lorentz, of the special theory of relativity. " In details this is the story: http://www.chez.com/cosmosaf/Poincare-RR3A.htm Henri PoincarÃ© : A decisive contribution to Special Relativity Introduction In April 1994 Â« la Jaune et la Rouge Â» published a survey from Jules Leveugle (Ecole Polytechnique) named Â«PoincarÃ© et la RelativitÃ© Â» (RÃ©f 7). Evidences of the major contribution of Henri PoincarÃ© to the Special Relativity theory are presented in this survey. According to the success encountered by this article, and the questions about it, Christian Marchal published an additional paper in order to answer to the questions. H. PoincarÃ© is very well known as a famous mathematician, even though he never taught mathematics but physics ( electromagnetism) as a professor at the â Ecole Polytechniqueâ. His work on Relativity is less known. The purpose of this paper is to demonstrate that he set up all the basic concepts of Special Relativity, several years before Einstein did in his the famous paper (1905: Annalen der Physik vol XVII 1905 p 891-921: ref 6). We will review briefly the controversy between Lorentz and H. PoincarÃ© about absolute space time (1898-1905). We will compare the very different approaches of PoincarÃ© (formal) and Einstein (physical), on Relativity (illustrated by the demonstration, within the theory, of the Lorentz equations by each of them) . We will end on some questions: Why the work of PoincarÃ© is so ignored, why Einstein did not mentioned any references at all, in his 1905 fundamental article, acting as he had invented everything, even though, at least the Relativity principle as well as the method for synchronizing clocks are borrowed from PoincarÃ© published papers (1898-1902). This should explain why Einstein was not awarded the Nobel Prize for the Relativity , but for the photo-electric effect! For a detailed bibliography of H. PoincarÃ© see http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Poincare.html â¦. Lorentz â PoincarÃ© Controversy (1898-1905) At the end of the 19 th century, when the detection (at the second order) by the Michelson Morley experience of the absolute motion âin the etherâ of the Earth failed, the science was under trouble. In 1895 Lorentz suggested that moving bodies should experience a âphysicalâ contraction, compute what it would be in accordance to the Michelson Morley experience and set up a theory on this basis. In 1899, Henri PoincarÃ©, who was teaching electromagnetism at the âEcole Polytechniqueâ wrote in one of his course [ref: âElectricitÃ© et Optiqueâpublished by CarrÃ© et Nadaud, 1901, p 536 ] about this hypothesis: â I am not satisfied with the explaination ( physical contraction) of the negative result of the Michelson experiment by the Lorentz theory, I would say that the laws of optics are only deponding on the relative motion of the involved bodiesâ. It was the beginning of the ( friendly) controversy with Lorentz , mainly about the concept of absolute Space and absolute time. In his book âLa science et lâhypothÃ¨seâ (1902), PoincarÃ© devoted a full chapter to the relativity principle: âThere is no absolute uniform motion, no physical experience can therefore detect any inertial motion ( no force felt) , there is no absolute time, saying that two events have the same duration is conventional, as well as saying they are simultaneous is purely conventional as they occur in different places â.One can still keep in mind the concept of ether, if it helps for thinking, but it is a unphysical concept, it is a metaphysical concept. He defines the way to synchronise all the clocks of an inertial frame, by using light signals ( 1900: La thÃ©orie de Lorentz et le principe de rÃ©action, published J.Bosscha]. In 1904 at the St Louis conference, he proposes to add the Relativity principle to the five classical âuniversalâ principles of the physics. He emphasised that the Lorentz contraction was an âad hocâ hypothesis, just made for adjusting the theory to the experience. Lorentz reported this point of view of PoincarÃ©, in his theory of electromagnetism (1904-Ref ). â PoincarÃ© has objected to the existing theory of electric and optical phenomena in moving bodies that, in order to explain Michelsonâs negative result, the introduction of a new hypothesis has been required, and that the same necessity may occur each time new facts will be brought to light. Surely this course of inventing special hypotheses for each new experimental result is somewhat artificial. It would be more satisfactory if it were possible to show by means of certain assumptions and without neglecting terms of one order of magnitude or another, that many electromagnetic actions are entirely independent of the motion of the systemâ¦..â He points out that the âformâ of the Lorentz formulae can be demonstrated from the Relativity principle alone, ( see annex 1) and therefore are implied by this principle alone ( with a parameter to specify, related to âcâ for the Special relativity), only one hypothesis is required, instead of the local time and the associated three new hypothesis of the article of Lorentz ( 1904). At last but not at least, In 1900, he noticed that the recoil of a radiation, of energy E, is m = E/cÂ² [ ref oeuvres de PoincarÃ© ,op.cit.t IX p 471] which is nothing else that the famous E = mcÂ². We can see that in 1905 PoincarÃ©, in different articles, had set up all the basic concepts of the special Relativity even though he did not summarize all of them in the framework of a formal theory as Einstein did.