According to the accepted view, the mathematician David Hilbert completed General Relativity five days before Albert Einstein in November 1915. Einstein may thus have copied crucial equations of this theory from Hilbert.
Members of an international research group at the Max Planck Institute for the History of Science, Berlin, argue in their study, published in this week's issue of Science, that it was instead Hilbert who appropriated crucial results from Einstein and then published his paper under a misleading dateline.
Albert Einstein submitted his conclusive paper on General Relativity on 25 November 1915. David Hilbert, one of the most eminent mathematicians of the 20th century, published a paper in March 1916 which also contains the correct field equations of General Relativity. Einstein came to know Hilbert's contribution in late November, even before he found his final equations. He immediately claimed that Hilbert had appropriated his results. The dateline of Hilbert's paper, "20 November 1915," however, suggests that it was submitted five days earlier than Einstein's contribution. Did Einstein even copy the correct field equations from Hilbert's paper, as has been argued? This possibility can now definitely be excluded.
The authors of the present paper succeeded in identifying proofs of Hilbert's article that are dated "6 December 1915," that is after the submission of Einstein's conclusive contribution. Their detailed analysis of these proofs has revealed that they contain only an immature version of General Relativity, without the explicit field equations. These equations must have been inserted only later - after 6 December and before the published version appeared in 1916. Hilbert was, so the authors argue, still deeply ingrained in wrong assumptions about the physical meaning of his formalism, asssumptions which Einstein had meanwhile painfully overcome. Einstein can hence definitively be freed from the charge of plagiarism.
Hilbert's contribution, on the other hand, cannot even be considered as an independent alternative discovery of the field equations of General Relativity. Clearly, before he published the final version of his article, he must have seen Einstein's conclusive paper. If Hilbert had only altered the dateline of this paper to the date when he inserted the correct equations into the proofs no later priority discussion could have arisen.
Although disputes about priority and plagiarism can be crucially important to working scientists, they are not necessarily a key issue in the history of science. Historians of science are often less interested in who made an important new discovery but rather in how new insights become possible. In the case of Einstein's and Hilbert's struggle for establishing the field equations of a new, relativistic theory of gravitation the situation is, however, different since the approaches taken by the two scientists were dramatically distinct: Whereas Einstein combined mathematical strategies with a search for physical meaning, Hilbert very much relied on the power of his superior mathematical formalism. Clearly, in this case, the who of the discovery tells indeed much about the how.
Since 1907 Einstein had attempted to carefully reconcile, step by step, tentative mathematical formulations of his heuristic goal to formulate a relativistic theory of gravitation with the then available physical knowledge. Hilbert, on the other hand, had only begun to work on General Relativity in the second half of 1915. He boldly aimed from the beginning at an axiomatic foundation of physics and at a kind of world formula, unifying gravitation with electromagnetism. This approach caused the wrong impression that the field equations of General Relativity could be found by pure mathematical reasoning.
The results reported in the article in Science are an outcome of an international research project dedicated to the history of General Relativity. The project is centered at the Max Planck Institute for the History of Science in Berlin and has produced in the last years several new insights into the development of this theory.
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Science