On 4th November 1915, Albert Einstein sent the Prussian Academy of Sciences the first of four communications (Zur allgemeinen Relativitätstheorie) that marked the birth of the general theory of relativity — universally considered the finest theory in the history of physics. Having two days later received, as usual, the proofs of the work due to be printed in the Academy’s Sitzungsberichte, Einstein hastily corrected them and sent them — on a Sunday — to a colleague in Göttingen, David Hilbert. The greatest mathematician of the time, Hilbert had in the previous months shown a distinct interest in the new theory of gravitation on which the Ulm physicist had been working for years:

Distinguished colleague,
I enclose the proofs of a work in which I have changed the gravitational equations after I myself recognised about four weeks ago that my previous demonstration procedure was wrong. … I am curious to know if you will look favourably on this new solution.
Best regards, yours
A. Einstein

What Einstein could not have known as he wrote these lines (though he would soon find out) was that Hilbert, too, was on the quest for the Holy Grail of gravitational theory, the field equation — although the mathematician was looking for it down other paths. Einstein's letter thus sparked a grandiose and dramatic competition: a race between giants, between the two greatest scientists of their time, pursuing the same objective.
Einstein presented his equation in Berlin on 25 November. Hilbert presented the same equation in Göttingen on 20 November: or maybe not, because his work (Die Grundlagen der Physik) would be published only at the beginning of 1916, in a different version from that of the previous November (which came to light a few years ago). So, who was it who discovered the equation of the gravitational field — the key formula of general relativity?
Apart from the few, rather meagre letters that Einstein and Hilbert sent one another in these hectic weeks in November 1915, there are no other ommunications between the two. The only documents they exchanged are the proofs Einstein sent to Hilbert. The recent discovery of these proofs in Italy sheds new light on one of the most mysterious and fascinating episodes in the history of contemporary physics. In fact — even aside from the content of the printed text (corrected on some points by Einstein), which represents the turning point in the elaboration of general relativity — the proofs also bear Hilbert’s handwritten notes and comments, testifying also to his own path towards the final theory. So, what do they have to tell us — and reveal — about this extraordinary scientific endeavour? A careful work of deciphering, analysis and research has allowed us to answer this question.

Vincenzo Barone teaches Theoretical Physics at the University of East Piedmont. His research encompasses the phenomenology of elementary particles and, more specifically, strong interactions. With Bollati Boringhieri he has published Relatività. Principi e applicazioni (Relativity. Principles and applications, 2004) and L’ordine del mondo. Le simmetrie in fisica da Aristotele a Higgs (The World Order. Symmetries in physics from Aristotle to Higgs, 2013), and edited Atomi Nuclei Particelle (Atoms, Nuclei, Particles, 2009), an anthology of thew writings of Enrico Fermi.

Jürgen Renn is director of the Max Planck Institute for the History of Science in Berlin. A professor of the history of science at the Humboldt University of Berlin and professor of physics at the Freie Universität of Berlin, from 1986 to 1992 he was co-editor of the Collected Papers of Albert Einstein at Boston University. One of the leading scholars of Einstein’s thought, with Bollati Boringhieri he has co-edited, with R. Schulmann, the Lettere d’amore (Love Letters) of Albert Einstein and Mileva Marič (1993 and 2020) and published Sulle spalle di giganti e nani. La rivoluzione incompiuta di Albert Einstein (On the Shoulders of Giants and Dwarfs. Albert Einstein’s unfinished revolution, 2012 and 2016).