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would tweak what he had done before, writing down a law, relaxing some assumptions while imposing others. And as he did so, he shed some of the physical prejudices that had held him back and delved deeper and deeper into the mathematics that he had learned. He realized that even though his physical intuition had served him well throughout his spectacular career, he had to be careful not to let it cloud the bigger picture coming out of the mathematics.
    Finally, by the end of November, he realized he had done it. He had finally discovered a general law for gravity that satisfied the general principle of relativity. On the scale of the solar system it was accurately approximated by Newtonian gravity, exactly as it should be. Moreover, it predicted Le Verrier’s precession of the perihelion of Mercury bang-on. And it predicted that as light rays passed by a heavy object, they would be bent even more—in fact twice as much as he had originally predicted when he first thought of the idea in Prague.
    Einstein’s completed general theory of relativity offered an entirely new way of understanding physics, one that superseded the Newtonian view that had held sway for centuries. His theory provided a set of equations that came to be known as the “Einstein field equations.” Although the idea behind them, relating the geometry of Gauss and Riemann with gravity, was beautiful—“elegant,” as physicists would want to call it—the detailed equations could look like a mess. They were, in practice, a set of ten equations of ten functions of the geometry of space and time, all nonlinearly tangled up and intertwined such that, in general, it was impossible to solve for one function at a time. They all had to be tackled together, head-on—a truly daunting prospect. Yet they held much promise, for their solutions could be used to predict what would happen in the natural world, from the motion of a bullet or an apple falling off a tree to the movement of planets in the solar system. The secrets of the universe, it seemed, were to be found by solving Einstein’s equations.
    On November 25, 1915, Einstein presented his new equations to the Prussian Academy of Sciences in a short three-page paper. His new law of gravity was radically different from what anyone had ever proposed before. In essence, Einstein argued that what we perceive as gravity is nothing more than objects moving in the geometry of spacetime. Massive objects affect the geometry, curving space and time. Einstein had finally arrived at his truly general theory of relativity.
    But Einstein was not alone. Hilbert had been mulling over Einstein’s Göttingen lectures and had, without Einstein realizing, made his own attempts at coming up with new gravitational equations. Completely independently, Hilbert had come up with exactly the same gravitational law. On the twentieth of November, five days before Einstein’s presentation to the academy in Berlin, Hilbert presented his own results to the Royal Society of Sciences in Göttingen. It seemed as if Hilbert had scooped Einstein.
    During the weeks following the announcements, relations between Hilbert and Einstein were strained. Hilbert wrote to Einstein claiming he didn’t remember the bit in one of his lectures in which Einstein had discussed his attempts at building the gravitational equations, and by Christmas, Einstein was satisfied that there hadn’t been any foul play. As Einstein said, in a letter to Hilbert, to begin with“there has been between us something like a bad feeling,” but he had come to terms with what had happened, so much so that “I once more think of you in unclouded friendship. . . .” They would indeed remain friends and colleagues, for Hilbert stepped back from claiming any credit for Einstein’s magnum opus. In fact, until he died, Hilbert always referred to the equations that both he and Einstein had stumbled upon as