After nearly a decade of work, Einstein described gravity not as a force but as the curvature of space and time by mass and energy. The equations he read on November 25, 1915, the last of four weekly lectures, correctly explained an anomaly in Mercury's orbit that Newton's theory could not. The mathematician David Hilbert arrived at closely related equations at about the same time. In 1919 observations of a solar eclipse confirmed the theory's prediction that gravity bends light, making Einstein world famous.
Einstein's special relativity of 1905 left gravity out. Two years later he had what he called "the happiest thought of my life": a person falling freely would not feel his own weight. From that idea he developed the principle of equivalence and set out to describe gravity as geometry, learning the difficult mathematics of curved spaces with the help of his friend Marcel Grossmann.
In 1913 he and Grossmann published a version that proved flawed. In the autumn of 1915, under pressure because Hilbert was working on the same problem, Einstein corrected his mistakes in a burst of work, presenting a new paper to the academy each Thursday in November. On November 18 he showed that the theory accounted for the 43 arcseconds per century by which Mercury's orbit shifted unexplained. He later said the result gave him heart palpitations.
The final equations, presented on November 25, relate the curvature of spacetime to the distribution of matter and energy. General relativity has since passed every test, and it underpins GPS satellite timing, the study of black holes and the detection of gravitational waves, first observed in 2015.
Key people: Albert Einstein, David Hilbert, Marcel Grossmann