Albert Einstein typically threw out drafts of his paradigm-shifting work. But thanks to the Nobel Prize-winning scientist’s friend and collaborator, a rare, working manuscript “almost miraculously” survived to the present – and it sold for a hammer price of nearly $11.5 million at an auction in Paris on Tuesday, to an anonymous private individual. The 54-page document, handwritten jointly by Einstein and Swiss engineer Michele Besso – his lifelong friend and only acknowledged collaborator – documents preparatory work for Einstein’s general theory of relativity, an idea that changed human understandings of the universe and has been described as the most beautiful theory in physics. Valued at between $2.4 million and $3.5 million before the auction, it was the most valuable Einstein manuscript to be sold. Most of the document was composed in June 1913, when Einstein was living in Zurich. It consists of calculations etched largely in ink on yellowed leaves of foolscap and squared paper, with 26 pages in Einstein’s handwriting, 25 pages in Besso’s and three containing entries from both scientists. The famous German scientist was working with Besso to test his theory of the relationship between gravitation and the space-time curvature by examining the anomaly of the planet Mercury’s orbit. Replete with errors, crossed-out equations and corrected calculations, the pages showcase what Christie’s called a “crucial stage” in the relativity theory’s development. Einstein later reworked the calculations and published the theory of general relativity under only his name in November 1915. The contribution upended understandings of gravity, space and time, opening up explorations of gravitational time dilation, light deflection and gravitational waves. It was one of the breakthroughs that helped make Einstein’s name synonymous with genius in popular culture. Einstein was awarded the Nobel Prize in physics for 1921. He died in 1955 at age 76.