A rare manuscript featuring equations that led to Albert Einstein's general theory of relativity fetched over $13 million at an auction in Paris on Tuesday, becoming the most expensive manuscript by the scientist.

Known as the Einstein-Besso Manuscript, the 54-page document was written by Einstein and his friend and colleague, the Swiss-Italian engineer Michele Besso, between June 1913 and early 1914. It was originally expected to fetch around $3.5 million, but was sold for nearly quadruple the pre-sale estimate by British auction house Christie’s.

Apart from a manuscript held at the Albert Einstein Archives at the Hebrew University in Jerusalem, the Einstein-Besso Manuscript is the only surviving work detailing the genesis of general relativity, Christie’s said in a statement.

The manuscript features 26 pages written in Einstein’s handwriting and 25 in Besso’s, with three pages of entries by both. It attempts to explain an anomaly in Mercury’s orbit using versions of the equations Einstein would use to prove his theory of general relativity that was first put forth on November 25, 1915.

Mistakes in findings

“The two men sought to confirm that Mercury’s perihelion, the point where the planet is closest to the Sun, changes slowly over time because of the curvature of spacetime. However, both scientists made a couple of mistakes in the manuscript, and Einstein later on realised that the equations were not quite the right ones yet. He would then correct his findings independently later,” the British auction house said on its website.

Einstein was not one to save early drafts of his work. However, the manuscript was preserved thanks to Besso, who kept the document safely in his home until his death in 1955.

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“The manuscript isn’t bound, and there are many different types of loose paper, so you get the impression of a working document that’s full of energy, as if both men would grab the first page they could find to scribble their findings on,’ said Vincent Belloy, specialist in the books and manuscripts department at Christie’s Paris as quoted on the Christie’s website.

It is however not clear if Besso took the manuscript or if Einstein sent it to him, asking him to work through their findings.

“What’s interesting is the sense of personality that comes across in these pages,” said Belloy.

“You get the impression that Einstein was perhaps more confident in his calculations since his sheets are much lighter in terms of textual content and reserved almost exclusively for calculations. Besso, by contrast, often added written notes in the margin,” Belloy added.