One of Albert Einstein's manuscripts has been sold at auction for $13.17m (£9.8m).

 

The 54-page paper, which is half-filled with the physicist's handwriting, is only one of two working documents known in which he approaches his famous theory of relativity.

 

Auction house Christie's had estimated the value of the manuscript, which was co-authored by Michele Besso, at between £1.7m ($2.3m) and £2.5m ($3.4m).

Einstein's theory laid the groundwork for modern cosmology and technology such as GPS navigation.

 

The pages had been kept in the safety of the Swiss physicist Besso, a close friend and academic partner of Einstein's, who co-authored the work between 1913 and 1914.

 

"That's also what makes it particularly important given that working documents by Einstein before 1919 are extremely rare," said Vincent Belloy, an expert at Christie's who hosted the auction in Paris.

 

"Einstein is someone who kept very few notes, so the mere fact that the manuscript survived and made its way to us already makes it absolutely extraordinary."

 

The pages are made up of calculations, written in black ink on yellowed paper.

 

It also challenges the scientists' popular image as an absolute genius because it shows that he sometimes made mistakes.

"Einstein makes errors in this manuscript, and that I think makes it even greater in a way, because we see the persistence, the thought that was in the process of being built, that is being corrected and redirected," Mr Belloy said.