The document includes preparatory notes and some errors while formulating the theory of relativity
The 54-page document was handwritten between 1913 en 1914 in Zurich, Switserland, by Einstein and his colleague Michele Besso, berig Die voog.
The documents contain preparatory calculations and notes that the scientist made while formulating his signature achievement, the theory of relativity.
The notes are written in black pen and include some errors in calculations that the scientist made on the way to formulating his seminal work. Once he noticed the errors, he dropped the notes, which were picked up by Besso and preserved for posterity.
Einstein, one of the greatest theoretical physicists, eventually published his theory of relativity in 1915, which transformed understanding of time, space and gravity.
The sale comes months after a letter written by Einstein containing the theory’s most famous equation, E=mc², sold for more than $1.2m (£897,000) in Mei.
Tuesday’s sale also surpassed previous records of his documents, including the $2.8m (£2m) for the so-called “God letter” in 2018, and $1.56m (£1.16m) in 2017 for a letter about the secret to happiness.
While the buyer of his notes on Tuesday was unknown, Christie’s auction house, which handled the sale on behalf of the Aguttes auction house, said the notes were “without a doubt the most valuable Einstein manuscript ever to come to auction.”
Prior to the auction, Christie’s had estimated that it would fetch between €2m (£1.6m) and €3m (£2.5m).
The auction house thanked Besso for preserving the documents and said that the sale had attracted collectors from across the world, berig BBC.
“Einstein is someone who kept very few notes, so the mere fact the manuscript survived and made its way to us already makes it extraordinary,” Vincent Belloy, an expert at the auction house.
Christie’s said that the papers offer “a fascinating plunge into the mind of the 20th century’s greatest scientist.”
“Being one of only two working manuscripts documenting the genesis of the theory of general relativity that we know about, it is an extraordinary witness to Einstein’s work,” the auction house added.
Einstein died at the age of 76 in 1955 and is also remembered for his contributions to quantum mechanics theory. He won the Nobel Prize in 1921.