A handwritten letter by Albert Einstein that contains his famous E=mc2 equation has sold at auction for more than $1.2m, about three times more than it was expected to get, a Boston-based auction house said on Friday.

Archivists at the Einstein Papers Project at the California Institute of Technology and the Hebrew University of Jerusalem say there are only three other known examples of Einstein writing the world-changing equation in his own hand.

RR Auction, which sold the most recent letter, says this fourth example is the only one in a private collection and only became public recently. The auction house had expected it to sell for about $400,000.

“It’s an important letter from both a holographic and a physics point of view,” Bobby Livingston, the executive vice-president at RR Auction said, calling the equation the most famous in the world.

Albert Einstein.
Albert Einstein. Photograph: Granger Historical Picture Archive/Alamy

The equation – energy equals mass times the speed of light squared – changed physics by demonstrating that time was not absolute and that mass and energy were equivalent.

The one-page handwritten letter in German to the Polish American physicist Ludwik Silberstein is dated 26 October 1946.

Silberstein was a well-known critic and challenger to some of Einstein’s theories. “Your question can be answered from the E=mc2 formula, without any erudition,” Einstein wrote in the letter written on Princeton University letterhead, according to a translation provided by RR Auction.

The letter was part of Silberstein’s personal archives, which were sold by his descendants.

The buyer was identified by RR only as an anonymous document collector.

The rarity of the letter set off a bidding war, Livingston said. Five parties were bidding aggressively at first, but once the price reached about $700,000, it became a two-party contest, he said.

The auction began on 13 May and concluded on Thursday.