A set of Albert Einstein's handwritten notes for the theory of relativity was auctioned in Paris on Tuesday for €11.7 million (almost NZ$19 million), more than four times the manuscript's estimate by Christie's.

The manuscript, which ran to 54 pages, comprised work on Einstein's general relativity theory, published in 1915.

"This is without a doubt the most valuable Einstein manuscript ever offered at auction," a Christie's spokeswoman stated. The auction house did not disclose the identity of the buyer.

The notes were composed in Zurich between 1913 and 1914 by Einstein and his lifelong companion, Swiss engineer Michele Besso.

Einstein was not known for retaining working documents, and analysts described its survival as "almost miraculous."

Christie describes it as a "fascinating journey into the mind of the twentieth century's greatest scientist."

Einstein and Besso collaborate to explain an anomaly in Mercury's orbit using the equations Einstein would later use to prove general relativity.

Their objective was to demonstrate that Mercury's perihelion, or closest approach to the Sun, varies throughout time due to the curvature of spacetime.

Numerous computations are scribbled in black ink on crumpled, lightly yellowed paper on the pages.

The text does, however, demonstrate that Einstein was not infallible. He and Besso both made numerous errors, and when Einstein realized his blunder, he discarded the notes.

Einstein later corrected the errors, but Besso preserved the original document in mint condition in his house until his death in March 1955.

It was unclear if Besso took the text or whether Einstein sent it to him for further work.

The document comprises 26 pages authored by Einstein, 25 pages by Besso, and three pages created collaboratively.

Einstein died a month after Besso, having earned the Nobel Prize and been generally recognized as one of history's greatest geniuses.

Einstein's scientific writings before 1919 are sporadic.

Apart from a manuscript maintained at the Albert Einstein Archives in Jerusalem, Christie's stated that the Einstein-Besso manuscript is the sole existing document illustrating the origins of general relativity.

The auction house described it as "one of the most significant scientific documents of the twentieth century."

"Because the manuscript is not bound and contains a variety of different types of loose paper, you get the impression of a dynamic working document, as if both men would grab the first page they came across to scribble their findings," said Vincent Belloy, a Christie's manuscript specialist.

"What's intriguing is the sense of self-awareness that permeates these pages.

"You get the idea that Einstein was possibly more confident in his calculations due to the fact that his sheets are far lighter in terms of textual material and nearly entirely allocated for calculations. By contrast, Besso frequently inserted marginal comments."

"Einstein makes errors in this manuscript," he continued, "which I believe enhances its significance in a way, because we see the persistence of the thought that was being built, that is being corrected and redirected."