Equation written on brown paper in blue and black ink

Einstein manuscript sold for record amount

Michel Janssen and Eran Moore Rea

On Tuesday, a stack of about 50 pages of scratchpad calculations of Albert Einstein and his close friend Michele Besso was sold at auction in Paris for a record $11.5 million, far exceeding the pre-sale estimate of $2–3 million. What’s in these pages? And how did they end up in Paris a century later? 

Einstein and Besso met as students in Zurich, Switzerland, in the late 1890s. They were colleagues for a few years in the Swiss patent office in Berne. Discussions with Besso helped Einstein formulate special relativity in 1905. While his friend continued to work as an engineer, Einstein embarked on an academic career. In 1912, he was appointed full professor at his alma mater in Zurich. For the next few years, he worked intensively on a new theory of gravity. According to this theory, large masses curve the space-time around them, while smaller masses follow the straightest possible paths in this curved space-time. Examples of such paths are the orbits of planets around the sun. The orbits predicted by Einstein’s theory are very nearly but not quite the same as those predicted by Newton’s. Newtonian theory had trouble accounting for the motion of Mercury’s perihelion, the point in its orbit closest to the sun. Over the course of a century, this perihelion motion (as seen from the sun) adds up to about 550 seconds of arc. A full circle is 360 degrees, a degree is 60 minutes and a minute is 60 seconds, so 550 seconds of arc is a tiny effect. Moreover, more than 90% of it could be chalked up to the gravitational pull on Mercury by other planets. Yet a gap of about 43 seconds remained. Einstein hoped his new theory could close this gap.

This then is what he and Besso set out to do in the spring of 1913. The manuscript sold on Tuesday is a record of their efforts. The end result given in the manuscript is 1821 seconds or 30 minutes of arc (see the figure), more than three times the total motion of Mercury’s perihelion. There are clear indications in the manuscript, however, that Besso found the trivial error that led them to overestimate the effect by a factor of 100. Yet 18 is still 25 shy of 43. They tried to make the theory yield a few more seconds in other ways but came up empty. In early 1914, Einstein mailed what they got so far to Besso and urged his friend to keep working on the project. Besso tried but made no further progress.

In March 1914, Einstein left Zurich to take up an even more prestigious position in Berlin. He did  not return to the problem with Mercury’s perihelion until November 1915. That month, he changed the equations determining how matter curves space-time that he and Besso had used, thereby arriving at general relativity as we know it today. He redid the calculations he had done with Besso and, as he later recalled, suffered heart palpitations when out popped the 43 seconds he had been looking for! Einstein found himself in a race that month with the great mathematician David Hilbert to see who could put the house of general relativity in order first. When Einstein wrote to Hilbert about his success with Mercury, Hilbert wrote back that he wished he could calculate that fast! Einstein never told Hilbert that he had done very similar calculations before.

In fact, had he not sent the manuscript with those earlier calculations to Besso, we probably could never have called Einstein’s bluff. Had it remained in Einstein’s possession, he would almost certainly have discarded it. Besso, however, held on to the manuscript for the rest of his life. His son Vero eventually gave it to Pierre Speziali, editor of the extensive correspondence between Michele and Einstein. Speziali recognized its intellectual and monetary value. In the late 1980s, he shared a photocopy with the Einstein Papers Project, then at Boston University, now at Caltech. One of us was lucky enough as a graduate student to get the plum assignment of preparing the manuscript for publication in Volume 4 of The Collected Papers of Albert Einstein. Speziali left the original to his two daughters, who sold it at auction in 1996 for $360 thousand. In 2002, it was acquired for half a million by a French company, Aristophil, as part of an impressive collection of historical documents. In 2015, however, French authorities arrested the company’s founder, who has been described as “the Bernie Madoff of France,” for using this collection to run a Ponzi scheme. The identity of the new owner has not (yet?) been revealed. We hope that he or she will consider donating it to the Albert Einstein Archives in Jerusalem, where it belongs together with all other manuscripts and letters that Einstein bequeathed to Hebrew University.   

Michel Janssen is a professor for history of science and Eran Moore Rea is a graduate student in physics and history of science in the School of Physics and Astronomy of the University of Minnesota