Manhattan Rare Book Company

AN IMPORTANT SCIENTIFIC LETTER FROM EINSTEIN TO HIS CLOSEST MATHEMATICAL COLLABORATOR, ACCOMPANIED BY A MANUSCRIPT LEAF OF CALCULATIONS IN EINSTEIN’S HAND ON THE SAME LINE OF RESEARCH.

Although the original association of the letter and the leaf of calculations cannot be confirmed, the two pieces clearly emerge from the same scientific context and have been preserved together. A superb pair from the final months of Einstein’s German period.

The Letter:

In this intense and intellectually urgent letter, Einstein writes to Walther Mayer, his indispensable mathematical collaborator (often referred to as “Einstein’s Calculator”), describing a newly conceived approach to the technical obstacles in their unified-field theory involving semi-vectors, spinors, and modified Dirac-type equations. Einstein tells Mayer he believes he “sees a new possibility,” one that determines key constants in the system without resorting to the semi-vector construction.

He then sketches the structure of the revised scheme, points to the condition under which the full set of field equations reduces to a single one, and warns that if this same collapse occurs in the general case, “the whole thing would be useless.” With his imminent departure from Germany, he urges Mayer to examine the issue quickly and gives instructions for where a reply will reach him while en route.

Dirac and De Broglie – Significance of the Scientific References:

Of particular importance is Einstein’s explicit engagement in this letter with the work of Paul Dirac and Louis de Broglie, two of the central figures in early quantum theory. Einstein refers directly to the Dirac equations, introduced only a few years earlier, which provided a relativistic formulation of the electron and played a foundational role in quantum mechanics. He also invokes the De Broglie equations for matter waves, reflecting his continued effort to reconcile quantum ideas with relativistic field theory. These references place the letter squarely at the intersection of Einstein’s unified-field program and the emerging quantum framework he famously regarded with both fascination and skepticism. The letter thus documents Einstein actively testing whether concepts originating in quantum mechanics—Dirac’s relativistic wave equation and De Broglie’s wave–particle duality—could be absorbed into a geometrically unified classical field theory. Letters in which Einstein explicitly grapples with Dirac and De Broglie at this technical level are rare and represent an important record of his engagement with the central theoretical developments of the early twentieth century.

Historical Context:

Einstein’s collaboration with Walther Mayer, beginning around 1930, produced some of the most technically sophisticated papers of Einstein’s later career. Together they developed new mathematical structures—semi-vectors, spinors, and higher-dimensional tangent-space formulations—used in their unified-field attempts. This letter dates from December 1932, only weeks before Einstein left Germany permanently, and belongs to the final phase of their joint work published in the Sitzungsberichte of the Prussian Academy.

Einstein valued Mayer so highly that he later persuaded the Institute for Advanced Study to create a permanent position for him, the only such appointment ever granted for one of Einstein’s collaborators.

The Manuscript Calculations:

Accompanying the letter is a two-page manuscript leaf containing Einstein’s working calculations: trial expressions, constraint conditions, and variant formulations of the same type of semi-vector and spinor problems addressed in the letter. While we cannot confirm that these pages were originally enclosed with the letter, they concern the same scientific material and have been preserved alongside it.

Einstein manuscript leaves of this depth and technical significance—especially when tied to a known collaborative problem—are scarce.

Significance:

Whether or not originally sent together, the letter and the calculations form a powerful and coherent scientific pair, offering a rare view of Einstein actively working through equations, testing ideas, and relying on Mayer to verify mathematical structure. They capture Einstein at a critical inflection point in both his scientific life and personal circumstances, as he prepared to leave Germany forever.

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The letter, from Einstein to Mayer, reads in full [translated from the original German]:

Dear Mr. Mayer! I believe I see a new possibility, which promises success. It is along the lines of the recently devised way, according to which one places zero on the right side of the Dirac-Equations. The novelty is in the fact that the constants a1 ... a4 (aside from a totally irrelevant factor) are completely known without passing on to the specific Semi-Vectors.

After omission of the _-terms, the equations read

Ee st ys = s (1)
xe

Or, for De-Broglie-Equations of the restless particle

E4 st ys = s (1a)
x4

Here is what's new: How does one choose the a(y), so that the De Broglie - [Choices] stay largely undetermined?

Result: The four equations (1a) reduce themselves into a single one, when and only when, if one lets a(1) = 1 a(2) = 1 a(3) = 1 a(4) = 1

I believe that with this selection, a(y) is [for] the equation describing the _-terms (1) the fitting substitute, for the DeBroglie-Equation. These equations are already supplied by the simplest Hamilton function.

See, if the general equations (1) degenerate with this placing for a as well. If this were the case, the whole thing would be useless. I leave on Saturday. A letter that is sent to Antwerp, to the `Oakland', Hapag, Antwerp harbor, will reach me until December 13.

Cordial greetings from your A. E.

Autograph Letter Signed, Written in German. One page (8.5 x 11 in.; 216 x 279 mm.), probably Caputh [near Potsdam, Germany, the location of Einstein's country home], Sunday, 4 December [1932]. Scattered spotting affecting four words; usual folds. WITH: Two-page leaf of mathematical calculations. Housed together in decorated half-leather box by noted book artist Sjoerd Hofstra.

Price: $65,000 .