# Claudia E. Graf-Grossmann. *Marcel Grossmann. For the Love
of Mathematics*. Translated by William D. Brewer. (Springer Biographies.) xviii + 261 pp., bibl.,
illus., index. Cham, Switzerland:
Springer, 2018. £24.99 (cloth),
ISBN 9783319900766.

*Isis* 111(1), 2020, 194–195.

Contemporary theoretical physics is so tightly bound to mathematics
that it is unthinkable to pursue it as a career without a solid
background in higher mathematics. This was not true at the turn of the
twentieth century, when the subdiscipline was in its infancy, and
Albert Einstein was a student at the Polytechnikum in Zurich (now the
Eidgenössische Technische Hochschule, or ETH). The mathematical
curriculum at the Polytechnikum was irreproachable in Einstein’s day,
and its teaching staff included two of the world’s finest
mathematicians: Adolf Hurwitz and Hermann Minkowski. Studying
alongside Einstein at the Polytechnikum were several bright students,
including his future wife, Mileva Marić, and the future mathematicians
Louis Kollros, Marcel Grossmann, Jacob Ehrat, and Louis-Gustave du
Pasquier. The young Einstein was inspired in particular by Minkowski’s
lectures on capillarity; at the time, Minkowski, like Einstein, was
reading the masterworks of theoretical physics, a predilection that
would soon lead him to abandon Zurich for Göttingen. He was
disappointed by Einstein’s performance in class, and was said to have
referred to him once as a “richtiger Faulpelz”, who paid no
attention to mathematics (Carl Seelig, *Albert Einstein: Leben
und Werk eines Genies unserer Zeit* [Europa, 1960], p. 45). By
Einstein’s own account, he was a middling student, whose high grades
in mathematics owed much to the lecture notes loaned him by Grossmann.

After graduation, Grossmann (1878–1936) went on to become a high school math teacher, a position for which Einstein was passed over. Einstein later found work at the Patent Bureau in Bern, on the strength of a recommendation from Marcel’s father Jules, a businessman acquainted with the Bureau’s director. In his spare time, Einstein rolled out a series of discoveries that rocked the world of physics, including the theory of relativity. Minkowski, now in Göttingen, took note of Einstein’s theory, and seized on the idea of the world as a four-dimensional spacetime manifold, thereby demonstrating the potential for pure mathematics to restructure the scientific worldview. Upon further formal elaboration by Arnold Sommerfeld, Einstein and others came to see the beauty and utility of Minkowski’s approach for a “generalized” theory of relativity that would include gravitational phenomena.

By 1911, Einstein occupied the chair of theoretical physics in Prague, while Grossmann, now a professor of descriptive geometry at the ETH, went about securing his brilliant friend a position on the faculty. Reunited in Zurich in the summer of 1912, the two men pursued the generalized theory of relativity, cosigning the two papers that are Grossmann’s claim to fame – as Einstein subsequently moved to Berlin and discovered the foundational field equations of general relativity.

Grossmann’s precise contribution to this discovery is better known, thanks to the preservation of a notebook kept by Einstein, referred to by Einstein scholars as the “Zurich notebook.” In a crucial step, Grossmann, following a literature search, introduced Einstein to Gregorio Ricci and Tullio Levi-Civita’s absolute tensor calculus (1901), a work known both to applied mathematicians and to physicists more attentive to the mathematical literature than Einstein, including Max Abraham and Friedrich Kottler.

Historical interest in Grossmann’s contribution to general relativity
reflects a broader scholarly interest in Einstein and his
sociointellectual milieu dating from the 1980s, when the
*Einstein Studies* series and the vast edition project, the
*Collected Papers of Albert Einstein* (*CPAE*) were
launched. The book under review is an English translation by the
physicist William D. Brewer of the biography in German (Römerhof,
2015) by Grossmann’s granddaughter, Claudia
Graf-Grossmann. Occasionally, biographical portraits by descendants
bring to light not only family history and genealogy, but archival
documents, private correspondence, photos, diaries, notebooks, oral
history, and more. In the case at hand, while there are numerous photos
of Grossmann’s family and friends, and of various residences, the
novelties are few. Grossmann’s granddaughter was born a generation
after his death, and consequently she has no personal memories to pass
on. Instead, she draws on the diaries of her father, Marcel Hans
Grossmann, as well as the transcribed recollections of her aunt
Elsbeth. The correspondence with Einstein, cited generously from the
*CPAE* and the Einstein Archives, is a delight to read,
comprising six letters from Grossmann, one of which is reproduced in
facsimile, and eleven from Einstein. The historical setting of the
exchange is sketched by one of the senior editors of the Einstein Papers,
Tilman Sauer, in a much-abridged version of an earlier work, although
surprisingly, Professor Sauer is not credited on the title page.

From the book’s subtitle – *for the love of mathematics* – I
had expected Grossmann’s life in mathematics to get a little
biographical love, but in this I was disappointed, as Sauer’s sketch
(pp. 171–193) alone engages with Grossmann’s training and
career. Apart from his collaboration with Einstein, Grossmann
published a handful of papers on non-Euclidean geometry and several
college textbooks on descriptive and analytic geometry. His scientific
productivity was hindered by debilitating illness beginning in 1915,
and he made no further significant contributions to
mathematics. Readers with no mathematics will have no difficulty
reading this biography, which should appeal to those with an interest
in the Grossmann family history.