![A lengthy, multiple-page physics computation by Gurari ends with "Bravo!" (circa 1951/52). - Image Courtesy of Gurari/Imbo/Shmotkin](https://w2.chabad.org/media/images/1319/MKvb13197914.png?_i=_n504BC99DD0473598AAE3BCDC5D75568D "A lengthy, multiple-page physics computation by Gurari ends with "Bravo!" (circa 1951/52). - Image Courtesy of Gurari/Imbo/Shmotkin")
For decades, thousands of pages languished, unread and all but forgotten, stored at numerous locations in Israel and elsewhere. These papers hold the as-yet unfulfilled intellectual legacy of Mark Gurari, who was born Yisroel Aryeh Leib (Leibel) Schneerson. Gurari was the youngest brother of the seventh Lubavitcher Rebbe, the most famous and influential rabbi of the twentieth century (Rabbi Menachem M. Schneerson, 1902-1994). He was born in Nikolayev (today Mykolaiv), Ukraine, in 1906, and died at the age of 46 in Liverpool, England.
Until now, the facts of Gurari’s life have remained shrouded in mystery, sometimes giving rise to fantastical mythologies. Now, however, due to the tenacious work of a small group of researchers, it is possible to reconstruct the story of his life and give a proper account of his intellectual achievements and aspirations.
One way to begin this story is to go back to the spring of 2018, when Professor Dovid (Tom) Imbo, a theoretical physicist at the University of Illinois Chicago—where he directs the Laboratory for Quantum Theory at the Extremes—chanced upon a published image purporting to show mathematical work in the handwriting of the Rebbe’s brother. Given his own expertise, he immediately knew he was actually looking at advanced quantum physics. Intrigued, Imbo—who is also a member of the Harvard University Society of Fellows—began to do some digging.
It didn’t take Imbo long to discover a 1953 paper published in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. It included a note: “Mark Gurari died on May 8, 1952. The present paper was prepared from notes left by him.—H. Fröhlich.”1 Imbo was amazed. Herbert Fröhlich had revolutionized solid-state physics by applying the methods of quantum field theory, and was awarded the prestigious Max Planck Medal in 1972. Reading the Gurari paper, Imbo quickly realized that he was already familiar with its methods, which have remained important to ongoing developments in fundamental physics. To this day, it continues to be cited in new scientific papers.
But this discovery didn’t satisfy Imbo. As a physicist who had recently embarked on a personal journey into the rich world of Chabad thought—in particular, the writings and discourses of the Rebbe—he found himself fascinated by the Rebbe’s brother. Gurari’s early death prevented him from further expounding and developing his theoretical contributions, yet his work had been taken up and advanced by no less a figure than Richard Feynman, and it directly shaped the theory of superconductivity for which Bardeen, Cooper, and Schrieffer were awarded the Nobel Prize in 1972. Schrieffer himself told Fröhlich that his work was motivated by the structure of the variational wave-function developed in Gurari’s 1953 paper.2 Imbo wondered whether there was more work yet to be found.
Imbo’s inquiries soon led him to Rabbi Elkanah Shmotkin, the Director of Jewish Educational Media (JEM), who had spent some twenty years leading a research project on the Rebbe’s life. Indeed, during this process, information and documents relating to his brother were also accumulated. Although Imbo didn’t know it, Shmotkin had also been corresponding with Gurari’s only child, Dr. Dalia Gurari, a connection which turned out to be pivotal in the discoveries that would follow. Shmotkin sent Imbo a long letter written in German, dated November 23, 1948. It was addressed to Mark Gurari, but the conclusion—including the signature—was missing, so it wasn’t immediately clear who had written it. Among other things, the letter writer discussed his own mathematical work in detail, leading Imbo to identify him as the mathematician Albrecht Fröhlich, a younger brother of the aforementioned Herbert Fröhlich. The breadth and depth of the discussion revealed a close and previously unknown relationship, which would later be revealed as central to Gurari’s story.
Over the next months and years, Imbo relentlessly tried to turn up more information and more documents. Even with Shmotkin’s help, however, the results were slim. The breakthrough didn’t come until 2021, when Shmotkin introduced Imbo to Dalia Gurari. An accomplished scientist in her own right, she completed a PhD in biochemistry at University College London in 1969, worked for four decades at the Weizmann Institute of Science in Rehovot, Israel, and has many published papers to her name. But at the time of her father’s passing, she was just seven years old. Although she had fond memories of her father’s friend, “Ali” Fröhlich, she knew little of their shared intellectual projects.
In conversations with Imbo and Shmotkin, Dalia Gurari recalled that there might be a very small collection of her father’s writings somewhere, whose contents may shed light on his scientific work. After several attempts to locate the material, she unexpectedly discovered some three hundred pages of assorted papers in Russian, German, Hebrew, and English. In addition to bound notebooks, correspondence, loose sheaves of neatly written script, and jottings scrawled on scraps, there was also a book-length essay in four chapters, typewritten, bound, and titled: Prices and Rates of Profit in “Pure” Capitalism.
In a brief preface to the work, Gurari explained that it intended to refute “certain parts of the Marxian theory of prices,” and to “outline” an alternative “theory of prices in a capitalist order of free competition.” It transpired that a Hebrew version of this essay had also been serialized in a journal called Hameshek Hashitufi, which also bore the English title “Co-operative Economics.” The English version is written in clipped and clear prose, articulating its arguments with organized precision. At the same time, the thesis is underpinned and driven forward by a set of complex mathematical calculations, which are explained with examples and also inscribed as algebraic formulae.
![Table of Contents and first page from Gurari's 114-page mathematical economics text "Prices and Rates of Profit in 'Pure' Capitalism" (circa 1944). - Image Courtesy of Gurari/Imbo/Shmotkin](https://w2.chabad.org/media/images/1319/ECCU13197910.png?_i=_n504BC99DD0473598AAE3BCDC5D75568D "Table of Contents and first page from Gurari's 114-page mathematical economics text "Prices and Rates of Profit in 'Pure' Capitalism" (circa 1944). - Image Courtesy of Gurari/Imbo/Shmotkin")
The discovery of such a wealth of material excited everyone involved. Over the years that followed, several more caches of papers were discovered by Gurari and the Imbo-Shmotkin collaboration. Gurari also enlisted the help of her one-time classmate, Dr. Naftali Loewenthal, an accomplished academic scholar of Chabad thought, as well as a member of the Chabad community in London. Together, they combed through Herbert Fröhlich’s archive, followed up other leads, and recovered additional documents relating to the brief period that her father had spent in England.
Soon, the team had amassed some 1,500 pages, in numerous languages and formats. Shmotkin dispatched a professional photographer to capture high-resolution images of each individual item. The images were uploaded to digital folders, and team members in London, New York and Chicago began weekly Zoom sessions to collaboratively work through the material. This was by no means an easy task. Many of the pages lacked dates or context, being personal notes scribbled for Gurari’s own use, but they revealed a tremendous amount about the preoccupations of his profound and active mind. When contextualized by correspondence and other documents, the arc of his stymied career began to emerge in mesmerizing detail.
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Records show that Leibel Schneerson studied physics and chemistry at the University of Leningrad from 1925 to 1930. At this point, he escaped the Soviet Union using papers that bore the name Mark Gurari. Though he was still known as ‘Leibel’ to his friends, this name would stay with him for the rest of his life. Arriving in Berlin, he was reunited with his older brother, Rabbi Menachem Mendel, and his sister-in-law, Rebbetzin Chaya Mushka, Schneerson, living in close proximity to them for the next few years. He studied mathematics at the University of Berlin until 1933. With the Nazis’ rise to power, he was forced to leave the university and denied the possibility of graduating.
In 1936, he moved to the Holy Land, then known as Palestine. Without the means to pay tuition, he was unable to continue his studies at the Hebrew University in Jerusalem. For a while, he was forced to earn a living through a variety of jobs, including work for a travel agency. Before long, though, he found more rewarding work at Tel Aviv’s iconic Blumstein bookstore. In that bibliographical environment, he was able to nourish all sorts of intellectual interests, both others’ and his own.
A fascinating document from the Tel Aviv period, most likely compiled in 1949, is a twelve-page book-list in Mark Gurari’s hand, apparently listing the items in his personal library. Titles in multiple languages cover mathematics, physics, and philosophy, along with economics, literature, Kabbalah and Chassidism. The last two items are Green Hills of Africa, by Ernest Hemingway, and Likutei Torah, the classical compendium of discourses by his own ancestor, Rabbi Schneur Zalman of Liadi. Also listed is “the prayerbook of my father, of blessed memory.” This refers to the kabbalist Rabbi Levi Yitzchak Schneerson, who passed away in the summer of 1944, while under forced exile to distant Kazakhstan in the Soviet Union.
Toward the end of the 1940s, Gurari’s correspondence shows a renewed interest in continuing his formal education. By this point, his attention seems to have shifted away from economics and back to pure mathematics. In this endeavor, he was encouraged and supported by the aforementioned Albrecht Fröhlich, whom he had probably met in Tel Aviv, circa 1942, and who was now at the University of Bristol, England, completing a PhD. Albrecht Fröhlich would go on to earn recognition as “one of the major mathematicians of the latter half of the twentieth century” and as “the creator of Galois module structure … an important branch of algebraic number theory.” In 1976, he was elected to the Fellowship of the Royal Society, joining his elder brother, Herbert, who had been elected in 1951.3 Since 2004, the London Mathematical Society has awarded the Fröhlich Prize to commemorate his name.
With Albrecht’s encouragement and help, Gurari applied for enrollment in University College London’s Department of Mathematics. Internal correspondence shows how impressed the faculty were by his abilities. On the 26th of June 1950, Professor Harold Davenport (a future President of the London Mathematical Society) wrote about the prospective student to Professor Lionel Cooper (with whom Albert Einstein had recently been corresponding regarding possible logical inconsistencies in quantum mechanics), noting that “it would be a waste of time” for Gurari “to spend three years on undergraduate work.” Davenport advised that he be fast-tracked “so that he could qualify as soon as possible for registration as a Ph.D. student.” Accordingly, he further noted, “we have advised Mr. Gurari to see you, as we think you would be in a better position to look after him than any of us.”
By the spring of 1951, Gurari had been awarded a Bachelor’s degree in Math and Physics from University College London, and was on his way to the University of Liverpool to work under the tutelage of Professor Herbert Fröhlich on the theory of electrons in solids. Unfortunately, he died suddenly on May 8, 1952, the 13th of Iyar 5712, less than a year after arriving in Liverpool, leaving his wife, Gina, and seven-year-old Dalia. His passing also brought to a halt the exceptional progress he had been making in his scientific work. Fröhlich’s lament was published in a London newspaper: “Mr. Gurari’s death is a huge loss to science.”4
Despite having only just begun work on his Ph.D. dissertation, his contributions would make a lasting impact. As noted, in 1953, Herbert Fröhlich published the work already drafted by Gurari, “Self energy of slow electrons in polar materials,” the original manuscript of which was in a cache discovered by the team. As Professor Imbo explains, this “elegant and detailed” paper “was one of the very first to develop and apply non-perturbative techniques in quantum field theory in general, and variational methods in quantum field theory in particular.”
Also in 1953, at an elite conference on superconductivity and quantum field theory, Fröhlich expounded on Gurari’s work before an audience that included such luminaries as Niels Bohr, Wolfgang Pauli, Werner Heisenberg, and Paul Dirac, among many others. More substantially, the longest section of Prof. Fröhlich’s influential 1954 paper “Electrons in Lattice Fields” is entitled “Gurari Method,” where he recounts, develops, and applies Gurari’s techniques. Many other leading physicists would utilize these techniques in the years to come, including the Nobel laureates T.D. Lee, J.R. Schrieffer, and Nevil Mott, as well as Richard Feynman. By this point, more than seven decades after its initial publication, Gurari’s paper has accumulated more than a hundred citations, and the count keeps rising.
This scientific achievement and recognition, however, is tempered by the simple fact that Gurari died before his name could ever become well-known, and, moreover, before he had the chance to develop a great many additional ideas that he was working on. As Imbo notes, the notebooks and jottings that have now been rediscovered contain exercises, computations, and theorems relating to many other aspects of quantum theory, “from mechanics, to electromagnetism, to statistical physics, to atomic physics, to relativistic quantum field theory, to nuclear physics, and beyond.” In mathematics, his interests ranged from abstract algebra, to geometry, to analysis, to matrix theory, and—as we have seen—to economic applications as well.
One additional paper by Gurari, a mathematical work whose original manuscript is amongst the discovered documents, was published posthumously, entitled “The Location of Eigenvalues and Eigenvectors of Complex Matrices.”5 Although it was initially completed while he was working independently in 1940s Tel Aviv, it wasn’t published until 1978, by Professor Paul C. Rosenbloom of Columbia University, at the initiative of the Rebbe. By this time, many of its contributions had been independently discovered by other mathematicians. Had it appeared at the time of its original composition, its impact would doubtless have been greater.
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To contemplate this diverse and incomplete body of lost and found knowledge is to contemplate the promises of a brilliant mathematical mind, with a knack for developing creative computational methods and applying them to diverse sets of problems. Unfortunately, Mark Gurari’s original contributions to science were never recognized with the formal award of the Ph.D. toward which he was working in the last year of his life.
In the meantime, the team continues to piece together this fascinating story. Imbo and Shmotkin have no doubt that other documents, manuscripts, correspondence, and oral stories are out there that may shed light on the whereabouts, activities, and intellectual interests of Mark Gurari, whether in Russia, Germany, Israel, or the United Kingdom. Anyone who does possess any such information or leads is asked to contact Professor Imbo at [email protected] or Rabbi Shmotkin at [email protected].
Gurari, Imbo, and Shmotkin would like to gratefully acknowledge the important contributions (and continued support) of Rabbi Boruch Hertz and Prof. Mark Mueller at critical stages of this project.
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