Bruria Kaufman

• 1. Introduction

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  Bruria Kaufman spent five years working alongside Albert Einstein at the Institute for Advanced Study in Princeton, co-authoring two articles with him and contributing to his book on relativity. She was a research associate there from 1948 to 1955, a period when some of the most consequential work in theoretical physics was taking shape. Yet her name is rarely the first that comes to mind when the history of that era is told.

  Born in New York City in 1918 to a Jewish family of Ukrainian origin, Kaufman lived across multiple continents, worked with giants of science and mathematics, and left her deepest mark on a problem that had stumped physicists for years. Who was this woman who moved from the streets of New York to the kibbutzim of Israel, from the lecture halls of Columbia to the offices of Einstein himself? And what did she actually solve?

• 2. From New York to Jerusalem

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  In 1926, when Kaufman was eight years old, her family left New York and emigrated to the British Mandate for Palestine. They settled first in Tel Aviv, then made their way to Jerusalem. Growing up, her two great passions were music and mathematics.

  She pursued the mathematical path formally, earning a Bachelor of Science from the Hebrew University of Jerusalem in 1938. The following decade took her across the Atlantic to Columbia University, where she completed her doctorate in 1948. That same decade brought a significant personal development as well: in 1941, she married the linguist Zellig S. Harris. Harris would later draw her into a mathematical linguistics project at the University of Pennsylvania during the years between her time at Princeton and her return to Israel.

• 3. The Ising Model Solution

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  Lars Onsager published his solution to the two-dimensional Ising model in 1944, and it was considered a landmark in statistical physics. The Ising model is a mathematical framework used to describe phase transitions, such as how a material becomes magnetic. Onsager's derivation, while correct, was formidably complex.

  Kaufman's principal academic achievement was finding a far more elegant path to the same result. Working alongside Onsager himself, she applied spinor analysis to rederive the partition function of the two-dimensional Ising model. Their joint work appeared in 1949, and the new solution was regarded as substantially simpler than Onsager's original 1944 approach. Her method was grounded in group theory, a branch of mathematics that identifies underlying symmetries in complex systems. The three-dimensional version of the Ising model, for reference, remains unsolved to this day.

• 4. Princeton and Einstein

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  Kaufman arrived at the Institute for Advanced Study in Princeton in 1948, the year she completed her doctorate. She worked there with John von Neumann during 1947 and 1948, and then with Albert Einstein from 1950 through 1955. The collaboration with Einstein focused on his general theory of relativity.

  She published two articles alongside Einstein and contributed to his book on relativity. One of her publications, a paper on the algebraic properties of the field in the relativistic theory of the asymmetric field, began as an appendix in later editions of a work before being revised and published separately. In 1955, she presented "Mathematical Structure of the Non-symmetric Field Theory" at the Fiftieth Anniversary Conference on Relativity, which appeared in that conference's proceedings.

• 5. Israel, the Mössbauer Effect, and Later Life

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  In 1960, Kaufman returned to Israel with Harris and joined the Weizmann Institute of Science in Rehovot, where she held a professorship from 1960 to 1971. That same year she settled on Kibbutz Mishmar Ha'emek and adopted a daughter named Tami. She later moved to the University of Haifa, where she taught from 1972 to 1988.

  During her years in Israel, Kaufman collaborated with Professor Harri Zvi Lipkin on the Mössbauer effect, a phenomenon in nuclear physics involving the recoil-free emission and absorption of gamma radiation by atomic nuclei in solids. The two published an article together in which Kaufman brought mathematical analysis to bear on the physics of the effect. John von Neumann, with whom she had also worked on this topic, was another collaborator on the Mössbauer work.

  Kaufman returned to the United States in 1982. Her husband Harris, who taught in Pennsylvania, died in 1992. She later moved to Arizona and in 1996 married the Nobel laureate Willis Eugene Lamb, though that marriage ended in divorce. Kaufman died on the 7th of January 2010 at Carmel Hospital in Haifa, following a stay at a nursing home in Kiryat Tiv'on, near Haifa. She had asked that her body be cremated.