Banesh Hoffmann
Quick Info
Richmond, London, England
New York, USA
Biography
Banesh Hoffmann was the son of Maurice Hoffmann (1877-1959) and Leah Brozel (1878-1946). Maurice Hoffmann, who was Jewish, had been born on 15 April 1877 in Włoszczowa, Poland although at that time Poland was not an independent country and Włoszczowa was in the Russian-controlled partition. He emigrated to England and married Leah Brozel in 1903. Leah, who was Jewish, had been born in Lithuania on 22 April 1878 but, like Maurice Hoffmann, this was Russian-controlled at that time. Both Maurice and Leah gave their nationality on official forms as Russian and their race as Hebrew. Maurice and Leah Hoffmann had three children: Jessie Hoffmann (1905-1975), born 14 May 1905 in Russell Square, London; Banesh Hoffmann (1906-1986), born 6 September 1906 in Richmond, London, the subject of this biography; and Percival Hoffmann (1908-1965), born in Richmond and known as Percy.At the 1911 census the family are living at 1 Salcombe Villas, Richmond, Surrey. Maurice is working from his home as a tailor having been awarded a First-Class Diploma from the Tailors' School of Art in 1910. Later in 1911 the family moved to Buxton Lodge, 20 The Vineyard, Richmond and Maurice placed an advertisement in the Richmond Herald as follows [41]:-
Buxton Lodge, 20 The Vineyard, RichmondMaurice Hoffman respectfully begs to state that, owing to increasing business, he has moved to the above address, where the premises are much larger and more convenient.
He takes this opportunity of saying that, since coming to Richmond, he has been the recipient of a First-class Diploma from the Tailors' School of Art - a much coveted distinction.In tendering thanks for past favours, he assures his patrons that, in the future, as in the past, it will be his earnest endeavour to give every satisfaction, and to supply highest quality productions at most moderate charges.
Banesh Hoffmann began his schooling in Richmond. The 1921 Census records Leah Hoffmann as Head of the family with Jessie Hoffmann, Banesh Hoffmann (listed as Benny Hoffmann) and Percival Hofmann (listed as Percy Hoffmann) all at school. It is noted that Maurice Hoffmann was in Austria at the time of the census. Banesh began his studies in St Paul's School in 1921. This famous independent school had been founded in 1509 by John Coley, Dean of St Paul's Cathedral. When Hoffmann studied there, the school was situated at 153 Hammersmith Road in West Kensington, London. It was considered one of the nine great independent schools of England.
In June 1922 Hoffmann sat the Scholarship Examination at St Paul's School and was awarded a Senior Scholarship (see [54]). He was a member of the C Club at St Paul's School and by 1925 both Banesh Hoffmann and his younger brother Percival Hoffmann were members of the C Club (see [48]). The Club system had been introduced into the school in 1899 as a games scheme:-
... the new organisation by which it is hoped that fresh vigour may be put into games, and into School life in general.Banesh was also involved in chess while at the school being in Mr Bewley's Team in 1924 and representing the school in competitions. He graduated from St Paul's School in 1925 and later that year matriculated at Oxford University.
Hoffmann was a student at Merton College, Oxford but at first struggled to find the right topics. He attended a lecture by G H Hardy but, finding it difficult, decided that pure mathematics was not for him. He concentrated on applied mathematics topics but found that Oxford did not teach a course on relativity which he was keen to learn more about. In 1926 Luther Pfahler Eisenhart, a professor at Princeton University in the United States, published the book Riemannian geometry. The book was written for mathematicians and theoretical physicists following the developments in general relativity and tensor calculus. Hoffmann read this book and then had some really good luck since Oswald Veblen, who had become Henry B Fine Professor of Mathematics at Princeton in 1926, arranged to teach at Oxford in 1928-29 in an exchange with G H Hardy who spent the year at Princeton. Hoffmann said [5]:-
I was at Oxford University. I was sort of a strange case. I had first of all taught myself Pitman's shorthand. Secondly I had fallen in love with relativity, and I had taught myself relativity because there was no one at Oxford who was giving any lectures on it. I was neglecting my regular course work, and I would have been in quite a sad situation if it hadn't been for the fact that in my last year there was an exchange of professors: G H Hardy, who was then at Oxford, went to Princeton for a year, and Oswald Veblen, who was at Princeton, came to Oxford for a year. And it just so happened that Veblen was interested in what he called projective relativity.Veblen gave lectures on relativity at Oxford during 1928-29 which Hoffmann attended. Hoffmann asked many questions during Veblen's lectures which pleased Veblen who invited Hoffmann to Princeton to undertake research for a PhD and to work as his assistant.
In 1929 Hoffmann was awarded a First Class Honours degree from Oxford and was also awarded a Goldsmith's Studentship to undertake studies for a PhD. He sailed from Southampton to New York on the ship Majestic, arriving on 1 October 1929. He stated on arrival that he intended to stay in the United States for three years. His arrival record contains the following data [9]: Height, 5 ft 5 in; Hair Colour, Brown; Eye Colour, Brown; Complexion, Fair.
At Princeton Hoffmann's duties as Veblen's assistant consisted in part of taking notes of his lectures and then making fair copy to be distributed. He also took notes from lectures given by visitors to Princeton. Of course this was also helpful for he had to take courses as part of his work towards a PhD. In addition to Veblen's lectures he took courses given by Howard Percy Robertson and attended weekly seminars by Robertson and Ed Condon. Edward Uhler Condon (1902-1974) had studied at Göttingen under Max Born and at Munich under Arnold Sommerfeld. He had been appointed as associate professor of physics at Princeton in 1928. Hoffmann also took a course on tensor analysis by T Y Thomas. Tracy Yerkes Thomas (1899-1983) had been awarded a Ph.D. from Princeton in 1923 with Veblen as his advisor, and had been appointed to the mathematics faculty at Princeton in 1926. Hoffmann and Veblen collaborated in research on projective relativity and published the joint paper Projective Relativity in 1930. The paper has the following Abstract [57]:-
In this paper we show that the formalism of O Klein's version of the five-dimensional relativity can be interpreted as a four-dimensional theory based on projective instead of affine geometry. The most natural field equations for the empty space-time case are a combination into a single invariant set of the gravitational and electromagnetic field equations of the classical relativity without modification. This seems to be the simplest possible solution of the unification problem.When we drop a restriction on the fundamental projective tensor which was imposed in order to reduce our theory to that of O Klein a new set of field equations is obtained which includes a wave equation of the type already studied by various authors. The use of projective tensors and projective geometry in relativity theory therefore seems to make it possible to bring wave mechanics into the relativity scheme.
At this point Veblen, realising that he had expertise in geometry but little physical intuition, while Hoffmann's expertise lay mostly in theoretical physics, suggested that Hoffmann should do something on his own for his doctoral thesis.
At the time of the 1930 US Census, Hoffmann was living in a hotel on West 116 Street, Manhattan, New York. Over the summer he returned to England coming back from Southampton to New York on the ship Homeric, arriving on 24 September 1930. There is one significant difference in the data he gave on entering the United States in 1930, namely he now indicated: "Citizenship Intention, Yes".
At Princeton he attended a course by Eugene Wigner, who arrived in Princeton towards the end of 1930. He published the single author paper Projective relativity and the quantum field (1931) related to the work he had done with Veblen. He attended the theoretical physics colloquium where Wigner and Robertson asked questions. Hoffmann solved them with the paper On general relativity in Reviews of Modern Physics (1932). This was still not enough for a PhD thesis so Robertson suggested he try working on gravitational waves and electromagnetic waves. This led to his 13-page thesis On the Spherically Symmetric Field in Relativity which was published as the paper [31]. We give the Introduction:-
It has long been known that according to the relativity theory a purely gravitational field, if spherically symmetric, must also be static. The question arises as to whether the same is true for a field of gravitation and electromagnetism; in particular, can we have spherically symmetric waves in the absence of matter? We shall show that such waves cannot exist and that indeed the field must be a static one; and furthermore we shall find the most general spherically symmetric field permitted by the field equations in the absence of matter.In classical electrodynamics no account is taken of the gravitational field; the field equations of general relativity, however, contain the gravitational potentials and the electromagnetic potentials together in the same equations, and there is thus, in general relativity, an interaction between the gravitational and the electromagnetic parts of the field, the theory of which interaction has not yet become a part of our intuitional approach towards either electromagnetism or gravitation. In solving the present problem, then, it is evidently not safe to appeal to ordinary intuitions regarding the behaviour of electromagnetism since the very possibility of waves of the type we seek implies, in view of Birkhoff and Eiesland's result, just such an interaction between the electromagnetic and gravitational parts of the field. It is necessary, therefore, to proceed mathematically from the field equations.
Before we move on, let us note that Howard Robertson, in addition to guiding Hoffmann in his doctoral studies, also provided an important social setting for him at Princeton [5]:-
H P Robertson had open house once a week at his apartment with his wife. I used to go there regularly as did various others; there might be half a dozen or more. It seemed as if many of them found this a home away from home because they were not indigenous Americans.Hoffmann had arrived in the United States in October 1929, and it was in that month that the stock market crash triggered the Great Depression. By 1932, when Hoffmann was awarded his PhD, the Depression had steadily become worse with not sign of recovery. Looking for jobs at this time was extremely difficult and indeed Hoffmann tried endlessly to find a position. Suddenly he had a real stroke of luck as he explained in [5]:-
I saw in the papers that George Eastman had died and had left several million to the University of Rochester. So I went to see Eisenhart, who was handling this sort of thing, and I said, "Maybe there's an opening there." He suggested, "Why don't you write?" I think he wrote also. Then I was called for an interview, and there was a man there, Charles Watkeys. He asked me to his house, and he began playing some music. One was a composition of his own. I didn't know it was his own, and I said, "You know that sounds very Elizabethan." He said, "Oh, you noticed." He said, "That's my composition. I did it in the form of an Elizabethan madrigal." He was a cellist, and I played the piano. I think that to some extent on that basis he urged that I should be given the job. And I got the job just like that. Pure accident.The Mathematics Department at the University of Rochester had three permanent staff and a number of instructors who were appointed for a maximum of three years. Hoffmann was appointed as an instructor in 1932 but when one of the permanent staff became ill he took over his duties. By 1935, although Hoffmann was told he had done well, since the permanent member of staff had recovered, Hoffmann was dismissed. He went back to Princeton to seek advice from Veblen who was very encouraging and offered him funding a one year with no duties. In fact this funding was extended for a second year. Hoffmann said in the interview [5]:-
... it's interesting that my being fired from Rochester led to my meeting Einstein and working with him.Hoffman writes about his first meeting with Einstein in [30]:-
I first met Albert Einstein in 1935, at the famous Institute for Advanced Study in Princeton, New Jersey. ... I was awe in of Einstein, and hesitated before approaching him about some ideas I had been working on. My hesitation proved unwarranted. When I finally knocked on his door, a gentle voice said, "Come" - with a rising inflection that made the single word both a welcome and a question. I entered his office and found him seated at a table, calculating and smoking his pipe. Dressed in ill-fitting clothes, his hair characteristically awry, he smiled a warm welcome. His utter naturalness at once set me at ease. As I began to explain my ideas, he asked me to write the equations on the blackboard so that he could see how they developed. Then, came the staggering - and altogether endearing - request: "Please go slowly. I do not understand things quickly." This from Einstein! He said it gently, and I laughed. From then on, all vestiges of fear were gone.Hoffmann wrote to Old St Paul's School telling them he was writing from the Institute for Advanced Study at Princeton where he was playing duets with Professor Einstein.
Leopold Infeld had met Einstein in Berlin in 1920-21 while undertaking research for his doctorate and had much useful advice from him. Being Jewish, Infeld had fled from the Nazi threat in 1936 and was able to leave Poland and visit to the Institute for Advanced Study in Princeton. Hoffmann and Infeld worked with Einstein and they wrote the joint paper The Gravitational Equations and the Problem of Motion. For the Introduction to this paper, see THIS LINK.
In 1937 Hoffmann was appointed as an Instructor in Mathematics at Queens College, part of the City University of New York [61]:-
Following the meeting of the Queens College administrative committee and the executive committee of the Board of Higher Education, President Paul Klapper announces the following supplementary appointments to the staff of Queens College: Banesh Hoffman, Ph.D., Princeton University, formerly instructor in mathematics and research associate at the University of Rochester, co-author with Dr Albert Einstein of a paper to be published soon, to be instructor in mathematics.In July 1938 Hoffmann, now living at Flushing, New York, married Doris Marjorie Goodday (1908-2002) who was a social worker, working for a private agency. Doris had been born in San Francisco on 4 April 1908 to the grocer Jacob Louis Goodday (1873-1945) and Maud Hyman (1877-1948). She had attended the Girls High School in San Francisco, was awarded a degree from University of California Berkeley and later earned a degree in social work from Columbia University. Banesh and Doris Hoffmann had two children: Laurence David Hoffmann, born 24 August 1943 at the New York Hospital, Manhattan; and Deborah Ann Hoffmann born in New York on 17 October 1947. Laurence Hoffmann was awarded a Ph.D. from the University of Wisconsin-Madison in 1970 for his thesis Analytic Functions in the Polydisc having been advised by Walter Rudin. He became professor of mathematics at Claremont McKenna College, then a Senior Investment Management Consultant with Morgan Stanley Smith Barney. Deborah Hoffmann became an award-winning documentary filmmaker.
On 19 December 1940 Hoffmann became an American citizen. At Queens College, Hoffmann continued to publish papers on mathematical physics, for example: Kron's method of subspaces (1944), Tensors and equivalent circuits (1946), The vector meson field and projective relativity (1947), The gravitational electromagnetic, and vector meson fields and the similarity geometry (1948), Kron's non-Riemannian electrodynamics (1949), Dirac's new classical theory of electrons (1952), The similarity theory of relativity and the Dirac-Schrödinger theory of electrons (1953), General relativistic red shift and the artificial satellite (1957), and The Einstein tensor in orthogonal coordinates in n dimensions (1960).
Hoffmann wrote a number of books including The Strange Story of the Quantum; An Account for the General Reader of the Growth of the Ideas Underlying our Present Atomic Knowledge (1947), The Tyranny of Testing (1962), About Vectors (1966), (with the collaboration of Helen Dukas) Albert Einstein. Creator and Rebel (1972), and Relativity and its roots (1983). He also edited, with Helen Dukas, Albert Einstein, the Human Side: New Glimpses from His Archives (1979). For more information about these books, see THIS LINK.
Although Hoffmann remained at Queens College for the rest of his career, he held several visiting positions. For example, in addition to being a member of the Institute for Advanced Study 1935-1937, he was also a member from February 1947 to May 1947 and from September 1947 to December 1947. He went to England with his family in the summer of 1950 and in the summer of 1955, spending time at University of London's King's College. He spent a sabbatical at Harvard University in 1966-67.
Hoffmann received several awards including: the Distinguished Teaching Award from Queens College Alumni Association in 1963; the 2nd Gravity Research Foundation Prize in 1960; the 1st Gravity Research Foundation Prize in 1964; and was the winner of the American Institute of Physics - United States Steel Foundation Science Writing Award in Physics and Astronomy for his book Albert Einstein. Creator and Rebel in 1973. The Banesh Hoffman Memorial Award is given at CUNY Queens College "to a graduating senior for outstanding work in mathematics."
Although Hoffmann retired in the 1960s, he continued to teach at Queens College until the late 1970s. In the spring semester he taught the special and general theories of relativity. In the autumn semester he taught a course on classical and quantum mechanics. He also taught an advanced mathematics course for students who had taken pre-calculus, solid geometry and advanced algebra before entering Queens College.
In August 1986 Hoffmann died at his home in Flushing, Queens. Following his death, his wife Doris Hoffmann moved back to California to be near her children. Her daughter Deborah Hoffmann, a film maker, made the film Complaints of a Dutiful Daughter (1994) which records and recounts the toll of Alzheimer's disease on her mother, Doris Hoffmann. In the film Deborah Hoffman traces the gradual course of the disease and all that she learned as she cared for her mother. The film won an Oscar in 1995.
Let us end with a quote from Hoffmann [30]:-
How shall I sum up what it meant to have known Einstein and his work? Like the Nobel prize winner who pointed helplessly at his watch, I can find no adequate words. It was akin to the revelation of the great art that lets one see what was formerly hidden. And, when for example, I walk on the sand of a lonely beach, I am reminded of his ceaseless search for cosmic simplicity - and the scene takes on a deeper, sadder beauty.
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Other websites about Banesh Hoffmann:
Written by J J O'Connor and E F Robertson
Last Update March 2026
Last Update March 2026